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1 Module I
Introduction to Image Processing Systems :
1
DIGITAL IMAGE PROCESSING
Unit Structure
1.0 Objectives
1.1 Introduction
1.2 An Overview
1.2.1 What is an Image?
1.2.2 What is a Digital image?
1.2.3 Types of Image
1.2.4 Digital Image Processing
1.3 Imag e Representation
1.4 Basic relationship between Pi xels
1.4.1 Neighbors of a Pixel
1.4.2 Adjacency, Connectivity, Regions and Boundaries
1.4.3 Distance Measures
1.4.4 Image operations on a Pixel Basis
1.5 Elements of Digital Image Processing system
1.6 Elements of Visual Perception
1.6.1Str ucture of Human Eye
1.6.2 Image Formation in the Eye
1.6.3 Brightness and contrast
1.6.5 Hue
1.6.6 Saturation
1.6.7 Mach band effect
1.7 Simple Image Formation Model
1.8 Vidicon and Digital Camera wor king Principle munotes.in

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2 1.8.1 Vidicon
1.8.2 Digital Camera
1.9 Colour Image Fundamentals
1.9.1 RGB
1.9.2 CMY
1.9.3 HIS Models
1.9.4 2D Sampling
1.9.5 Quantization
1.10 Summary
1.11 References
1.12 Unit End Exercises
1.0 OBJECTIVES
After going through this unit, yo u will be able to:
❖ Gain the knowledge about evoluti on of digital image processing
❖ Analyse the limits of digital images
❖ Derive the representation and relationship of pixels
❖ Describe the functioning of digital image processing system
❖ Specify the color models of image processing such as RGB, CMY
and Hue
1.1 I NTRODUCTION
Digital Images plays main role in the day -to-day life. The visual effect
plays major role than any other media. When we see an image without
saying, without explaining anything we understand t he concept.
Evolution of Digital Images:
The digit al images started its role from newspapers. The pictures that are
sent through submarine cable between London to New York are the first
journey of digital Images.
1921
Bartlane cable picture transmission s ystem used specialized printing
equipment coded pic tures and then reproduced on telegraph printer fitted
with typefaces simulating a halftone pattern. This technology reduced the
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3 Level of coding images was 5. Figure 1.1 shows the pic ture transmitted in
this way.
1922
Visual quality is improved through selection of printing procedures and
distribution of intensity levels. A technique based on photographic
reproduction made from tapes perforated at telegraph receiving terminal.
Level o f coding images was 5. Figure 1.2 shows the picture transmitted in
this way.
1929
The intensity level was increased to 15. Figure 1.3 shows the picture
transmitted in this way.
1964
The digital image used through digital computer and its advanced
technique s lead to Digital image processing. The Ranger 7 spacecraft of
U.S. took the first image of moon, shown in Figure 1.4. The enhanced
methods from the lessons learned from this imaging served as the basis fo r
Surveyor missions to moon, Mariner series mission s to Mars and Appolo
manned flights to the moon and others.





1970
In parallel to space applications, the medical imaging, remote earth
resources and astronomy the digital image processing was applied. Ex.
CAT - Computerized Axial Tomography and X -rays uses DIP.
1992
Berners -Lee uploaded the first image to the internet, in 1992. It was of Les
HorriblesCernettes, a parody pop band founded by CERN employees.
1997
Fractals: Computer generated images are in troduced based on the iterative
reproduction of a b asic pattern according to some mathematical rules.



Figure 1.1 : Figure 1.2 : Figure 1.1 : Figure 1.4 : munotes.in

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4 1.2 AN OVERVIEW
1.2.1. What is an Image?
Visual representation of an object is called as Image. An image is a two -
dimensional function that represents a m easure of some characteristic such
as brightness or color of a viewed scene.

Fig. 1.5. Sample Image1
(1 https://www.designyourway.net/diverse/amazingworld/28899053723 .
jpg)
1.2.2 What is a digital image?
Digital image is c omposed of a finite number of elements having a
particular location and value. These elements are called picture elements,
image elements, pels and pixels
A real image can be represented as a two dimension al continuous light
intensity function g(x,y) where x and y denote the spatial coordinates and
the value of g is proportional to the brightness (or gray level) of the image
at that point.
1.2.3 Types of Image
Generally the images can be classified into two types. They are
i) Analog Image
ii) Digital Image
i)Ana log Image
The image which is having continuously varying physical quantity in the
spatial data such as x, y of the particular axis is known as Analog Image.
Analog image can be mathematically represented a s a continuous range of
values representing positio n and intensity. The image produced on the
screen of a CRT monitor, Television and medical images are analog
images.
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5 ii) Digital Image
A digital image is composed of picture elements called pixels with
discrete data. Pixels are the smallest sample of an im age. A pixel
represents the brightness at one point. The common formats of digital
images are TIFF, GIF, JPEG, PNG, and Post -Script.
Advantages of Digital Images
i) The processing of images is faster and cost-effective.
ii) Digital images can be effectiv ely stored and efficiently transmitted
from one place to another.
iii) Immediate output display to see the image.
iv) Copying a digital image is easy. The quality of the digital image will
not be degraded even if it is copied for several times.
v) The reproduction of the image is both faster and cheaper.
vi) Digital technology supports various image manipulations.
Drawbacks of Digital Images
i) Misuse of images has become easier.
ii) During enlarging the image, the quality of the image will be
compromised.
iii) Large volume o f memory is required to store and process the images.
iv) Fast processors required to process digital image processing
algorithms.
1.2.4. Digital Image Processing (DIP)
Processing the images using digital computers is termed as Digital Image
Processing .
Digital image processing concepts are allied in the fields of defence,
medical diagnosis, astronomy, archaeology, industry, law enforcement,
forensics, remote sensing etc.
Flexibility and Adaptability
Mod ification in hardware components is not required in order to
reprogram digital computers to solve different tasks. This feature makes
digital computers an ideal device for processing image signals adaptively.
Data Storage and Transmission
The digital data can be effectively stored since the development of
different image compression algorithm is in progress. The digital data can
be easily transmitted from one place to another and from one device to
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6 Different image processing techniques include image enhancem ent, image
restoration, image fusion and image watermarking for its effective
applications.
1.3 IMAGE REPRESENTATION
● Represented as M N matrix.
● Each element in the matrix is a number that represents sa mpled
intensity.
● M N gives resolution by pixel.

Figure 1.6. Coordinate convention
used to represent digital images.

Digital image is a finite collection of discrete data samples (pixels) of any
visible object. The pixels represent a two or higher d imensional “view” of
the object, each pixel having its own discrete value in a finite range. The
pixel values may represent the amount of visible light, infra -red light,
absorption of x -rays, electrons, or any other measurable value such as
ultrasound wave impulses.
The result of sampling and quantization is matrix of real numbers. Assume
that an image f(x,y) is sampled so that the resulting digital image has M
rows and N Columns. The values of the coordinates (x,y) now become
discrete quantities thus the value of thecoordinates at origin become (x,y)
= (0,0). The next Coordinates value along the first signify the image along
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7 f(x,y) =

Fig 1.7 Matrix representation format of a digital image

The right side of this equation is by defin ition a digital image. Each
element ofthis matrix a rray is called an image element , picture element ,
pixel , or pel.
Or the same can be represented as
A=

1.4 BASIC RELATIONSHIP BETWEEN PIXELS
There are several important relationships between pixels in a digital
image.
1.4.1 Neighbors of a Pixel
A pixel p at coordinates (x,y) has four horizontal and vertical neighbours
whose coordinates are givenby:
This set of pixels, called the 4 -neighbors of p, is denoted by N 4(p). Each
pixel is one unit distance fro m (x,y) and some of the neighbors of p lie
outside the digital image if (x,y) is on the border of the image. The four
diagonal neighbors of p have coordinates and are denoted by N D(p).
.These points, together with the 4 -neighbors, are called the 8 -neighbo rs of
p, denoted by N 8(p). (x,y-1) (x-1,
y) p(x,y) (x+1,y) (x, y+1)

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8 1.4.2 Adjacency, Connectivity, Regions and Boundaries
● To define adjacency the set of grey –level values V is considered.
● In a binary image, the adjacency of pixels with value 1 i s referred as
V={1}.
● In a grey -scale image, the ide a is the same, but Vtypically contains
more elements for example, V= {100, 101,…,150} that is subset of
any 256 values from 0 -255
Types of Adjacency:
(i) 4- Adjacency – two pixels p and q with value from V ar e 4 –
adjacency if A is in the set N 4(p)
(ii) 8- Adjacency – two pixels p and q with value from V are 8 –adjacency
if A is in the set N 8(p)
(iii) M -adjacency –two pixel p and q with value from V are m – adjacency
if
a) Q is in N 4(p) or
b) Q is in N D(q) and theSet N 4(p) ∩ N 4(q) has no pixel whose values are
fromV.
Mixed adjacency is a modification of 8 -adjacency. It is introduced to
eliminate the ambiguities that often arise when 8 -adjacency is used.




Fig.1.8 Arrangement of
pixels Fig.1.9 pixels that are 8 -adjacen t
(dashed lines) to the center pixel Fig.1.10 m -adjacency
Digital Path:
A digital path from pixel p(x,y) to pixel q(s,t) is a sequence of distinct
pixels with coordinates (x 0,y0), (x 1,y1), …, (x n, yn) where (x 0,y0) = (x,y)
and (x n, yn) = (s,t) and pixels (xi, yi) and (x i-1, y i-1) are adjace nt for 1 ≤ i
≤n, n is the length of the path.
If (x 0,y0) = (x n, yn), the path is closed.
Based on the type of adjacency paths are specified as 4, 8 or m -paths.
In figure 1.9 the paths between the top right and bottom right pixels are 8 -
paths. And the path between the same 2 pixels in figure 1.10 is m -path
0 1 1
0 1 0
0 0 1 0 1 1
0 1 0
0 0 1 0 1 1
0 1 0
0 0 1
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9 Connectivity:
Let S represent a subset of pixels in an image, two pixels p and q are said
to be connected in S if there exists a path between them consisting entirely
of pixels in S.
For any pixel p in S , the set of pixels that are connected to it in S is called
a connected component of S. If it only has one connected component, then
set S is called a connected set .
Region and Boundary:
Region: Let R be a subset of pixels in an image, R is a region of th e image
if R is a connected set. Any pixels in the boundary of the region that
happen to coincide with the border of the image are included implicitly as
part of the region boundary.
Boundary: The boundary of a region R is the set of pixels in the region
that have one or more neighbors that are not in R.
If R is an entire image, then its boundary is defined as the set of pixels in
the first and last rows and columns in the image. There are no neighbors
beyond the pixels’ borders.
.1.4.3. Distance Measures
For pixel p,q and z with coordinate (x.y) ,(s,t) and (v,w) respectively D is
a distance function or metric if
D [p.q] ≥ 0 {D[p.q] = 0 iff p=q
D [p.q] = D [p.q] and
D [p.q] ≥ 0 {D[p.q]+D(q,z)
The Euclidean Distance between p and q is defined as:

Pixels ha ving a distance less than or equal to some value r from (x,y) are
the points contained in a disk of radius “ r” centered at (x,y)
The D 4distance (also called city -block distance) between p and q is
definedas:
D4(p,q) = | x – s | + | y – t |
Pixels having a D4 distance from (x,y), less than or equal to some value r
form a Diamond centered at (x,y)
Example:
The pixels with distance D 4≤ 2 from (x,y) form the following contours of
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10 The pixels with D 4= 1 are the 4 -neighbors of (x,y)
2
2 1 2
2 1 0 1 2
2 1 2
2
The D 8distance (also called chessboard distance) between p and q is
defined as:
D8(p,q) = max(| x – s |,| y – t |)
Pixels having a D 8 distance from (x,y), less than or equal to some value r
form a square Centered at (x,y).
2 2 2 2 2
2 1 1 1 2
2 1 0 1 2
2 1 1 1 2
2 2 2 2 2
Example:
D8distance ≤ 2 from (x,y) form the following contours of constant
distance.
DmDistance:
Dm is the shortest m -path between the points.In this case, thedistance
between two pixels will depend on the values of the pixels along the path,
as well as the values of their neighbors.
Example:
P
3 P
4
P
1 P
2
p
Consider the fo llowing arrangement of pixels and assume that p, p2, and
p4 have value 1 and that p1 and p3 can have can have a value of 0 or 1
Consider the adjacency of pixels values; V ={1}.Compute the D m between
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11 There are 4 cases:
p p2 p4
Case1: If p1 =0 and p 3 = 0
Length of the shortest m -path (the D m distance) is 2;
Case2: If p 1 =1 and p 3 = 0
p1 and p will no longer be adjacent then, the length of the shortest path
will be 3
p p1 p2 p4 Case3: If p 1 =0 and p 3 = 1
p p2 p3 p4 The shortest –m-path will be 3 ;
Case4: If p 1 =1 and p 3 = 1
p p1 p2 p3 p4 The shortest –m-path will be 4 ;
1.4.4 Image operations on a Pixel Basis
For doing arithmetic and logic operations between the images, the
corresponding pixels in the images are involved i n those operations.
If any image is divided by another then the division is carried out between
the corresponding pixels in the two images.
Let f and g are two images
Applying the division operation, h=f/g
First element of image ‘h’ is the resultant of first pixel of image ‘f’
divided by image ‘g’
1.5 ELEMENTS OF DIGITAL IMAGE PROCESSING
SYSTEMS:
The basic elements of digital image processing systems are
i) Image Acquisition devices
ii) Image storage devices
iii) Image processing e lements
iv) Image display devices
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i) Image Acquisition devices
The term image acquisition refers to the process of capturing real -world
images and storing them into a computer. Conventional silver -based
photographs in the form of negatives, tra nsparencies or prints can be
scanned using a variety of scanning devices. Digital cameras which
capture images directly in digital form are more popular nowadays. Films
are not used in digital cameras. Instead, they use a charge -coupled device
or CMOS devi ce as the image sensor that converts light into electrical
charges. An image sensor is a 2D array of light -sensitive elements that
convert photons to electrons. Most of the digital cameras use either a CCD
or a CMOS image sensor.
Solid -state image sensor c onsists of
a) Discrete photo -sensing elements b) charge -transport mechanism c) an output circuit.
❖ The photo sensitive sites convert the incoming photons into electrical
charges and integrate these charges into a charge packet.
❖ The charge packet is then transferred through the transport
mechanism to the output circuit where it is converted into a
measurable voltage.
❖ The types of photo -sensing elements used in solid state imagers
include photodiodes, MOS capacitors, Schottky -barrier diodes and
photoconductive layers.
❖ The output circuit typically consists of a floating diffusion and
source -follower amplifier.
❖ In practical applications, image sensors are configured in a one -
dimensional (linear devices) or a two -dimensional manner.
Fig. 1.11 Elements of DIP system Image storage
devices
 Computer Memory
 Frame Buffers
 Magnetic tapes
 Optical disks Image Acquisition
devices
 CCD Sensor
 CMOS Sensor
 Image Scanners Image processing
 Computer Image display
devices
 CRT
 Computer Monitor
 Printer
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13 ii) Image storage devices
If the image is not compressed the enormous volume of storage is required
There are three categories of storage devices. They are :
a) Short term storage b) Online storage c) Archival Storage
Short term storage : Used at the time of proc essing, Example: computer
memory, frame buffers. Frame buffers stores more than one image and can
be accessed rapidly at video rates. Image zoom, scrolling and pan shifts
are done through frame buffers.
Online storage : It is used while accessing the data o ften. It encourages the
fast recall, Example; magnetic disk or optical media.
Archival storage: It is characterized by frequent access, example:
magnetic tapes and optical disks. It requires large amount of storage space
and the stored data is accessed in frequently.
iii) Image processing elements
Computer and its related devices are the image processing elements for
various applications.
iv) Image display devices
Image displays are color TV monitors. These monitors are driven by the
output of image and gr aphics display cards which are a part of the
computer system.
1.6 ELEMENTS OF VISUAL PERCEPTION
1.6.1 Structure of Human Eye
Characteristics of Eye
❖ Nearly spherical
❖ Approximately 20 mm in diameter
❖ Three membranes
i) Cornea and Sclera
ii) Choroid
iii) Retina
i) Cornea; Sclera
The cornea is a tough, transparent tissue that covers the anterior , front
surface of eye. The sclera is an opaque membrane that is continuous with
the cornea and encloses the remaining portion of the eye.
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14 ii) Choroid
It is loc ated directly below the sclera. It contains network of blood vessels
which provides nutrition to the eye. The outer cover of the choroid is
heavily pigmented to reduce amount of extraneous light entering the eye.
Also contains the iris diaphragm and ciliar y body








Iris diaphragm
It contracts and expands to control the amount of light entering into the
eye. The central opening of the iris which appears black is known as pupil
whose diameter varies from 2mm to 8mm.
Lens
It is made up of many laye rs of fibrous cells. It is suspended and is
attached to the ciliary body. It contains 60% to 70% water and 6% fat and
more protein. The lens is colored by a slightly yellow pigmentation. This
coloring increases with age, which leads to clouding of lens. Ex cessive
clouding of lens happens in extreme cases which are known as cataracts .
This leads to poor color discrimination and loss of clear vision.
The lens absorbs approximately 8% of the visible light spectrum, with
relatively higher absorption at shorter wavelengths. Both infrared and
ultraviolet light are absorbed appreciably by proteinswithin the lens
structure and, in excessive amounts, can damage the eye.
iii) Retina
It is the inner most membrane, objects are imaged on the surface. The
central portio n of retina is called the fovea . Two types of receptors in
retina are Rods and Cones
Rods are long small receptors and Cones are short thicker in structure.The
rods and cones are not distributed evenly around the retina.


Fig. 1.12 St ructure of human Eye
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15 Cones
Cones are highly sensitiv e to color and are located in the fovea . There are
6 to 7 million cones. Each cone is connected with its own nerve end.
Therefore humans can resolve fine details with the use of cones. Cones
respond to higher levels of illumination; their response is calle d photopic
vision or bright light vision
Rods
Rods are more sensitive to low illumination than cones. There are about
75 to 159 million rods. Many numbers of rods are connected to a common,
single nerve. Thus the amount of detail recognizable is less. Th erefore
rods provide only a general overall picture of the field of view. Due to
stimulation of rods the objects that appear color in daylight will appear
colorless in moon light. This phenomenon is called scotopic vision or dim
light vision.
The area where there is absence of receptors is called the blind spot

Fig 1.13 Rods and Cones in Retina
Receptor density measured in degrees from the fovea (the angle formed
between the visual axis and a line extending from the center of the lens to
the retin a
1.6.2 Image Formation in the Eye
The lens of eye is flexible, whereas the optical lens is not.
The radius of curvature of the anterior surface of the lens is greater than
the radius of its posterior surface.
The tension in the fibers of the ciliary bod y controls the shape of the lens
To focus distant object greater than 3m the lens is made flattened by the
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16
Fig. 1.14 Graphical representation of the eye Point C is the optical center of
the lens

To focus nearer objects the muscles allow the lens to become thicker,and
strongest refractive index.
The distance between the centre of the lens and the retina is called focal
length.
It ranges from 14mm to 17mm as the refractive power decreases from
maximum to minimum.
1.6.3 Brightness
The following terms are used to define color light:
i)Brightness or Luminance: This is the amount of light received by the eye
regardless of color.
ii) Hue: This is the predominant spectral color in the light.
iii)Saturation: This indicates the spectral purity of the color in the light

Fig. 1.15 Color attributes
The range of light intensity levels to which the human visual system can
adapt is enormous from scotopic threshold to the glare limit. Subjective
brightness is a logarithmic function of the light intensity incident on the
eye.
Brightness adaptation :The human visual system has the ability to operate
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17 iris of the eye can account for a change of only 16 times in the light
intensity falling on the retina. The process which allows great extension of
this range by changes in the sensitivity of the retina is called brightness
adaptation .
1.6.4 Contrast
The response of the eye to chan ges in the intensity of illumination is non -
linear
This does not hold at very low or very high intensities and it is dependent
on the intensity of the surround.
Perceived brightness and intensity
Perceived brightness is not a function of intensity. This can be explained
by Simultaneous contrast and Mach band effect
Simultaneous contrast
The small squares in each image are the same intensity.
Because the different background intensities, the small squares do not
appear equally bright.
Perceiving the t wo squares on different backgrounds as different, even
though they are in fact identical, is called the simultaneous contrast effect.
Psychophysically, we say this effect is caused by the difference in the
backgrounds.
The term contrast is used to emphas ise the difference in luminance of
objects. The perceived brightness of a surface depends upon the local
background which is illustrated in Fig. 1.16. In Fig. 1.16, the small square
on the right -hand side appears brighter when compared to the brightness
of the square on the left -handside, even though the gray level of both the
squares are the same. This phenomenon is termed ‘simultaneous contrast’.
It is to be noted that simultaneous contrast can make the same colours look
different.


Fig. 1.16 Simultane ous contrast

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18 1.6.5 Hue
Hue refers to the dominant color family like Yellow, Orange, Red, Violet,
Blue, and Green tertiary colors would also be considered hues. Hue is
mixed colors where neither color is dominant.





The pure hues are around the perime ter. The closer to the center of the
circle are more desaturated the colors, with white at the center. This Fig
1.17 shows hues, saturation and lightness.

Fig. 1.17 Hue

1.6.6 Saturation
Saturation is how “pure” the color is. For example, if its hue is cyan, its
saturation would be how purely cyan it is. Less saturated would mean
more whitish or grayish. If a color has greater -than-0 values for all three of
its red, green and blue primaries then it’s somewhat desaturated.
1.6.7 Machband effect
The Mec hband describes an effect where the human brain subconsciously
increases the contrast between two surfaces with different luminance . The
Mcehband effect is described in Fig 1.18. The intensity is uniform over the
bar.
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19 Visual appearance of each strip is da rker at its leftside than its right. The
special interaction of luminance from an object and its surrounding creates
the Mechband effect which shows that brightness is not a monotonic
function of luminance.
Mechband is caused by lateral inhibition of recep tors in the eye.
Receptors receive the light they draw light -sensitive chemical compound
Receptors directly on the lighter side of the boundary can pull in unused
chemicals from the darker side, and produce a stronger response,and the
darker side of the boundary, gives a weaker effect..
Luminance within each block is constant
The apparent lightness of each strip vary across its length.
Close to the left edge of the strip it appears lighter than at the centre, and
close to the righ t edge of the strip it appears darker than at the centre.
The visual system is exaggerating the difference in luminance (contrast) at
each edge in order top detect it.
It shows that the human visual system tends to undershoot or overshoot
around the boun dary regions of different intensities.

1.18. Machband Effect
• The intensity is uniform over the width of each bar.
• However, the visual appearance is that each strip is darker at its right
side than its left.
1.7 SIMPLE IMAGE FORMATION MODEL
An image is denoted by a two dimensional function of the form f{x, y}.
The value or amplitude of f at spatial coordinates {x,y} is a positive scalar
quantity whose physical meaning is determined by the source of the
image. When an image is generated by a physical process, its values are
proportional to energy radiated by a physical source. As a consequence,
f(x,y) must be non -zero and finite; that is oThe function f(x,y) may be characterized by two components -
i) Illumination Component: The a mount of the source illumination incident
i(x,y) on the scene being viewed;
ii) Reflectance components: The amount of the source illumination r(x,y)
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20 The functions combine as a product to form f(x,y). The intensit y of a
monochrome image at any coordinates (x,y) the gray level (l) of the image
at that point l= f (x, y.)
Lmin ≤ l ≤ L maxLminis to be positive
Lmaxmust be finite
Lmin=iminrmin
Lmax =imaxrmax
The interval [L min, Lmax] is called gray scale. The interval [0, L -l] where
l=0 is considered black and l= L -1 is considered white on the gray scale.
All intermediate values are shades of gray of gray varying from black to
white.
1.8 VIDICON AND DIGITAL CAMERA WORKING
PRINCIPLE
Vidicon
The vidicon is a storage -type camera tube in which a charge -density
pattern is formed by the imaged scene radiation on a photoconductive
surface which is then scanned by a beam of low velocity electrons.
The Vidicon operates on the principle of photo conductivity, where the
resistance of the target material shows a marked decrease when exposed to
light.
Vidicon is a short tube with a length of 12 to 20 cm and diameter between
1.5 and 4 cm.
Its life is estimated to be between 5000 and 20,000 hours.

The target consists of a thin photo conductive layer of eitherselenium or
antimony compounds which behaves like an insulator.
This is deposited on a transparent conducting film, coated on theinner
surface of the face plate. This conductive coating is known assignal
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21 With light focused on it, the photon energy enables more electronsto go to
the conduction band and this reduces its resistivity.
Image side of the photolayer, which is in contact with the signalelectrode,
is connected to DC supply through the load resistance.
The beam that emerges from the electron gun is focused on surfaceof the
photo conductive layer by combined action of uniformmagnetic field of an
external coil and electrostatic field of grid No 3.
Grid No. 4 provides a uniform decelerating field between its elf, andthe
photo conductive layer, so that the electron beam approachesthe layer with
a low velocity to prevent any secondary emission.
The fluctuating voltage coupled out to a video amplifier can be usedto
reproduce the target.
Digital camera
A digital camera is a camera that captures images and turns them into
digital form.
Digital camera shares an optical system which uses a lens with a variable
diaphragm to focus light onto an imagepickup device.
The diaphragm and shutter admit the correct amount ofli ght to the imager.

Digital camera contains image sensors that captures theincoming light rays
and turns them into electrical signals.
This image sensors can be of two types - i) charge -coupled device (CCD)
or ii)CMOS image sensor.
Light from the object zo oms into the camera lens.
This incoming light hit the image sensor, which breaks it upinto millions
of pixels.
The sensor measures the color and brightness of each pixeland stores it as
a number.
The output digital photograph is effectively a long string o fnumbers
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22 1.9 COLOUR IMAGE FUNDAMENTALS
1.9.1 RGB
In the RGB model, an image consists of three independent image planes,
one in each of the primary colors: red, green and blue. (The standard
wavelengt hs for the three primaries are as shown in figure). Specifying a
particular color is by specifying the amount of each of the primary
components present. Figure 1.21 shows the geometry of the RGB color
model for specifying colors using a Cartesian coordinat e system. The
grayscale spectrum, i.e. those colors made from equal amounts of each
primary, lies on the line joining the black and white vertices.
Fig 1.21 Schematic of the RGB color cube
Fig.1.21 The RGB color cube. The gray scale spectrum lies on th e line
joining the black and white vertices.
This is an additive model, i.e. the colors present in the light add to form
new colors, and is appropriate for the mixing of colored light for example.
The image on the left of figure 1.22 shows the additive mix ing of red,
green and blue primaries to form the three secondary colors yellow (red +
green), cyan (blue + green) and magenta (red + blue), and white ((red +
green + blue). The RGB model is used for color monitors and most video
cameras.





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23 Fig.6.2 RGB 24 bit color cube

Fig. 1.22 24 -bit color cube
Fig.1.23 The figure on the left shows the additive mixing of red, green and
blue primaries to form the three secondary colors yellow (red + green),
cyan (blue + green) and magenta (red + blue), and white (red + g reen +
blue). The figure on the right shows the three subtractive primaries and
their pairwise combinations to form red, green and blue, and finally black
by subtracting all three primaries from white.



Fig 1.23 generating the RGB image of
the cross s ectional color plane Fig. 1.24 safe 216 RGB colors and
gray in 256 -color RGB system

Pixel Depth:
The number of bits used to represent each pixel in the RGB space is called
the pixel depth. If the image is represented by 8 bits then
the pixel depth of e ach RGB color pixel = 3*number of bits/plane=3*8=24
A full color image is a 24 bit RGB color image. Therefore total number of
colors in a full color image = (28)3 = 16,777,216

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24 Safe RGB colors:
Most of the system use 256 colors. Withoutt depending on the h ardware
capabilities of the system the system reproduces subset of colors which is
called the set of RGB colors or the set of all systems safe colors.
Standard safe colors:
It is assumed that a minimum number of 256 colors can be reproduced by
any system. Among these, 40 colors are found to be processed differently
by different operating system. The remaining 216 colors are called as
standard safe colors.
Component values of safe colors:
Each of the 216 safe colors can be formed from three RGB component
values. But each component value should be selected only from the set of
values {0, 51,102,153,204,255}, in which the successive numbers are
obtained by adding 51 and are divisible by 3 therefore total number of
possible values= 6*6*6=216
Hexadecimal represe ntation
The component values in RGB model should be represented using
hexadecimal number system. The decimal numbers 1,2,….14,15
correspond to the hex numbers 0,1,2,….9,A,B,C,D,E,F. the equivalent
representation of the component values is given in table:
Number System Color Equivalents
Hex 00 33 66 99 CC FF
Decimal 0 51 102 153 204 255

Applications:
Color monitors, Color video cameras
Advantages:
● Image color generation
● Changing to other models such as CMY is straight forward
● It is suitable for hardware implementation
● It is based on the strong perception of human vision to red, green
andblue primaries.
Disadvantages:
● It is not acceptable that a color image is formed by combining three
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25 ● This model is not suitable for describing colors in a w ay which is
practical for human interpretation.
1.9.2 CMY
The CMY (Cyan Mmagenta Yellow) model is a subtractive model
appropriate to absorption of colors. The CMY model asks what is
subtracted from white. The primary colors are cyan, magenta and yellow,
and secondary colors are with red, green and blue
The surface coated with cyan pigment is illuminated by white light, no red
light is reflected, and similarly for magenta and green, and yellow and
blue. The relationship between the RGB and CMY models is giv en by:
C 1 R
M = 1 - G
Y 1 B
The CMY model is used by printing devices and filters.
1.9.3 HIS MODELS
Colors are specified by the three quantities hue, saturation and intensity
which is similar to the way of human interpretation.
Hue: It is a color attribute that describes a pure color.
Saturation: It is a measure of the degree to which a pure color is diluted by
white light.
Intensity: It is a measureable and interpretable descriptor of
monochromatic imag es, which is also called the gray level.
i) Hue:
The hue of a color can be determined from the RGB color cube. if the
three points black, white and any one color are combined, a triangle is
formed. All the points inside the triangle will have the same hu e. This is
due to the fact that black and white components cannot change the hue.
HSI color space
The HIS color space is represented by vertical intensity axis and locus of
color points that lie on planes perpendicular to the axis. The shape of the
cube is defined by the intersecting points of these planes with the faces of
cube. As the planes move up and down along the intensity axis, the shape
can either be a triangle or a hexagon. In HSI space, primary colors are
separated by 120°. Secondary colors are also separated by 120° and the
angle between the secondary’s and primaries’ is 60°.

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26 Representation of Hue:
The hue of a color point is determined by an angle from some reference
point.
The angle between the point and the red axis is 0° is zero hue.
If the angle from red axis increases in the counter clock wise direction
then hue increases.
Fig. 1.25 Conceptual relationship between the RGB and HSI color models

ii) Intensity:
The intensity can be extracted from an RGB image because an RGB color
imag e is viewed as three monochrome intensity images.
Intensity Axis:
A vertical line joining the black vertex (0, 0, 0) and white vertex(1,1, 1) is
called intensity axis. The intensity axis represents the gray scale.
iii)saturation:
All points on the int ensity axis are gray which means that the saturation
i.e., purity of points on the axis is zero.
When the distance of a color from the intensity axis increases, the
saturation of that color also increases.
Representation of saturation
The saturation is described as the length from the vertical axis.
In the HSI space, it is represented by the length of the vector from the
origin to the color point.
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27

Fig.1.26 HIS Components of the images

Converting colors from RGB to HSI
Given an image in RGB color format the H component of each RGB
pixel is obtained usin the equation
H=




Converting colors from HSI to RGB
Converting equations depend on the value of H (H – Hue)> f or three
sectors the equation for conversion is given below:
RG (Red, Green) Sector (0
) : When H is in
this sector the RGB components are given by the equations
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28 GB (Green, Blue) Sector (120
) : When H
(H=H -120
is in this sector the RGB components are given by the
equations:

BR (Blue, Red) Sector (240
) : When H
(H=H -240
is in this sector the RGB components are given by the
equations:

Advantages of HSI model:
● It describes colors in terms that are suitable for human interpretation.
● The model all ows independent control over the color describing
quantities namely hue, saturation and intensity.
● It can be used as an ideal tool for developing image processing
algorithms based on color descriptions.
1.9.4 2D SAMPLING
To create a digital image, conver t the continuous sensed data into digital
form. This involves two processes.
i) Sampling
ii) Quantization
An image, f(x, y), may be continuous with respect to the x - and y -
coordinates, and also in amplitude. To convert it to digital form, sample
the func tion in both coordinates and in amplitude.
Digitizing the coordinate values is called Sampling.
The one -dimensional function in Fig. 1.27(b) is a plot of amplitude
(intensity level) values of the continuous image along the line segment AB
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29 To sample this function, equally spaced samples along line AB, are
depicted in Fig. 1.27 (c). The spatial location of each sample is indicated
by a vertical tick mark.
The samples are shown as small white squares super imposed on the
function. The se t of these discrete locations gives the sampled function.
However, the values of the samples still span (vertically) a continuous
range of intensity values.
The intensity values must be (quantized) to form a digital function
The right side of Fig. 1.27 (c) shows the intensity scale divided into eight
discrete intervals, ranging from black to white. The vertical tick marks
indicate the specific value assigned to each of the eight intensity intervals.
The continuous intensity levels are quantized by assign ing one of the eight
values to each sample. The assignment is made depending on the vertical
proximity of a sample to a vertical tick mark. The digital samples resulting
from both sampling and quantization are shown in Fig1.27 (d). Starting at
the top of t he image and carrying out this procedure line by line produces
a two -dimensional digital image.


Fig. 1.27 Generating a digital image. (a) Continuous image. (b) A scan
line from A to B in the continuous image, used to illustrate the concepts
of sampling and quantization. (c) Sampling and quantization. (d) Digital scan line.

1.9.5 QUANTIZATION
Digitizing the amplitude values is called Quantization.
Quantisation involves representing the sampled data by a finite number of
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30 Quantisers can be classified into two types, namely, i) scalar quantisers
and ii) vector quantisers. The classification of quantisers is shown in
Fig. 1.29.


Selecting the number of individual mechanical increments for spatial
sampling at which the sensor to collect data for activation. Limits on
sampling accuracy are determined by the factors, such as the quality of the
optical components of the system.
Mechanical mot ion in the other direction can be controlled more
accurately, but it makes little sense to try to achieve sampling density in
one direction that exceeds the sampling limits established by the number
of sensors in the other.
The accuracy achieved in quantiz ation is highly dependent on the noise
content of the sampled signal. The method of sampling is determined by
the sensor arrangement used to generate the image.
When an image is generated by a single sensing element combined with
mechanical motion, and th en the output of the sensor is quantized as given
in Fig. 2.18.
The image after sampling and quantization is shown in fig 2.18 (b).
The quality of a digital image is determined to a large degree by the
number of samples and discrete intensity levels u sed in sampling and
quantization.
1.10 SUMMARY
Since1921 when the Bartlane cable picture transmission system was
introduced the Digital images started its evolution. In 1964 the computers
are used to process digital images and the actual digital image pro cessing
started working.
Digital image composed of elements called pixels. For the immediate
output display, fast processing and huge storage the digital images are
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31 The position of the pixels to represent the digital images are identified
through n eibors of the pixels, adjacency, boundaries and connectivities of
the pixels.
Image Acquisition devices, Image storage devices, Image processing
elements and Image display devices are the basic elements of the digital
image processing sytem which are used to process the digital images. The
structure of human eye helps the human to understand and sense the colors
and structure of the images.
RGB , CMY are useful in representing the images with different colors,
brightness and contrasts.
1.11 REFERENCES
1. R.C.G onzalez&R.E.Woods, Digital Image Processing, Pearson
Education, 3rd edition, ISBN. 13:978 -0131687288
2. S. Jayaraman Digital Image Processing TMH (McGraw Hill)
publication, ISBN - 13:978 -0-07- 0144798
3. William K. Pratt, “Digital Image Processing”, John Wil ey, N J, 4th
Edition,2007
4. The Origins of Digital Image Processing & Application areas in
Digital Image Processing Medical Images,Mukul, Sajjansingh, and
Nishi
1.12 UNIT END EXERCISES
1. Define Image and Digital Image
2. Classify the images.
3. Write the advantages a nd di sadvantages of digital images.
4. What is digital image processing?
5. How do you represent the digital Images? Explain
6. Describe the relationship between pixels
7. How do measure the distance between pixels?
8. Explain the elements of digital image processing sys tem.
9. Explain the structure of human eye
10. Write short note on i) Hue ii)Mach band effect
11. Elucidate the working principles of digital camera with neat diagram
12. Write short note on i) RGB ii)CMY

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32 Module II
Image Enhancement in the spatial domain
2
SPATIAL DOMAIN METHODS
Unit Structure
2.0 Objectives
2.1 Introduction
2.2 An Overview
2.3 Spatial Domain Methods
2.3.1 Point Processing
2.3.2 Intensity transformations
2.3.3 Histogram Processing
2.3.4 Image Subtraction
2.4 Let us Sum Up
2.5 List of References
2.6 Bibliography
2.7 Unit End Exercises
2.0 OBJECTIVES
Enhancement's main goal is to improve the quality of an image so that it
may be used in a certain process.
● Enhancement of images Enhancement in the spatial domain and
Frequency domain f all into two categories.
● The word spatial domain refers to the Image Plane itself, which is
DIRECT pixel manipulation.
● Frequency domain processing approaches work by altering an image's
Fourier transform.


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33 2.1 INTRODUCTION
The aggregate of pixels that m ake up an image is known as the spatial
domain.
Spatial Domain Methods are procedures that work on these pixels directly.
g(x,y)=T[f(x,y)]
F(x,y): Input Image, T: Image Operator g(x,y): Image that has been
processed.
T can also work with a group of images .
The neighborhood is defined as:
Input for Process: A one -pixel neighborhood around a point (x,y) The
most basic kind of input is a one -pixel neighborhood. s=T(r)
T:Transformation Function s,r: f(x,y) and g(x,y) grey levels, respectively.
The most basic t echnique is a rectangular sub -picture region centred at
(x,y).
● SPATIAL DOMAIN METHODS
The value of a pixel in the enhanced picture with coordinates (x,y) is the
outcome of executing some operation on pixels in the vicinity of (x,y) in
the input image, F.
Neighbourhoods can be any shape, however they are most commonly
rectangular.
● GREY SCALE MANIPULATION
When the operator T just acts on a pixel neighborhood in the input image,
it is the simplest kind of an operation because it only depends on the value
of F at that point (x,y). This is a greyscale mapping or transformation.
Thresholding is the simplest case, in which the intensity profile is replaced
with a step function that is active at a set threshold value. In this scenario,
any pixel in the input image w ith a grey level below the threshold is
mapped to 0 in the output image. The rest of the pixels are set to 255.






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34 Figure 1 depicts further greyscale adjustments.


● EQUALIZATION OF HISTOGRAMS
Equalization of histograms is a typical approach for im proving the
appearance of photographs. Assume that we have a largely dark image.
The visual detail is compressed towards the dark end of the histogram, and
the histogram is skewed towards the lower end of the greyscale. The
image would be much clearer if w e could stretch out the grey levels at the
dark end to obtain a more consistently distributed histogram. Figure 2 shows the original image, histogram, and equalised versions. Both photos have been quantized to a total of 64 grey levels.
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35 Finding a grey scale translation function that produces an output image
with a uniform histogram is the goal of histogram equalisation (or nearly
so).
What is the procedure for determining the grey scale transformation
function? Assume that our grey levels are continuous and that they have
been normalised to a range of 0 to 1.
We need to identify a transformation T that converts the grey values r in
the input image F to grey values s = T(r) in the converted image.
The assumption is that
● T is single valued and monotonicall y increasing, and
●
for
.
The inverse transformation from s to r is given by
r = T-1(s).
We have a probability distribution for grey levels in the input image Pr if
we take the histogram for the input image and normalise it so that the area
under the hist ogram is Pr(r).
What is the probability distribution Ps(s) if we transform the input image
to s = T(r)?
It turns out that, according to probability theory,

where r = T-1(s).
Consider the transformation

The cumulative distribution function of r is repre sented by this. The
derivative of s with respect to r is calculated using this definition of T.

Substituting this back into the expression for Ps, we get
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36 for all
.Thus, Ps(s) is now a uniform distribution
function, which is what we want.
● DISCRETE FORM ULATION
The probability distribution of grey levels in the input image must first be
determined. Now

where nk is the number of pixels having grey level k, and N is the total
number of pixels in the image.
The transformation now becomes

Note that
,
the index
,and
.
So that the output values of this transformation span from 0 to 255, the
values of
must be scaled up by 255 and rounded to the nearest integer.
As a result of the discretization and rounding of
to the nearest in teger,
the modified image's histogram will not be exactly uniform.
● SMOOTHING AN IMAGE
Image smoothing is used to reduce the impact of camera noise, erroneous
pixel values, missing pixel values, and other factors. Image smoothing can
be done in a variety of ways; we'll look at neighborhood averaging and
edge -preserving smoothing.
● NEIGHBOURHOOD AVERAGING
The average pixel value in a neighbourhood of
is obtained from
the average pixel value in a neighbourhood of ( x,y) in the input image.
For example, if we u se a
neighbourhood around each pixel we
would use the mask
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37 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9
Each pixel value is multiplied by 1/9and then totalled before being placed
in the resulting image. This mask is moved across the image in steps until
every pixel is covered. This soothing mask is used to convolve the image
(also known as a spatial filter or kernel).
The value of a pixel, on the other hand, is normally expected to be more
strongly related to the values of pixels nearby than to those further away.
This is because most points in a picture are spatially coherent with their
neighbours; in fact, this hypothesis is only false at edge or feature points.
As a result, the pixels towards the mask's center are usually given a higher
weight than those on the edges.
The rectangular weighting function (which just takes the average over the
window), a triangular weighting function, and a Gaussian are all typical
weighting functions.
Although Gaussian smoothing is the most widely utilized, there isn't much
of a difference between alternative weighting functions in practice.
Gaussian smoothing is characterized by the smooth modification of the
image's frequency components.
Smoothing decreases or attenuates the image's higher frequencies. Other
mask shapes can c ause strange things to happen to the frequency
spectrum, but we normally don't notice much in terms of image
appearance.
Smoothing that preserves the edge
Because the image's high frequencies are suppressed, neighborhood
averaging or Gaussian smoothing wil l tend to blur edges. Using median
filtering as an alternative is a viable option. The grey level is set to the
median of the pixel values in the pixel's immediate vicinity.
The median m of a set of values is the value at which half of the values are
less than m and the other half are greater. Assume that the pixel values
3 x 3 in a given neighborhood are (10, 20, 20, 15, 20, 20, 20, 25, 100). We
obtain (10, 15, 20, 20, |20|, 20, 20, 25, 100) if we order the values, and the
median is 20.
The result of median filtering is that pixels with outlying values are forced
to become more like their neighbors while maintaining edges. Median
filters, by definition, are non -linear.
Median filtering is a morphological operation. Pixel values are replaced
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38 When distorting an image, the greatest value in the neighborhood is used
to replace pixel values. Median filtering replaces pixels with the
neighborhood's median value. The type of morphological o peration is
determined by the rank of the value of the pixel used in the neighborhood.
Figure 3: Image of Genevieve with salt and pepper noise, averaging result, and median filtering result.

2.2 AN OVERVIEW
The spatial domain technique is a well -know n denoising technique. It's a
noise -reduction approach that uses spatial filters to apply directly to digital
photos. Linear and nonlinear spatial filters are the two types of spatial
filtering algorithms (Sanches et al., 2008). Filtering is a method used in
image processing to do several preprocessing and other tasks such as
interpolation, resampling, denoising, and so on. The type of task
performed by the filter method and the type of digital image determine the
filter method to be used. Filter methods ar e used in digital image
processing to remove undesirable noise from digital photographs while
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39 Nonlinear filters are used in a variety of ways, the most common of which
is to rem ove a certain sort of unwanted noise from digital photographs.
There is no built -in way for detecting noise in the digital image with this
method. Nonlinear filters often eliminate noise to a certain point while
blurring images and hiding edges. Several ac ademics have created various
sorts of median (nonlinear) filters to solve this challenge throughout the
previous decade. The median filter, partial differential equations, nonlocal
mean, and total variation are the most used nonlinear filters. A linear fil ter
is a denoising technique in which the image's output results vary in a
linear fashion. Denoising outcomes are influenced by the image's input.
As the image's input changes, the image's output changes linearly. The
processing time of linear filters for picture denoising is determined by the
input signals and the output signals. The mean linear filter is the most
effective filter for removing Gaussian noise from digital medical pictures.
This approach is a simple way to denoise digital photos (Wieclawek a nd
Pietka, 2019). The average or mean pixels values of the neighbour pixels
are calculated first, and then replaced with every pixel of the digital image
in the mean filter. To reduce noise from a digital image, it's a very useful
linear filtering approach . Wiener filtering is another linear filtering
technique. This technique requires all additive noise, noise spectra, and
digital picture inputs, and it works best if all of the input signals are in
good working order. This strategy reduces the mean square error of the
intended and estimated random processes by removing noise.
2.3 SPATIAL DOMAIN METHODS
For image enhancement, there are primarily two methods: one for images
in the spatial domain and the other for images in the frequency domain.
The first meth od is based on editing individual pixels in an image,
whereas the second way is based on altering an image's Fourier transform.
Spatial domain methods
Here, image processing functions can be expressed as :

f(x,y) is the input picture, g(x,y) is the proce ssed image (i.e. the result or
output image), and an operator on f is defined over some neighbourhood N
of (x,y). We usually employ a rectangle subimage centred at N for (x,y).
a) N is a 1×1 neighbourhood (point -processing)

N encompasses exactly one pix el in this case. The operator T is then
transformed into a gray -level transformation function, which is written as:

The gray levels of f(x,y) and g are represented by r,s (x,y). We can
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40 stretching and bi -level mapping (here an image is converted so that it only
contains black and one color white). The challenge is to define T in such a
way that it darkens grey levels below a particular threshold k and
brightens grey levels above it. A bl ack-and-white image is created when
the darkening and brightening are both consistent (black and white). This
technique is known as 'point -processing' since s is only dependent on the
value (i.e. the gray -level) of T in a single pixel.
b) N is a m×m neighb ourhood (spatial filtering)
In this situation, N refers to a small area. It's worth noting that this
technology isn't limited to image enhancement; it can also be used to
smoothen photos, among other things. The values in a predefined
neighborhood (i.e. the mask/filter) of g(x,y) are used to determine the
value of g(x,y) (x,y). The value of m can range from 3 to 10 in most cases.
These procedures are known as mask processing' or 'filtering.'
METHODS IN THE FREQUENCY DOMAIN
The convolution theorem is at the h eart of these techniques. The following
is an example of what it means:
Assume that g(x,y) is a convolution of an image f(x,y) and a linear,
position invariant operator h(x,y):

Applying the convolution theorem yields :

The Fourier transforms of f, g, a nd h are F, G, and H, respectively. The
following is the result of applying the inverse Fourier transform to G(u,v):

H(u,v), for example, enhances the high -frequency components of f(u,v),
resulting in a g(x,y) picture with exaggerated edges.
Some intrigu ing features can be noticed when looking at the theory of
linear systems (see figure 1): A system with the function of producing an
out-put image g(x,y) from an input image f (x,y) is referred to as h(x,y).
The Fourier notation for this operation is equiva lent to this.
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41

Figure 1 : Linear systems.
2.3.1 POINT PROCESSING
When making a film, it's common to lessen the overall intensity to create a
unique atmosphere. Some people go overboard, and the effect is that the
observer can only see blackness. So, what exactly do you do? You take
out your remote and press the brightness button to alter the light intensity.
When you do this, you're performing a type of image processing called
point processing.
Let's say we have an input image f(x, y) that we want to alte r to get a
different image, which we'll call the output image g. (x,y). When altering
the brightness of a movie, the input picture is the one saved on the DVD
you're watching, and the output image is the one that appears on the
television screen. Point pro cessing is now described as an operation that
calculates the new value of a pixel in g(x, y) based on the value of the
same pixel in f(x, y) and some action. That is, in f(x, y), the values of a
pixel's neighbours have no influence, hence the name point pr ocessing.
The adjacent pixels will play a significant role in the upcoming subjects.
Figure 4.1 depicts the principle of point processing. Some of the most
fundamental point processing operations are explained in this topic.
When you use your remote to adj ust the brightness, you're actually
changing the value of b in the following equation:
The value of b is increased every time you press the '+' brightness button,
and vice versa. As b is increased, a higher and higher value is added to
each pixel in the i nput image, making the image brighter. The image
becomes brighter if b > 0, and darker if b 0. Figure 2 .2 depicts the effect of
altering the brightness.
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42 Figure 2 .1: The point -processing principle. A pixel in the input image is
processed, and the result i s saved in the output image at the same location.

Figure 2 .2: The resultant image will be equivalent to the input image if b
in Eq. 2 .1 is zero. If b is a negative quantity, the image produced will be
smaller.
If b is a positive number, the brightness of the resulting image will be
increased.
The us e of a graph, as shown in Fig. 2 .3, is often a more convenient
manner of illustrating the brightness action. The graph depicts the
mapping of pixel values in the input image (horizontal axis) to pixel
values in the output picture (vertical axis) (vertical axis). Gray -level
mapping is the name given to such a graph. The mapping does nothing in
the first graph, i.e., g(142,42) = /. (142,42).
In the following graph, all pixel values are increased (b > 0), resulting in a
brighter image. This has two effects: I no pixel in the output image will be
fully dark, and ii) some pixels in the output image will have a value
greater than 255. The latter is undesirable due to an 8 -bit image's upper
limit, hence all pixels above 255 are set to 255, as shown in the graph's
horizontal section. When b 0 is set to zero, some pixels will have negative
values and will be set to zero in the output, as shown in the previous
graph.
You can adjust the contrast in the same way that you can adjust the
brightness on your TV. The gray -level values that make up an image's
contrast are how distinct they are. When we look at two pixels with values
112 and 114 adjacent to each other, the human eye has trouble
distinguishing them, and we remark ther e is a low contrast. If the pixels
are 112 and 212, on the other hand, we can readily differentiate them and
claim the contrast is great.
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43

Three instances of gray -level mapping are shown in Figure 2 .3. The input
is shown at the top of the page. The three additional images are the result
of the three gray -level mappings being applied to the input. Eq. 4.1 is used
in all three gray -level mappings.

Figure 2.4: If the value of an in Eq. 2 .2 is one, the output image will be the
same as the input image. If an is less than one, the resulting image will be
less contrasted; if an is greater than one, the resulting image will be more
contrasted.
Changing the slope of the graph1 changes the contrast of an image:

If an is more than one, the contrast is raised; if it is less than one, the
contrast is diminished. When a = 2, the pixels 112 and 114, for example,
will have the values 224 and 228, respectively. The contrast is raised by a
factor of two because the difference between them is increased by a factor
of two. The effect of adjusting the contrast may be observed in Fig. 4.4. munotes.in

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44 When the equations for brightness (Eq. 2.1) and contrast (Eq. 2 .2) are
combined, we get

Which is a straight line's equation. Consider an example of how to use this
equation. Let's say we' re interested in a section of the input image where
the contrast isn't quite right. As a result, we determine the range of pixels
in this region of the image and map them to the complete [0, 255] range in
the output image. Assume that the input image's min imum and maximum
pixel values are 100 and 150, respectively.
Changing the contrast implies that in the output image, all pixel values
below 100 are changed to zero, and all pixel values above 150 are set to
255. Eq. 2 .3 is used to map the pixels in the ran ge [100, 150] to [0, 255],
where a and b are defined as follows:

Non-linear Gray -Level Mapping
Gray -level mapping isn't confined to Eq. 2 .3-defined linear mappings. In
fact, the designer is free to specify the gray -level mapping as she wants as
long as e ach input value has just one output value. Rather than creating a
new equation/graph, the designer will frequently use one that is already
defined. The following are three of the most frequent non -linear mapping
functions.
Gamma Mapping
It is the process of converting one colour into another.
Because humans have a non -linear sense of contrast, it is useful to be able
to adjust the contrast in the dark grey levels and the light grey levels
separately in various cameras and display devices (for example, flat panel
televisions). Gamma mapping is a typical non -linear mapping that is
defined for positive as
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45

Fig. 4.5 Curves of gamma -mapping for various gammas
Figure 2 .5 depicts a few gamma -mapping curves. We get the identity
mapping if = 1. We boost the mid -levels for 0 1 to increase the dynamics
in the dark sections. We decrease the mid -levels to increase the dynamics
in the bright areas for > 1. The gamma mapping is set up so that both the
input and output pixel values are between 0 and 1. Before applying th e
gamma transformation, the input pixel values must first be transformed by
dividing each pixel value by 255. After the gamma transformation, the
output values should be scaled from [0, 1] to [0, 255].
There is a specific case presented. A pixel with the v alue vin = 120 in a
gray-scale picture is gamma mapped with = 2.22. Initially, the pixel value
is divided by 255 to convert it to the interval [0,1], v = 120/255 = 0.4706.
Second, v2 = 0.47062.22 = 0.1876 is used to do gamma mapping. Finally,
the result is vout = 0.1876 • 255 = 47, which is transferred back to the
interval [0,255]. Figure 4.6 depicts some examples.

Figure 2 .6: With a value of 0.45, gamma mapping to the left is 0.45, while
with a value of 2.22, gamma mapping to the right is 2.22. The origi nal
image is in the middle.
Mapping on a Logarithmic Scale
The logarithm operator is used in an alternate non -linear mapping. The
logarithm of the pixel value is used to replace each pixel. Low -intensity
pixel values are amplified as a result of this. It's commonly employed
when an image's dynamic range is too high to display or when there are a munotes.in

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46 few bright spots on a dark background. Because there is no logarithm for
zero, the mapping is defined as

Where c is a scaling constant that guarantees a maximum output value of
255 It is calculated as follows:

Where umax is the input image's maximum pixel value. Changing the
pixel values of the input image using a linear mapping before the
logarithmic mapping can alter the behavior of the logarithmic mapping.
Figure 4.7 shows the logarithmic mapping from [0,255] to [0,255]. This
mapping will stretch low -intensity pixels while suppressing high -intensity
pixels' contrast. Figure 4 .7 shows one example.
2.3.2 INTENSITY TRANSFORMATIONS
When working with grayscale ima ges, it's common to wish to change the
intensity levels. For example, you might wish to flip the black and white
intensities or make the darks darker and the lights lighter. Intensity
modifications can be used to improve the contrast between various
intens ity values so that details in an image can be seen. The next two
photos, for example, illustrate an image before and after an intensity
modification.
The cameraman's jacket was originally black, but an intensity
transformation enhanced the contrast between the black intensity values,
which were previously too near, allowing the buttons and pockets to be
seen. (This example is taken from the Image Processing Toolbox, User's
Guide, Version 5 (MATLAB documentation) —found in the help menu or
online at:


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47 In general, Intensity Transformation Functions are used to adjust the
intensity. The four main intensity transformation functions are discussed
in the following sections:
1. photographic negative (using imcomplement)
2. gamma transformation (using imadjust)
3. logarith mic transformations (using c*log(1+f))
4. contrast -stretching transformations
(using 1./(1+(m./(double(f)+eps)).^E)
● PHOTOGRAPHIC NEGATIVE
The Photographic Negative is the most straightforward of the intensity
conversions. Assume we're dealing with grayscale d ouble arrays with
black equal to 0 and white equal to 1. The notion is that 0s become 1s, and
1s become 0s, with any gradients in between reversed as well. This means
that genuine black becomes true white and vice versa in terms of intensity.
Incomplement provides a function in MATLAB that allows you to
produce photographic negatives (f). The graph below displays the
mapping between the original values (x -axis) and the incomplement
function, with a=0:.01:1.

An example of a photography negative is shown be low. Take note of how
much easier it is to read the text in the middle of the tyre now than it was
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48 Original
Photographic Negative
The MATLAB code that created these two images is:
I=imread('tire.tif');
imshow(I)
J=imcomplement(I);
figure, imsh ow(J)
● GAMMA TRANSFORMATIONS
Gamma Transformations allow you to curve the grayscale components to
brighten or darken the intensity (when gamma is less than one) (when
gamma is greater than one). These gamma conversions are created using
the MATLAB functio n:
imadjust(f, [low in high in], [low out high out], gamma) The input image
is f, the curve is gamma, and the clipping is [low in high in] and [low out
high out].
Values below low in and above high in are clipped to low out and high
out, respectively. Both [low in high in] and [low out high out] are used in
this lab with []. This indicates that the input's full range is mapped to the
output's full range. The plots below show the effect of varying gamma
with a=0:.01:1. Notice that the red line has gamma=0.4, which creates an
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49

The outcomes of three of the gamma transformations indicated in the plot
above are shown below. Notice how numbers greater than one result in a
darker image, whilst values between 0 and one resu lt in a brighter image
with more contrast in dark places, allowing you to appreciate the tire's
intricacies.
Original (and
gamma=1)
gamma=3
gamma=0.4

The MATLAB code that created these three images is:
I=imread('tire.tif');
J=imadjust(I,[],[],1);
J2=imadjust(I,[],[],3);
J3=imadjust(I,[],[],0.4);
imshow(J);
figure,imshow(J2);
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50 The gamma transformation is a crucial step in the image display process.
You should find out more information about them. Charles Poynton, a
digital video systems expert who previously worked for NASA, has a
great gamma FAQ that I recommend you read, especially if you plan to
handle CGI. He also dispels several common misunderstandings
concerning gamma.
● LOGARITHMIC TRANSFORMATIONS
Logarithmic Transformations (such as the Gamma Transformation, where
gamma 1) can be used to brighten an image's intensity. It's most
commonly used to boost the detail (or contrast) of low -intensity values.
They're particularly good at bringing out detail in Fourier transformations
(covered in a later lab). The equation for obtaining the Logarithmic
transform of image f in MATLAB is:
g = c*log(1 + double(f))
The constant c is typically used to scale the log function's range to fit the
input domain. For an uint8 picture, c=255/log(1+2 55), or c=1/log(1+1)
(~1.45) for a double image. It can also be used to boost contrast —the
higher the c value, the brighter the image appears. The log function, when
used in this manner, can produce results that are excessively bright to
display. The graph ic below shows the result for various values of c when
a=0:.01:1. For the plots of c=2 and c=5, the min function clamps the y -
values at 1. (teal and purple lines, respectively).

The original image and the outcomes of applying three of the
transformations from above are shown below. When c=5, the image is the
brightest, and the radial lines on the interior of the tyre can be seen (these
lines are barely viewable in the original because there is not enough
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51

The MATLAB co de that created these images is:
I=imread('tire.tif');
imshow(I)
I2=im2double(I);
J=1*log(1+I2);
J2=2*log(1+I2);
J3=5*log(1+I2);
figure, imshow(J)
figure, imshow(J2)
figure, imshow(J3)
Notice how the bright sections, when intensity levels are capped, los e
detail. Any values generated by the scaling that is more than one are
presented as 1 (full intensity) and should be capped. The min(matrix,
upper bound) and max(matrix, lower bound) functions in MATLAB can
be used to clamp data, as indicated in the legen d for the plot above.
Although logarithms can be calculated in a variety of bases, including
MATLAB's builtin log10, log2, and log (natural log), the resulting curve
is the same for all bases when the range is scaled to match the domain.
Instead, the curve 's shape is determined by the range of values to which it
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52

If you want to use logarithm transformations properly, you should be
aware of this effect. Here's what happens when you scale an image's
values to those ranges before applying the logarithm transform:

The MATLAB code that produced these images is:
tire = imread('tire.tif');
d = im2double(tire);
figure, imshow(d);
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53 f = d;
c = 1/log(1+1);
j1 = c*log(1+f) ;
figure, imshow(j1);
%log on domain [0, 255]
f = d*255;
c = 1/log(1+255);
j2 = c*log(1+f);
figure, imshow(j2);
%log on domain [0, 2^16]
f = d*2^16;
c = 1/log(1+2^16);
j3 = c*log(1+f);
figure, imshow(j3);
The effects of the logarithm transform are barely evident in domain
[0, 1], but they are greatly accentuated in domain [0, 65535]. It's also
worth noting that, unlike linear scaling and clamping, gross detail
remains visible in light areas.
● CONTRAST -STRETCHING TRANSFORMATIONS
The contrast between the dar ks and the brightness is increased via
contrast -stretching procedures. In lab 1, we saw a simplified version of
section 5.3 of the textbook's automated contrast adjustment. That
adjustment simply expanded the histogram to fill the image's intensity
domain while keeping everything at about identical levels. You might
want to push the intensity to a particular point every now and again. There
are only a few degrees of grey around the level of interest, so everything
darker darks are a lot darker and everythin g lighter is a lot lighter. In
MATLAB, you can use the following function to make a contrast -
stretching transformation:
g=1./(1 + (m./(double(f) + eps)).^E)
The function's slope is controlled by E, and the mid -point, m, is where you
wish to switch from dar k to bright values. The distance between 1.0 and
the next greatest integer that may be expressed in a double -precision
floating -point is represented by eps, a MATLAB constant. It is utilized in
this equation to prevent division by zero if the image contain s any zero -
valued pixels. The outcomes of adjusting both m and E are represented in
two plot/diagram sets below. Given a=0:.01:1 and m=0.5, the results for
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54

The original image and the outcomes of applying the three c hanges from
above are shown below. The m value used in the following examples is
the average of the image intensities (0.2104). The function becomes more
like a thresholding function with threshold m for very high E values,The
resulting image is more black and white than grayscale, for example.

The MATLAB code that created these images is:
I=imread('tire.tif');
I2=im2double(I);
m=mean2(I2)
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55 contrast2=1./(1+(m./(I2+eps)).^5);
contrast3=1./(1+(m./(I2+eps)).^10);
imshow(I2)
figure,imshow(contrast1)
figure,imshow(contrast2)
figure,imshow(contrast3)
This second plot shows how changes to m (using E=4) affect the contrast
curve:

The following shows the original image and the results of applying the
three transformations from ab ove. The m value used below is 0.2, 0.5, and
0.7. Notice that 0.7 produces a darker image with fewer details for this tire
image.
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56 The MATLAB code that created these images is:
I=imread('tire.tif');
I2=im2double(I);
contrast1=1./(1+(0.2./(I2+eps)).^4)
contrast2=1./(1+(0.5./(I2+eps)).^4);
contrast3=1./(1+(0.7./(I2+eps)).^4);
imshow(I2)
figure,imshow(contrast1)
figure,imshow(contrast2)
figure,imshow(contrast3)
● The intrans and changeclass Functions
Except for the contrast stretching transform, the file intran s.m Digital
Image Processing, Using MATLAB[2] provides a function that performs
all of the intensity transformations discussed above. You should go
through the code and figure out how to implement that feature.
A second function named changeclass is used b y the intrans function.
The intrans function's comments, which begin on the second line, explain
how to use it. Please take note of the description of the missing contrast
stretch transform, which states that it should take changing arguments and
what defa ults to use for missing values. The table below shows how
intrans can be used to correlate to the four Intensity Transformation
Functions. Consider the case when I=imread('tire.tif'); Transformation Intensity
Transformation
Function Corresponding intrans C all photographic
negative neg=imcomplement(I); neg=intrans(I,'neg'); logarithmic I2=im2double(I);
log=5*log(1+I2); log=intrans(I,'log',5); gamma gamma=imadjust
(I,[],[],0.4); gamma=intrans(I,'gamma',0.4); contrast -
stretching I2=im2double(I);
contrast=1. /(1+(0.2./(I2
+eps)).^5); contrast=intrans(I,'stretch',0.2,5);
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57 2.3.3 HISTOGRAM PROCESSING
● HISTOGRAMS INTRODUCTION
The histogram is a graphical representation of a digital image used in
digital image processing. A graph is a representation of each tonal va lue as
a number of pixels. In today's digital cameras, the image histogram is
available. They are used by photographers to see the dispersion of tones
captured.
The horizontal axis of a graph represents tonal fluctuations, whereas the
vertical axis represe nts the number of pixels in that specific pixel. The left
side of the horizontal axis depicts black and dark parts, the middle
represents medium grey colour, and the vertical axis reflects the area's
size.




Histogram of the scenery
APPLICATIONS OF HIS TOGRAMS
1. Histograms are employed in software for simple computations in
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58 2. It's a tool for analyzing images. A careful examination of the
histogram can be used to predict image properties.
3. The image's brightness can be modified by loo king at the histogram's
features.
4. Having information on the x -axis of a histogram allows you to
modify the image's contrast according to your needs.
5. It is used to equalize images. To create a high contrast image, the
grey level intensities are extended alo ng the x -axis.
6. Histograms are utilized in thresholding because they improve the
image's appearance.
7. We can figure out which type of transformation is used in the method
if we have the input and output histograms of an image.
HISTOGRAM PROCESSING TECHNIQUES
● HISTOGRAM SLIDING
The entire histogram is shifted rightwards or leftwards in histogram
sliding. When a histogram is adjusted to the right or left, the brightness of
the image changes dramatically. The intensity of light released by a
particular light sour ce determines the brightness of the image.

● HISTOGRAM STRETCHING
The contrast of an image is boosted through histogram stretching. The
contrast of an image is defined as the difference between the maximum
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59 If we wish to increase the contrast of an image, we expand the histogram
till it covers the entire dynamic range of the histogram.
We may determine whether an image has low or high contrast by looking
at its histogram.


● HISTOGRAM EQUALIZATION
Equalizing all of an imag e's pixel values is done through histogram
equalization. The transformation is carried out in such a way that the
histogram is uniformly flattened.
Histogram equalization broadens the dynamic range of pixel values and
ensures that each level has an equal n umber of pixels, resulting in a flat
histogram with great contrast.
When extending a histogram, the shape of the histogram remains the
same, however, when equalizing a histogram, the shape of the histogram
changes, and just one image is generated.

2.3.4 IMAGE SUBTRACTION
● IMAGE SUBTRACTION
Image enhancement and segmentation (where an image is divided into
various 'interesting' elements like edges and areas) are two applications for
this approach. The foundations are built on subtracting two images, which
is defined as computing the difference between each pair of related pixels
in the two images. It can be written as:
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60 A fascinating application is in medicine, where h(x,y) is called a mask and
subtracted from a succession of photos fi(x,y), yielding some fascinating
images. It is possible to watch a dye propagate through a person's brain
arteries, for example, by doing so. The portions in the photos that look the
same get darkened each time the difference is calculated, while the
differences become more hi ghlighted (they are not subtracted out of the
resulting image).
● IMAGE AVERAGING
Consider a noisy image g(x,y), which is created by adding a specific
amount of noise n(x,y) to an original image f(x,y):

The noise is expected to be uncorrelated (thus homo geneous across the
image) and have an average value of zero at each pair (x,y). By
introducing a set of noisy images g(x,y), the goal is to lessen the noise
effects.
Assume we have an image that was created by averaging noisy images:

We now calculate the expected value of
which is :
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61

2.4 LET US SUM UP
Enhancement aims to improve the quality of an image so that it may be
used in a certain process. The word spatial refers to the Image Plane itself,
which is DIRECT pixel manipulation. Frequency domain processing
approaches work by altering an image's Fourier transform. Equalization of
histograms is a typical approach for improving the appearance of
photographs. We need to identify a transformation T that converts grey
values r in the input image F to gr ey values s = T(r) in the converted
image.
Figure 2 shows the original image, histogram, and equalized versions.
Image smoothing can be done in a variety of ways. We'll look at edge -
preserving smoothing. The average pixel value is obtained from the
averag e pixel value in a neighborhood of (x,y) in the input image. Other
mask shapes can cause strange things to happen to the image's frequency
spectrum.
2.5 LIST OF REFERENCES
1. https://www.mv.helsinki.fi/home/khoramsh/4Image%20Enhancemen
t%20in%20Spatial%20Domain.pdf
2. https://homepages.inf.ed.ac.uk/rbf/CVonline/L OCAL_COPIES/OWE
NS/LECT5/node3.html
3. https://www.sciencedirect.com/topics/engineering/spatial -domain
4. http://www.faadooengineers.com/online -study/post/cse/digital -imge -
processing/674/spatial -domain -methods
5. https://www.google.com/search?q=point+processing+in+image+p
rocessing&rlz=1C1CHZN_enIN974IN974&oq=POINT+PROCE
SSING&aqs=chrome.1.0i512l10.1767j0j15&sourceid=chrome&ie
=UTF -8
6. https://www.cs.uregina.ca/Links/class -info/425/Lab3/ munotes.in

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62 7. https://www.javatpoint.com/dip -
histograms#:~:text=In%20digital%20image%20processing%2C%20h
istograms,the%20details%20of%20its%20histogram .
8. http://www.faadooengineers.com/online -study/post/ece/digital -
image -processing/1123/image -subtraction -and-image -averaging
2.6 BIBLIOGRAPHY
1. https://www.mv.helsinki.fi/home/khoramsh/4Image%20Enhancement
%20in%20Spatial%20Domain.pdf
2. https://homepages.inf.ed.ac.u k/rbf/CVonline/LOCAL_COPIES/OWE
NS/LECT5/node3.html
3. https://www.sciencedirect.com/topics/engineering/spatial -domain
4. http://www.faadooengineers.com/online -study/post/cse/digital -imge -
processing/674/spatial -domain -methods
5. https://www.google.com/search?q=point+processing+in+image+pr
ocessing&rlz=1C1CHZN_enIN974IN974&oq=POINT+PROCESS
ING&aqs=chrome.1.0i512l10.1767j0j15&sourceid=c hrome&ie=U
TF-8
6. https://www.cs.uregina.ca/Links/class -info/425/Lab3/
7. https://www.javatpoint.com/dip -
histograms#:~:text=In%20digital%20image%20processing%2C%20hi
stograms,the%20details%20of%20its%20histogram .
8. http://www.faadooengineers.com/online -study/post/ece/digital -
image -processing/1123/image -subtraction -and-image -averaging
2.7 UNIT END EXERCISES
1. What is the goal of spatial domain image enh ancement?
2. What are the different types of filters used in the spatial domain?
3. What Did You Mean When You Said "Digital Image Shrinking"?
4. What are intensity transformations and how do they work?
5. Which of the following processes broadens the rang e of intensity
levels?
6. In digital image processing, what is histogram processing?
7. What exactly is the point of image subtraction?
8. How does applying an average filter to a digital image affect it?
9. What are the most common applications for smooth ing filters?
10. Why is frequency domain preferable to time domain?

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63 3
IMAGE AVERAGING SPATIAL
FILTERING
Unit Structure
3.0 Objectives
3.1 Introduction
3.2 An Overview
3.3 Image Averaging Spatial Filtering
3.3.1 Smoothing Filters
3.3.2 Sharpening Filters
3.4 Frequency Domain Methods
3.4.1 Low Pass Filterning
3.4.2 High Pass Filtering
3.4.3 Homomorphic Filter
3.5 Let us Sum Up
3.6 List of References
3.7 Bibliography
3.8 Unit End Exercises
3.0 OBJECTIVES
● The Spatial Filtering technique is applied to individual pixels in an
image. A mask is typically thought to be increased in size so that it has a
distinct center pixel. This mas k is positioned on the image so that the
mask's center traverses all of the image's pixels.
● Spatial filtering is frequently used to "clean up" laser output,
reducing aberrations in the beam caused by poor, unclean, or damaged
optics, or fluctuations in the laser gain medium itself.
3.1 INTRODUCTION
Spatial filtering is a method of modifying the features of an optical image
by selecting deleting certain spatial frequencies that make up an object,
such as video data received from satellites and space probes, or raster
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64 Average (or mean) filtering is a technique for smoothing photographs by
lowering the intensity fluctuation between adjacent pixels. The average
filter replaces each value with the average valu e of neighboring pixels,
including itself, as it moves through the image pixel by pixel.
Filtering is a method of altering or improving an image. The processed
value for the current pixel depends on both itself and adjacent pixels in a
spatial domain opera tion or filtering... Filters or masks will be defined.
Filtering is a method of altering or improving an image. The processed
value for the current pixel depends on both itself and adjacent pixels in a
spatial domain operation or filtering... Filters or ma sks will be defined.
3.2 AN OVERVIEW
IMAGE ENHANCEMENT OVERVIEW

By working with noisy photos we can filter signals from noise in two
dimensions. Two types of noise: binary and Gaussian.
The user specifies a percentage value in the binary case (a numbe r
between 0 and 100). This value is randomly set equal to the maximum
grey level value and reflects the percentage of pixels in the image whose
values will be completely lost (corresponding to a white pixel).
The value of the pixel x(k,l) is changed in the Gaussian case by additive
white gaussian noise x(k,l)+n, with noise n~N(0,v) being normally
distributed and variance v set by the user (a number between 0 and 2 in
this exercise).
The image is the same in binary noise, except for a set of points where the
image's pixels are set to white. The noisy image seems blurred in the case
of Gaussian noise.
Original Image Image with binary noise



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65 Image with Gaussian noise

The method of removing noise or sharpening photogr aphs to increase
image quality is known as image enhancement. Even though image
enhancement is a well -established approach, we will concentrate on two
strategies based on the notion of filtering an original image to produce a
restored or better image. Both linear and nonlinear actions are possible
with our filters.
1. Median filtering
A pixel is replaced by the median of the pixels in a window around it in
median filtering. That is to say,
W is a suitable window that surrounds the pixel. The median filtering
algorithm entails sorting the pixel values in the window in ascending or
descending order and selecting the middle value. In most cases, a square
window with an odd square size is chosen.
2. Spatial averaging
Each pixel is replaced by an average of its nearby pixels in the case of
spatial averaging. That is to say,

Where W is the number of pixels in the window, and Nw is the number of
pixels in the window. Because spatial averaging causes a distortion in the
form of blurring, the size of the window W is limi ted in practice.
To introduce noise to an image and then recover it using the techniques
as described above. You'll notice that the best picture enhancement
strategy is determined by the type of noise as well as the amount and level
of noise in the image.



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66 3.3 IMAGE AVERAGING AND SPATIAL FILTERING
SPATIAL FILTERING AND ITS TYPES
The Spatial Filtering technique is applied to individual pixels in an image.
A mask is typically thought to be increased in size so that it has a distinct
centre pixel. This mas k is positioned on the image so that the mask's
centre traverses all of the image's pixels.
Using linearity as a criterion for classification:
There are two kinds of them:
1. Linear Spatial Filter
2. Non -linear Spatial Filter
Classification in General:
Smoothing Spatial Filter: A smoothing spatial filter is used to blur and
reduce noise in an image. Blurring is a pre -processing technique for
removing minor details, and it is used to achieve Noise Reduction.
Types of Smoothing Spatial Filter:
1. Linear Filt er (Mean Filter)
2. Order Statistics (Non -linear) filter
These are explained in the next paragraphs.
1. Mean Filter: A linear spatial filter is just the average of the pixels in the
filter mask's neighborhood. The goal is to replace the value of each pixe l
in a picture with the average of the grey levels in the filter mask's
neighborhood.
Types of Mean filter:
(i) Averaging filter: This filter is used to reduce image detail. The
coefficients are all the same.
(ii) Weighted averaging filter: Pixels are mult iplied by various coefficients
in this filter. The average filter is multiplied by a higher value than the
centre pixel.
1. Order Statistics Filter:
This filter is based on the ordering of pixels within the image region it
covers. It substitutes the value in dicated by the ranking result for the value
of the centre pixel. This filtering preserves the edges better.
(i) Minimum filter: The 0th percentile filter is the smallest of the order
statistics filters. The smallest value in the window replaces the value in the
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67 (ii) Maximum filter : The maximum filter is the 100th percentile filter.
The largest value in the window replaces the value in the center.
(ii) Median filter : Every pixel in the image is taken into account. The
original values of the pixel ar e replaced by the median of the list after
surrounding pixels are sorted first.
Sharpening Spatial Filter :
(also known as a derivative filter) is a type of spatial filter that sharpens
the image. The sharpening spatial filter serves the exact opposite ob jective
as the smoothing spatial filter. Its primary goal is to eliminate blurring and
highlight the edges. The first and second -order derivatives are used.
First order derivative:
● Must be zero in flat segments.
● Must be non zero at the onset of a grey leve l step.
● Must be non zero along ramps.
First order derivative in 1 -D is given by:
f' = f(x+1) - f(x)
Second order derivative:
● Must be zero in flat areas.
● Must be zero at the onset and end of a ramp.
● Must be zero along ramps.
Second order derivative in 1 -D is given by:
f'' = f(x+1) + f(x -1) - 2f(x)
3.3.1 SMOOTHING FILTERS
SMOOTHING FILTERS
To reduce the amount of noise in an image, image smoothing filters such
as the Gaussian, Maximum, Mean, Median, Minimum, Non -Local Means,
Percentile, and Rank filters can b e used. Although these filters can
efficiently reduce noise, they must be applied with caution so that crucial
information in the image is not altered. It's also worth noting that, in most
circumstances, edge detection or augmentation should come after
smoothing.
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● MEAN
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68 ● MEDIAN
● NON-LOCAL MEANS
● GAUSSIAN
When you ap ply the Gaussian filter to an image, it blurs it and removes
information and noise. It's comparable to the Mean filter in this regard. It
does, however, use a kernel that represents a Gaussian or bell -shaped
hump. Unlike the Mean filter, which produces an evenly weighted
average, the Gaussian filter produces a weighted average of each pixel's
neighborhood, with the average weighted more towards the center pixels'
value. As a result, the Gaussian filter smoothes the image more gently and
maintains the edges better than a Mean filter of comparable size.
The frequency response of the Gaussian filter is one of the main
justifications for adopting it for smoothing. Lowpass frequency filters are
used by the majority of convolution -based smoothing filters. As a res ult,
they have the effect of removing high spatial frequency components from
an image. You can be quite certain about what range of spatial frequencies
will be present in the image after filtering by selecting an adequately big
Gaussian, which is not the c ase with the Mean filter. Computational
biologists are also interested in the Gaussian filter since it has been
associated with some biological plausibility. For example, some cells in
the brain's visual circuits often respond in a Gaussian fashion.
Becaus e many edge -detection filters are susceptible to noise, Gaussian
smoothing is typically utilised before edge detection.
MEAN
Mean filtering is a straightforward technique for smoothing and reducing
noise in photographs by remo ving pixel values that aren't indicative of
their surroundings. Mean filtering is a technique that replaces each pixel
value in an image with the mean or average of its neighbors, including
itself.
The Mean filter, like other convolution filters, is based on a kernel, which
describes the shape and size of the sampled neighborhood for calculating
the mean. The most common kernel size is 3x3, but larger kernels might
be utilized for more severe smoothing. It's worth noting that a small kernel
can be applied m ultiple times to achieve a similar, but not identical, result
to a single pass with a large kernel.
Although noise is reduced after mean filtering, the image has been
softened or blurred, and high -frequency detail has been lost. This is
mainly caused by th e filter's limits, which are as follows:
• A single pixel with a very atypical value can have a considerable impact
on the mean value of all the pixels in its vicinity.
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69 The filter will interpolate new values for pixels on the edge when the filter
neighbor hood straddles an edge. If crisp edges are required in the output,
this could be a problem.
The Median filter, which is more commonly employed for noise reduction
than the Mean filter, can solve both of these concerns. Smoothing is often
done with other co nvolution filters that do not calculate the mean of a
neighborhood. The Gaussian filter is one of the most popular.
MEAN SHIFT
Mean shift filtering is based on a data clustering algorithm extensively
used in image processing a nd can be utilized for edge -preserving
smoothing. The collection of surrounding pixels is determined for each
pixel in an image with a spatial location and a specific grayscale value.
The new spatial center (spatial mean) and the new mean value are
calcula ted for this set of adjacent pixels. The new center for the following
iteration is determined by the calculated mean values. Iterate the specified
technique until the spatial and grayscale mean cease changing. The final
mean value will be set to the iterat ion's beginning point at the end of the
iteration.
MEDIAN
The Median filter is typically used to minimise image noise, and it can
often preserve image clarity and edges better than the Mean filter. This
filter, like the Mean f ilter, examines each pixel in the image individually
and compares it to its neighbours to determine whether it is typical of its
surroundings. Instead of merely replacing the pixel value with the mean of
nearby pixel values, the median of those values is u sed instead. Median
filters are especially good for reducing random intensity spikes that
commonly appear in microscope images.
This filter's operation is depicted in the diagram below. The median is
derived by numerically ordering all of the pixel values in the surrounding
neighborhood, in this case, a 3x3 square, and then replacing the pixel in
question with the middle pixel value.
Median filter
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70 The center pixel value of 150, as seen in the picture, is not typical of the
surrounding pixels and is substi tuted with the median value of 124. It's
worth noting that larger neighborhoods will result in more severe
smoothing.
The Median filter has two key advantages over the Mean filter since it
calculates the median value of a neighborhood rather than the mean: • The
median is more robust than the mean, thus a single very unrepresentative
pixel in a neighborhood will not have a substantial impact on the median
value. For example, in datasets contaminated with salt -and-pepper noise
(scatter dots).
● Since the media n value must be the value of one of the pixels in the
neighborhood, the Median filter does not create unrealistic pixel values
when the filter straddles an edge. For this reason, it is much better at
preserving sharp edges than the Mean filter.
● However, th e Median filter is sometimes not as subjectively good at
dealing with large amounts of Gaussian noise as the Mean filter. It is
also relatively complex to compute.
NON-LOCAL MEANS
Unlike the Mean filter, which smooths a pictur e by taking the mean of a
set of pixels surrounding a target pixel, the Non -Local Means filter takes
the mean of all pixels in the image, weighted by their similarity to the
target pixel. When compared to mean filtering, this filter can result in
improved post-filtering clarity with minimum information loss. When
smoothing noisy images, the Non -Local Means or Bilateral filter should
be your first choice in many circumstances.
It's worth noting that non -local means filtering works best when the noise
in the data is white noise, in which case most visual characteristics,
including small and thin ones, will be maintained.
3.3.2 SHARPENING FILTERS
Image preprocessing has long been a feature of computer vision, and it can
considerably improve the performance of machine learning models. Image
processing is the process of applying several sorts of filters to our image.
Filters can assist minimize image noise while also enhancing the image's
qualities.
Sharpening filters are discussed as below.
• When compared to sm ooth and blurry images, sharpening filters make
the transition between features more recognizable and evident.
• What occurs when a sharpening filter is applied to an image?
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71 When compared to their neighbors, the brighter pixels are rendered
brighter (boos ted).
Sharpening or blurring an image can be reduced to a series of matrix
arithmetic operations.
When we apply a filter to our image, we're doing a convolution operation
on it with a Xen kernel. A kernel is a square matrix with nxn dimensions.
CONVOLUTION AND KERNEL
Each image can be represented as a matrix, with its features represented as
numerical values, and we use convolution with various types of matrices
known as kernels to extract or enhance distinct features.
The act of adding each element of the image to its nearby neighbors,
weighted by the kernel, is known as convolution. This has something to do
with a type of mathematical convolution. Despite being marked by "*,"
the matrix operation being performed —convolution —is not ordinary
matrix multiplic ation.

The kernel is what determines the type of operation we're doing, such as
sharpening, blurring, edge detection, gaussian blurring, and so on.
The following is an example of a sharpening kernel:

SHARPENING
• Sharpening is a technique for enhancing the transition between features
and details by sharpening and highlighting the edges. Sharpening, on the
other hand, does not consider whether it is enhancing the image's original
features or the noise associated with it. It improves both.
Blurring vs Sha rpening
● Blurring: Blurring/smoothing is accomplished in the spatial domain by
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72
● Sharpening: Sharpening is a technique for identifying and emphasizing
diffe rences in the neighborhood. It is a differentiation process.
Sharpening Filters of Various Types
1) High Boost Filtering and Unsharp Masking
Using a smoothing filter, we can sharpen an image or perform edge
improvement.
1. Make the image blurry. Blurring i s the process of suppressing the
majority of high -frequency components.
2. Original Image - Blurred Image (Output (Mask)). Most of the high -
frequency components that were previously blocked by the blurring
filter are now present in this output.
3. By apply ing the mask to the original image, the high -frequency
components will be enhanced.
This procedure is called UNSHARP MASKING since we are using a
blurred image to create our personalized mask.
As a result, Unsharp Mask m(x, y) can be written as:

● f(x,y) = original image.
● fb(x,y) = blurred image.
When you apply this mask to the original image, the high frequency
components are enhanced.

The value k determines how much weight should be given to the mask that
is being added.
1. Unsharp Masking is represente d by k = 1.
2. High Boost Filtering is represented by k > 1 since we are boosting high -
frequency components by adding higher weights to the image's mask
(edge features).
This approach, like most other sharpening filters, will not yield adequate
results if the image contains noise.
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73 2) Laplacian Filters
A second -order derivative mask is a Laplacian Filter. It attempts to
eliminate the INWARD and O UTWARD edges. This difference in
second -order derivatives aids in determining whether the changes we're
seeing are caused by pixel changes in continuous regions or by an edge.
Positive values are found at the center of a general Laplacian kernel, while
negative values are found in a cross pattern.

To proceed with the derivation of this kernel matrix, knowledge of partial
derivatives and Laplacian operators is required.
Let us consider our image as function of two variables, f(x, y) .
We will be dealing wit h partial derivatices along the two spatial axes.

Discrete form of Laplacian





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74 Resultant resultant Laplacian Matrix

Laplacian Operators' Effects
• It emphasizes and intensifies grey discontinuities while deemphasizing
continuous regions (regions w ithout edges), i.e. derivatives that vary
slowly.
We'll utilize some approximate Laplacian Filters for our programming.
Let us perform sharpening using different methods
Using OpenCV as a tool
OpenCV is a python -based library for dealing with computer visi on issues.
Let's have a look at the code below and figure out what's going on.
● We'll start by importing the libraries we'll need to sharpen our image.
● Numpy -> For conducting quick matrix operations OpenCV -> For
image operations
● cv2.imread -> cv2.imread -> cv2.imread -> To read the input image
from our disc in the form of a numpy array.
● cv2.scale -> To resize our image to fit in the dimensions of (400, 400).
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75 • kernel -> kernel is a 3X3 matrix that we define based on how we want to
slide the picture acros s for convolution.
• cv2.filter2D -> cv2.filter2D -> cv2.filter2D To convolve a kernel with an
image, Opencv includes a function called filter2D.
It accepts three parameters as input:
1. img -> picture input
2. ddepth -> the depth of the output image
3. ke rnel-> kernel of convolution

This is how we can use OpenCV to conduct sharpening.
Changing the magnitudes of the kernel matrix allows us to experiment
with the kernel to obtain different levels of sharpened images.
Original Image

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76 • ImageFilter has a n umber of pre -defined filters, such as sharpen
and blur, that may be used with the filter() method.
• We sharpen our image twice and save the results in the sharp1
and sharp2 variables.
Image after 1st sharp operation

Image after 2nd sharp operation

Sharpening effects can be seen, with the features becoming brighter and
more distinguishable.

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77 3.4 FREQUENCY DOMAIN METHOD
Frequency domain methods
In the frequency domain, image enhancement is simple. To create the
enhanced image, we simply compute the Four ier transform of the image to
be enhanced, multiply the result by a filter (rather than convolve in the
spatial domain), and then take the inverse transform.
The concept of blurring an image by lowering the magnitude of its high -
frequency components or sha rpening an image by increasing the
amplitude of its high -frequency components is intuitively simple. However,
implementing similar actions as convolutions by modest spatial filters in
the spatial domain is typically more computationally efficient.
Understa nding frequency domain principles is crucial since it leads to
enhancement approaches that would otherwise go unnoticed if attention
was focused solely on the spatial domain.
Filtering
Low pass filtering is the process of removing high -frequency components
from an image. The image is blurred as a result of this (and thus a
reduction in sharp transitions associated with noise). All low -frequency
components would be retained while all high -frequency components
would be eliminated in an ideal low pass filter. Ideal filters, on the other
hand, have two flaws: blurring and ringing. The shape of the related
spatial domain filter, which includes a huge number of undulations, is the
source of these issues. Smoother frequency -domain filter transitions, such
as the Bu tterworth filter, produce substantially superior outcomes.
Figure 5: An ideal low pass filter's transfer function.

3.4.1 LOW PASS FILTERING
The high -frequency content of an image's Fourier transform is heavily
influenced by edges and sudden changes i n gray values. • In an image,
regions of relatively uniform gray values contribute to the Fourier
transform's low -frequency content. • As a result, a picture can be
smoothed in the Frequency domain by lowering the Fourier transform's
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78 simplicity, we'll just discuss real and radially symmetric filters. • A perfect
lowpass filter with r0 as the cutoff frequency


Ideal LPF with r0 = 57
The origin (0, 0) is in the image's center, not i ts corner (remember the
"fftshift" operation).
• Using electrical components, the sudden shift from 1 to 0 of the transfer
function H (u,v) is impossible to achieve in practice. It can, however, be
simulated on a computer.
Ideal LPF examples
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79

The blurre d images have a pronounced ringing effect, which is a hallmark
of perfect filters. The discontinuity in the filter transfer function is to
blame.
In an ideal LPF, the cutoff frequency is chosen.
• The number of frequency components passed by the filter is determined
by the ideal LPF's cutoff frequency 0 r.
• The smaller the 0 r value, the more image components are removed by
the filter.
• In general, the value of 0 r is selected so that the majority of the
components of interest pass through while the major ity of the non -
interesting components are deleted. This is usually a set of contradictory
needs. We'll look at some of the specifics of image restoration.
• Computing circles that contain a given fraction of the total picture power
is a good technique to e stablish a set of standard cut -off frequencies.
• Suppose − = − = = 1 0 1 0 ( , ) N v M u TP P u v , where 2 P(u,v) =
F(u,v) , is the total image power.
• Consider a circle of radius () r0 α as a cutoff frequency in relation to a
threshold, such that T v u ∑∑P(u,v) = αP
• After that, we can set a threshold and c alculate an acceptable cutoff
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80

• A two -dimensional Butterworth lowpass filter has the following transfer
function:
• r0: cutoff frequency, n: filter order
• Because the frequency response does not have a fast transition like the
ideal L PF, it is better for image smoothing because it does not introduce
ringing. n r u v H u v 2 0
Butterworth LPF example

Original Image LPF image, r0 =18
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81 Butterworth LPF example: False contouring

Image with false contouring due to insufficient Lowpass filtered
version of previous image
bits used for quantization
Butterworth LPF example: Noise filtering
Butterworth LPF example: Noise filtering
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82

Low-pass Gaussian filters
• In two dimensions, the form of a Gaussian lowpass filter is 2 2 ( , ) / 2
( , ) − σ = D u v H u v e , where 2 2 D(u,v) = u + v is the frequency plane
distance from the origin.
• The parameter σ represents the Gaussian curve's spread or dispersi on.
The greater the value of σ , the higher the cutoff frequency and the less
severe the filtering.
• The filter is reduced to 0.607 of its maximum value of 1 when D(u,v) =σ
3.4.2 HIGH PASS FILTERING
HIGHPASS FILTERING
• The high -frequency content of a F ourier transform is heavily influenced
by edges and sudden transitions in gray values in a picture.
• Low -frequency content of a Fourier transform is influenced by regions of
relatively uniform gray values in an image.
• As a result, image sharpening in th e Frequency domain can be
accomplished by lowering the Fourier transform's low -frequency
content. A highpass filter would be this.
• Only real and radially symmetric filters will be considered for the sake of
simplicity.
• With a cutoff frequency of 0 r, a n ideal highpass filter is:
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83

Ideal HPF with r0 = 36
The origin (0, 0) is in the image's centre, not its corner (remember the
"fftshift" operation).
• Using electrical components, the sudden shift from 1 to 0 of the transfer
function H (u,v) is impossibl e to achieve in practise. It can, however, be
simulated on a computer.
Ideal HPF examples
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84

• Note how the output images have a strong ringing effect, which is a
hallmark of ideal filters. The discontinuity in the filter transfer function
is to blame.
• A two -dimensional Butterworth highpass filter has the following transfer
function:

• n: filter order, r0: cutoff frequency


• Because the frequency response does not have a sharp transition like the
ideal HPF, it is better for image sharpening because it does not introduce
ringing.


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85 Butterworth HPF example


High -pass Gaussian filters
• In two dimensions, the form of a Gaussian lowpass filter is 2 2 (,) / 2 (,)
1 − σ = -D u v H u v e, where 2 2 D(u,v) = u + v is the distance from the
origin in the frequency plane.
The greater the value of, the higher the cutoff frequency and the harsher
the filtering
3.4.3 HOMOMORPHIC FILTER
HOMOMORPHIC FILTERING
Light reflected f rom objects is used to create images. The image F(x,y) has
two basic characteristics: (1) the amount of source light incident on the
scene being viewed, and (2) the amount of light reflected by the objects in
the scene. The illumination and reflectance com ponents of light are
indicated by the letters i(x,y) and r(x,y), respectively. The image function
F is created by multiplying the functions i and r:
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86 where
and 0 < r(x,y) < 1. We cannot easily use the
above product to operate separa tely on the frequency components of
illumination and reflection because the Fourier transform of the product of
two functions is not separable; that is

Let's say, on the other hand, that we define

Then

or

The Fourier transforms of
and are Z, I, and R, respectively. The
Fourier transform of the sum of two images: a low frequency illumination
image and a high frequency reflectance image is represented by the
function Z.
Figure 6: Transfer function for homomorphic filtering.

We may now suppre ss the light component while enhancing the
reflectance component by using a filter with a transfer function that
suppresses low frequency components while enhancing high frequency
components. Thus
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87 Where S is the result's Fourier transform. In the realm o f space,

By letting

and

We get
s(x,y) = i'(x,y) + r'(x,y).
Finally, because z was calculated by taking the logarithm of the original
image F, the inverse produces the desired augmented image:

As a result, the following figure can be used to summari se the
homomorphic filtering process:
Figure 7: The process of homomorphic filtering.

3.5 LET US SUM UP
The Spatial Filtering technique is applied to individual pixels in an image.
A mask is typically thought to be increased in size so that it has a d istinct
center pixel. Average (or mean) filtering is a technique for smoothing
photographs by lowering intensity fluctuation between adjacent pixels.
The best picture enhancement strategy is determined by the type of noise
as well as the amount and level o f noise in an image. Both linear and
nonlinear actions are possible with our filters.
We will concentrate on two strategies based on the notion of filtering an
original image. The averaging filter is used to reduce image detail. This
filtering preserves th e edges better. A sharpening spatial filter serves the
exact opposite objective as the smoothing spatial filter. Its primary goal is
to eliminate blurring and highlight the edges. The first and second -order
derivatives are used.
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88 3.6 LIST OF REFERENCES
1. https://www.geeksforgeeks.org/spatial -filtering -and-its-types/
2. http://www.seas.ucla.edu/dsplab/ie/over.html
3. https://www.geeksforgeeks.org/spatial -filtering -and-its-types/
4. https://www.theobjects.com/dragonfly/dfhelp/3 -
5/Content/05_Image%20Processing/Smoothing%20Filters.htm#:~:te
xt=Mean%20filtering%20is%20a%20simple,of%20its%20neighbor s
%2C%20including%20itself .
5. http://saravananthirumuruganathan.wordpress.com/2010/04/01/introd
uction -tomean -shift-algorithm/
6. https://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/O
WENS/LECT5/node4.html#:~: text=Image%20enhancement%20
in%20the%20frequency,to%20produce%20the%20enhanced%2
0image .
7. file:///E:/MY%20IMP%20documents/Lecture_9.pdf
8. file:///E:/MY%20IMP%20documents/Lecture_9.pdf
3.7 BIBLIOGRAPHY
1. https://www.geeksforgeeks.org/spatial -filtering -and-its-types/
2. http://www.seas.ucla.edu/dsplab/ie/over.html
3. https://www.geeksforgeeks.org/spatial -filtering -and-its-types/
4. https://www.theobjects.com/dragonfly/dfhelp/3 -
5/Content/05_Image%20Processing/Smoothing%20Filters.htm#:~:te
xt=Mean%20filtering%20is%20a%20simple,of%20its%20ne ighbors
%2C%20including%20itself .
5. http://saravananthirumuruganathan.wordpress.com/2010/04/01/introd
uction -tomean -shift-algorithm/
6. https://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/
OWENS/LECT5/node4.ht ml#:~:text=Image%20enhancement%
20in%20the%20frequency,to%20produce%20the%20enhanced
%20image .
7. file:///E:/MY%20IMP%20documents/Lecture_9.pdf
8. file:///E:/MY%20IMP%20documents/Lecture_9.pdf
9. https://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/OWE
NS/LEC T5/node4.html#:~:text=Image%20enhancement%20in%20th
e%20frequency,to%20produce%20the%20enhanced%20image . munotes.in

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89 3.8 UNIT END EXERCISES
Q1. Why does the averaging filter cause the image to blur?
Q2. How does applying an average filter to a digital image affect it?
Q3. What does it mean to sharpen spatial filters?
Q4. What is the primary purpose of image sharpening?
Q5. What is the best way to sharpen an image?
Q6. How do you figure out what a low -pass filter's cutoff frequency is?
Q7. What is the purpose of a low -pass filter?
Q8. What is the effect of high pass filtering on an image?
Q9. In homomorphic filtering, which filter is used?
Q10. In homomorphic filtering, which high -pass filter is used?




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90 Module III
4
DISCRETE FOURIER TRANSFORM -I
Unit Structure
4.1 Objectives
4.2 Introduction
4.3 Properties of DFT
4.4 FFT algorithms ñ direct, divide and conquer approach
4.4.1 Direct Computation of the DFT
4.4.2 Divide -and-Conquer Approach to Computation o f the DFT
4.5 2D Discrete Fourier Transform (DFT) and Fast Fourier Transform
(FFT)
4.5.1 2D Discrete Fourier Transform (DFT)
4.5.2 Computational speed of FFT
4.5.3 Practical considerations
4.6 Summary
4.7 References
4.8 Unit End Exercises
4.1 OBJECTI VES
After going through this unit, you will be able to:
● Understood the fundamental concepts of Digital Image processing
● Able to discuss mathematical transforms.
● Describe the DCT and DFT techniques
● Classify different types of image transforms
● Examine the use of Fourier transforms for image processing in the
frequency domain

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91 4.2 INTRODUCTION
In the realm of image processing, the Fourier transform is commonly
employed. An image is a function that varies in space. Decomposing an
image into a series of orth ogonal functions, one of which being the Fourier
functions, is one technique to analyse spatial fluctuations. An intensity
image is transformed into the spatial frequency domain using the Fourier
transform.
The sampling process converts a continuous -time s ignal x(t) into a
discrete -time signal x(nT), where T is the sample interval.
x(t) sampling to x(nT)
The Fourier transform of a finite energy discrete time signal x(nT) is given
by [1]


where X(ejω ) is a continuous function of ω and is known as Discrete -Time
Fourier Transform (DTFT).
The relationship between ω and Ω is defined by
ω = ΩT
Replacing Ω by 2πf
ω =2πf ×T
where T is the sampling interval and is equal to 1/fs. Replacing T by 1/fs
ω = 2π f × 1/fs
where fs is the sampling frequency

ω = k × 2π
To limit the infinite number of values to a finite number, Eq. is modified
as

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92 The Discrete Fourier Transform (DFT) of a finite duration sequence x(n)
is defined as

where k = 0, 1......, N – 1
The discrete -frequency representation (DFT) transfers a discrete signal
onto a complex sinusoidal basis.
4.3 PROPERTIES OF DFT
We checked the periodicity of the combination by applying the DFT on a
combination of two periodic sequences x1(n), x2(n). Becaus e DFT is
defined over a single period, the DFT of combination must have a single
periodicity to be well described. In the continuous example, there are three
types of combinations: linear ax1+bx2, convolution of x1 & x2, and
multiplication x1 x2. For the c ontinuous case, x1(n) is combined with x2
to define both linear combination and multiplication (n). Similarly, each
x1(i) in the discrete case should be coupled with x2 (i). As a result, x1(n)
and x2(n) have the same periodicity N, and the resultant series has the
same periodicity N. If two sequences have distinct periodicities N1 and
N2, padding transforms the periodicity N1 sequence into periodicity N2
by adding zeros at the end of N1.
i) Linearity Property :
Let X1(k) = DFT of x1(n) & X2(k) = DFT of x2(n)
∴ DFT {a x1(n) + b x2(n) } = a X1(k) + b X2(k) where a,b are
constants.
ii) Periodicity :
If a sequence x(n) periodic with periodicity N then N point DFT, X(k) is
also periodic with periodicity N .
Let x(n+N ) = x(n) ∀ .
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93 iii) Circular Time shift :
It states that if discrete time signal is circularly shifted in time by m units
then it’s DFT is multiplied by

If DFT x(n) = X(k) Then DFT


iv) Circular Frequency shift :
If discrete time signal multiplied by

then DFT is circularly shifted by m units.
If DFT x(n) = X(k) Then DFT

v) Multiplication :
DFT of product of two discrete time sequence equivalent to circular
convolution of DFT of individual sequences scaled by factor 1/ .
If DFT x(n) = X (k), Then DFT {x1(n) x2 (n)}= 1 / {1() ⊛ 2()}
4.4 FFT ALGORITHMS Ñ DIRECT, DIVIDE AND
CONQUER APPROACH [2]
DFT calculation is made more efficient using FFT algorithms. The
method, which employs a divide -and-conquer strategy, reduces a DFT o f
size N, where N is a composite number, to the computation of smaller
DFTs from which the bigger DFT is computed. We describe essential
computational strategies, known as fast Fourier transform (FFT)
algorithms, for computing the DFT when the size N is a power of two or
power of four.
According to the formula, the computing challenge for the DFT is to
compute the sequence {X(k)} of N complex -valued integers given another
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94

where
Similarly, IDFT given as,

We see that di rect computation of X(k) requires N complex
multiplications (4N real multiplications) and N —1 complex adds (4N —
2 real additions) for each value of k. As a result, computing all N DFT
values necessitates N2 complex multiplications and N — N complex
addit ions.
Direct DFT computation is inefficient primarily because it does not take
advantage of the phase factor IN's symmetry and periodicity features.
These two properties in particular are:
Property of symmetry:

Property of periodicity:


These two essential features of the phase factor are used by the
computationally efficient algorithms presented in this section, commonly
known as fast Fourier transform (FFT) algorithms.
4.4.1 Direct Computation of the DFT
For a complex -valued sequence x (n) of N points, the DFT may be
expressed as


The direct computation of above equations requires:
● 2N2 evaluations of trigonometric functions.
● 4N2 real multiplications.
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95 ● 4N(N -1) real additions.
● A number of indexing and addressing operations.
These are com mon operations in DFT computational techniques. The DFT
values X R(k) and X I(k) are obtained by the procedures in items 2 and 3. To
retrieve the data x(n), 0 to N - 1, and the phase factors, as well as to store
the results, indexing and addressing procedure s are required. Each of these
computing operations is optimized differently by the various DFT
methods.
4.4.2 Divide -and-Conquer Approach to Computation of the DFT
If we take a divide -and-conquer method, we can design computationally
efficient DFT algorit hms. This method is based on decomposing an N -
point DFT into smaller and smaller DFTs. The FFT algorithms are a class
of computationally efficient algorithms based on this basic principle.
To illustrate the computation of an N -point DFT, where N can be fa ctored
as a product of two integers, that is,
N =LM
Because we can pad any sequence with zeros to secure a factorization of
the form above equation, the condition that N is not a prime integer is not
limiting.
As shown in Fig. 1, the sequence x(n), 0< n< N —1, can be stored in a
one-dimensional array indexed by nor a two -dimensional array indexed by
1 and m, where 0 The row index is /, but the column index is m.
As a result, the sequence x(n) can be saved in a recta ngular format.
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96

Fig. 1 Two dimensional data array for storing the sequence x(n) 0 < n
< N-1
array in a variety of ways, each of which depends on the mapping of index
n to the " indexes (l, m). For example, suppose that we select the mapping
n = Ml + m
This leads to an arrangement in which the first row consists of the first M
elements of x(n), the second row consists of the next M elements of x(n),
and so on, as illustrated in Fig. 2(a). On the other hand, the mapping
n = 1 + mL
stores the first L elem ents of x(n) in the first column, the next L elements
in the second column, and so on, as illustrated in Fig.2(b).
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97

Fig. 2 Two arrangements for the data arrays
The computed DFT values can be stored in a similar manner.
The mapping is specifically from the index k to a pair of indices (p, q),
with 0

The DFT is stored on a row -by-row basis if the mapping
K = Mp+q
is chosen, with the first row containing the first M elements of the DFT
X(k), the second row containing the foll owing set of M elements, and so
on.
The mapping
k = qL+ p,
leads in column -wise X(k) storage, with the first L elements stored in the
first column, the second set of L elements in the second column, and so
on.
Assume that x(n) is mapped to the rectangula r array x(l, m) and that X(k)
is mapped to a comparable rectangular array X(p, q).
The DFT can therefore be written as a double sum over the rectangle
array's elements multiplied by the phase factors. Then,
,

But

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98

The expression involves the c omputation of DFTs of length M and length
L. To elaborate, let us subdivide the computation into three steps:
i) we compute the M -point DFTs

for each of the rows l = 0, 1, ... , L — 1.
ii) we compute a new rectangular array G(l, q) defined as

iii) Finally, we compute the L -point DFTs

for each column q = 0, 1, ... ,M - 1, of the array G(1, q).
On the surface, the computing process given above appears to be more
complicated than the direct DFT computation. The first phase entails
computing L DFTs with M points each. As a result, LM complex
multiplications and LM(M - 1) complex additions are required in this
phase. The second phase necessitates the application of LM complex
multiplications. Finally, MLV complex multiplications and ML(L - 1)
complex additions are required in the third step of the algorithm. As a
result, the computational difficulty is
Complex multiplications: N(M + L + 1)
Complex additions: N(M + L - 2)
where N = ML.
As a result, the number of multiplications has decreased from N2 to N(M +
L + 1), while the number of additions has decreased from N(N - 1) to N(M
+ L - 2).
To summarize, the algorithm that we have introduced involves the
following computations:
Algorithm 1
1. Store the signal column -wise.
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99 3. Multiply the resulting array by the phase factors

4. Compute the L -point DFT of each column
5. Read the resulting array row -wise.
An additional algorithm with a similar computational structure can be
obtained if the input signal is stored row -wise and the resulting
transformation is column -wise. This case we select,
n = Ml + m
k = qL + p
This choice of indices leads to the formula for the DFT in the form,

Thus we obtain a second algorithm.
Algorithm 2
1. Store the signal row -wise.
2. Compute the L -point DFT at each co lumn.
3. Multiply the resulting array by the factors

4. Compute the M -point DFT of each row.
5. Read the resulting array column -wise.
4.5 2D DISCRETE FOURIER TRANSFORM (DFT) AND
FAST FOURIER TRANSFORM (FFT)[1]:
3.1.5.1 2D Discrete Fourier Transform (DFT) :
The 2D-DFT of a rectangular image f(m, n) of size M × N is represented
as F(k, l)
f (m, n) ----2D DFT →F(k, l)
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100


For a square image f (m, n) of size N × N, the 2D DFT is defined as

The inverse 2D Discrete Fourier Transform is given by

The Fourier transform F (k, l) is given by
F(k,l) = R(k,l) + jI(k,l)
where R(k, l ) repre sents the real part of the spectrum and I(k, l) represents
the imaginary part.
The Fourier transform F (k, l ) can be expressed in polar coordinates as
F( k,l)= mod ( F(k,l)) ejkl
where mod (F(k, l)) = (R2{F(k, l)}+ I2{F(k, l)})1/2 is called the magnitud e
spectrum of the Fourier transform and


is the phase angle or phase spectrum. Here, R{F(k, l)}, I{F(k, l)} are the
real and imaginary parts of F(k, l) respectively.
The Fast Fourier Transform is the most computationally efficient type of
DFT (FFT).
The FFT of an image can be represented in one of two ways: (a)
conventional representation or (b) optical representation.
High frequencies are collected at the centre of the image in the standard
form, whereas low frequencies are distributed at the edges, as seen in Fig.
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101

Fig. 1 – Standard representation of FFT of an image [1,3]
The frequency range is [0, N] X [0, M], where M is the image's horizontal
resolution and N is the image's ver tical resolution.
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102

Fig. 2 optical representation of the FFT of the same image.
Discreteness in one domain leads to periodicity in another as in Fig. 2, as
we all know. As a result, the spectrum of a digital image will be unique in
the range – π to π or between 0 and 2π.
4.5.2 Computational speed of FFT [4]:
The DFT requires N2 comple x multiplications. At each stage of the FFT
(i.e. each halving) N/2 complex multiplications are required to combine
the results of the previous stage. Since there are (log 2N) stages, the
number of complex multiplications required to evaluate an -point DFT
with the FFT is approximately N/2 log 2N.

4.5.3 Practical considerations [4] :
If N is not a power of 2, there are 2 strategies available to complete N -
point FFT.
1. take advantage of such factors as N possesses. For example, if N is
divisible by 3‰ (e.g. N=48), the final decimation stage would include a
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103 2. pack the data with zeroes; e.g. include 16 zeroes with the 48 data
points (for N=48) and compute a 64 -point FFT. (However, you should
again be wary of abrupt transitions between the tra iling (or leading) edge
of the data and the following (or preceding) zeroes; a better approach
might be to pack the data with more realistic “dummy values”). Zero
padd ing cannot improve the resolution of spectral components, because
the resolution is “proportional” to 1/M rather than 1/N. Zero padding is
very important for fast DFT implementation (FFT).
4.6 SUMMARY :
Frequency smoothing and frequency leaking are example s of DFT
applications on finite pictures with MxN pixels. DFT is based on
discretely sampled pictures (pixels), which suffer from aliasing. DFT takes
into account periodic boundary conditions including centering, edge
effects, and convolution. Images have borders and are truncated (finite),
resulting in frequency smoothing and leakage. All drawbacks of DFT
overcomes by FFT.
4.7 REFERENCES
1] S. Jayaraman Digital Image Processing TMH (McGraw Hill)
publication, ISBN - 13:978 -0-07- 0144798
2] John G. Proakis, Digital Signal Processing: Principles, Algorithms,
And Applications, 4/E
3] Gonzalez, Woods & Steven, Digital Image Processing using MATLAB,
Pearson Education, ISBN -13:978 -0130085191
4] https://www.robots.ox.ac.uk/~sjrob/Teaching/SP/l7.pdf
4.8 UNIT END EXE RCISES
1. Find the N × N point DFT of the following 2D image f(m, n), 0 ≤ m, n
≤ N
2. Prove that DFT diagonlises the circulant matrix.
3. Which of the following is true regarding the number of computations
required to compute an N -point DFT?
a) N2 complex multiplications and N(N -1) complex additions
b) N2 complex additions and N(N -1) complex multiplications
c) N2 complex multiplications and N(N+1) complex additions
d) N2 complex additions and N(N+1) complex multiplications
Answer : a
4. Which of the followi ng is true regarding the number of computations
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104
a) 4N -2 real multiplications and 4N real additions
b) 4N real multiplications and 4N -4 real additions
c) 4N -2 real multiplications and 4N+2 real additions
d) 4N real multiplications and 4N -2 real additions
Answer : d
5. Divide -and-conquer approach is based on the decomposition of an N -
point DFT into successively smaller DFTs. This basic approach leads to
FFT algorithms.
a) True
b) False
Answer : a
6. How many c omplex multiplications are performed in computing the N -
point DFT of a sequence using divide -and-conquer method if N=LM?
a) N(L+M+2)
b) N(L+M -2)
c) N(L+M -1)
d) N(L+M+1)
Answer : d
7. Define discrete Fourier transform and its inverse.
8. State and prove the translation property.
9. Give the drawbacks of DFT.
10. Give the property of symmetry and Periodicity of Direct DFT.



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104 5
DISCRETE FOURIER TRANSFORM -II
Unit Structure
5.1 Objectives
5.2 Introduction
5.2.1 Image Transforms
5.2.2 Unitary Transform
5.3 Properties of 2 -D DFT
5.4 Classification of Image transforms
5.4.1 Walsh Transform
5.4.2 Hadamard Transform
5.4.3 Dis crete cosine transform
5.4.4 Discrete Wavelet Transform
5.4.4.1 Haar Transform
5.4.4.2 KL Transform
5.5 Summary
5.6 References
5.7 Unit End Exercises
5.1 OBJECTIVES
After going through this unit, you will be able to:
● Understood the fundamental conc epts of Digital Image processing
● Able to discuss mathematical transforms.
● Describe the DCT and DFT techniques
● Classify different types of image transforms
● Examine the use of Fourier transforms for image processing in the
frequency domain

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105 5.2 INTRODUCTION
5.2.1 Image Transforms
A representation of an image is called as Image transform. The reasons for
transforming an image from one representation to another are as -
i. The transformation may isolate critical components of the image
pattern so that they are di rectly accessible for analysis.
ii. The transformation may place the image data in a more compact form
so that they can be stored and transmitted efficiently.
5.2.2 Unitary Transform [1] :
A discrete linear transform is unitary if its transform matrix conforms to
the unitary condition
A × AH = I
where A = transformation matrix, AH represents Hermitian matrix.
AH= A*T
I = identity matrix
When the transform matrix A is unitary, the defined transform is called
unitary transform.
Example) Check whether the DFT matr ix is unitary or not [1].
Step 1 : Determination of the matrix A
Finding 4 -point DFT (where N = 4)
The formula to compute a DFT matrix of order 4 is given below

where k = 0, 1..., 3
1. Finding X(0)

2. Finding X(1)
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= x(0) − jx(1)−x(2)+ jx(3)
3. Finding X(2)


X(2) = x(0) −x(1)+ x(2)−x(3)
4. Finding X(3)


X (3) = x(0)+ jx(1) −x(2)− jx(3)
Collecting the coefficients of X(0), X(1), X(2) and X(3), we get

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107
( A*)T = AH =



The result is the identity matrix, which shows that Fourier transform
satisfies unitary condition.
Sequency - It refers to the number of sign changes. The sequency for a
DFT matrix of ord er 4 is given below.




1 1 1 1
1 j - 1 - j
1 - 1 1 -1
1 - j - 1 j
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108 5.3 PROPERTIES OF 2 -D DFT [1] :
The properties of 2D DFT are shown in table 1.

Table 1 - properties of 2D DFT [1]
5.4 CLASSIFICATION OF IMAGE TRANSFORMS :
A) Walsh transform : transforms with non -sinusoidal orthogonal basis
functi ons
B) Hadamard transform : transforms with non -sinusoidal orthogonal
basis functions
C) Discrete cosine transform : transforms with orthogonal basis
functions
D) Discrete wavelet transform
● Haar Transforms : transforms with non -sinusoidal orthogonal basis
functions
● KL transform : transforms whose basis functions depend on the
statistics of the input data
5.4.1 Walsh Transform [1] :
The representation of a signal by a set of orthogonal sinusoidal waveforms
is known as Fourier analysis. The frequency components are the
coefficients of this representation, and the waveforms are arranged by
frequency. To express these functions, Walsh created a comprehensive set
of orthonormal square -wave functions. The Walsh function's
computational simplicity stems from the fact that it is a real function with
only two possible values: +1 or –1.
The one -dimensional Walsh transform basis can be given by the following
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109

where n = time index,
k = frequency index
N = order
m = number bits to repr esent a number
bi(n) = i th (from LSB) bit of the binary value
n decimal number represented in binary.
The value of m is given by m = log 2 N.
The two -dimensional Walsh transform of a function f (m, n) is given
by[1],

Example) Find the 1D Walsh basis for the fourth -order system (N = 4).
the value of N is given as four. From the value of N, the value of m is
calculated as N = 4;
m = log 2 N
=log 2 4 = log 2 22
=2*log 22
m = 2
In this, N = 4. So n and k have the values of 0, 1, 2 and 3. I varies from 0
to m–1. From the above computation, m = 2. So i has the value of 0 and 1.
The construction of Walsh basis for N = 4 is given in Table 1.
When k or n is equal to zero, the basis value will be 1/N.


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110 Sequency : The Walsh functions may be ordered by the number of zero
crossings or sequency, and the coefficients of the representation may be
called sequency components. The sequency of the Walsh basis function
for N = 4 is shown in Table 2.

Table 2 : Walsh transform basis for N = 4 [1]


Likewise, all the values of the Walsh transform can be calculated. After
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111

Note: When looking at the Wals h basis, every entity has the same
magnitude (1/N), with the only difference being the sign (whether it is
positive or negative). As a result, the following is a shortcut approach for
locating the sign:
Step 1 Write the binary representation of n.
Step 2 W rite the binary representation of k in the reverse order.
Step 3 Check for the number of overlaps of 1 between n and k.
Step 4 If the number of overlaps of 1 is
i) zero then the sign is positive
ii) even then the sign is positive
iii) odd then the sign is negative
5.4.2 Hadamard Transform :
The Hadamard transform is similar to the Walsh transform with the
exception that the rows of the transform matrix are re -ordered.
The elements of a Hadamard transform's mutually orthogonal basis
vectors are either +1 or –1, resulting in a minimal computing complexity
in calculating the transform coefficients.
The following approach can be used to create Hadamard matrices for N = 2n:
The order N = 2 Hadamard matrix is gi ven as,
H2 =


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112 The Hadamard matrix of order 2N can be generated by Kronecker product
operation:

H2N =

Substituting N = 2 in above equation,
H4 =



=


Similarly, substituting N = 4 in H 2N equation,
The Hadamard matrix of order N = 2n may be generated from the order
two core matrix. It is not desirable to store the entire matrix.
5.4.3 Discrete cosine transform :
Membe rs of a family of real -valued discrete sinusoidal unitary transforms
are discrete cosine transforms. A discrete cosine transform is made up of a
set of sampled cosine functions and a set of basis vectors. DCT is a signal
compression technique that breaks d own a signal into its fundamental
frequency components.
If x[n] is the signal of length N, the Fourier transform of the signal x[n] is
given by X[k] where,

where k varies between 0 to N − 1.
Consider extending the signal x[n], which is indicated by xe[n] , so that the
expanded sequence has a length of 2N. There are two ways to expand the
sequence x[n].
Consider the following sequence (original sequence) of length four: x[n] =
[1, 2, 3, 4]. Fig. 1 depicts the original sequence. There are two ways to
length en the sequence. By simply copying the original sequence again, as
shown in Fig. 2, the original sequence can be extended. HN HN
HN - HN
H2 H2
H2 - H2
1 1 1 1
1 -1 1 -1
1 1 -1 -1
1 -1 -1 1
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113 As demonstrated in Fig. 2, the expanded sequence can be created by
simply replicating the original sequence. The biggest disadvantag e of this
method is the variance in sample value between n = 3 and n = 4.

Fig. 1 Original sequence


Fig. 2 Extended sequence obtained by simply copying the original
sequence


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114

Fig. 3 Extended sequence obtained by folding the origin al sequence
The phenomena of 'ringing' is unavoidable due to the extreme fluctuation.
A second approach of producing the expanded sequence, as illustrated in
Fig. 3, is to copy the original sequence in a folded fashion. When
comparing Figs. 2 and 3, it is obvious that the variance in the sample value
at n = 3 and n = 4 in Fig. 3 is the smallest when compared to Fig. 2. The
expanded sequence created by folding the initial sequence is shown to be a
better choice as a result of this.
The length of the expanded sequence is 2N if N is the length of the
original sequence, as seen in both Figs. 2 and 3.
In this example, the length of the original sequence is 4 (refer Fig. 1) and
the length of the extended sequence is 8(refer Fig. 2 and Fig. 3).
The Discrete Fourier Transform (DFT) of the extended sequence is given
by Xe[k] where

Split the interval 0 to 2N – 1 into two parts,

Let m = 2N – 1 − n. Substituting in above equation,
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115



But,


Replacing m by n and Multiplying both sides by


Upon simplificatio n,

Thus, the kernel of a one -dimensional discrete cosine transform is given
by

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116 The process of reconstructing a set of spatial domain samples from the
DCT coefficients is called the inverse discrete cosine transform (IDCT).
The inverse discrete cosine transformation is given by,

The forward 2D discrete cosine transform of a signal f(m, n) is given by,

The 2D inverse discrete cosine transform is given by

5.4.4 Discrete Wavelet Transform: Haar Transform, KL Transform
5.4.4.1 Haar Transform :
The Ha ar transform is based on a class of orthogonal matrices with
elements of 1, –1, or 0 multiplied by powers of √2 as its elements. The
Haar transform is computationally efficient since it only requires 2(N – 1)
additions and N multiplications to change an N -point vector.
Algorithm to Generate Haar Basis [1]: The algorithm to generate Haar
basis is given below:
Step 1 Determine the order of N of the Haar basis.
Step 2 Determine n where n = log 2 N.
Step 3 Determine p and q.
(i) 0 ≤ p < n –1
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117 Step 4 Determine k.
k = 2p + q – 1
Step 5 Determine Z.

Step 6 If k = 0 then H(Z) = 1/ √N
Otherwise
,

The flow chart to compute Haar basis is given Fig. 4

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118 5.4.4.2 KL Transform ( KARHUNEN –LOEVE TRANSFORM ) :
Harold Hotelling was the first to study the discrete formulation of the KL
transform, which is why it is also known as the Hotelling transform. The
KL transform is a reversible linear transform t hat takes advantage of a
vector representation's statistical features.
The orthogonal eigenvectors of a data set's covariance matrix are the basic
functions of the KL transform. The input data is optimally decorrelated
using a KL transform. The majority of the 'energy' of the transform
coefficients is focused inside the first few components after a KL
transform. A KL transform's energy compaction property is this.
Drawbacks of KL transform :
i. A KL transform is input -dependent, and the fundamental function for
each signal model on which it acts must be determined. There is no unique
mathematical structure in the KL bases that allows for quick
implementation.
ii. The KL transform necessitates multiply/add operations in the order of
O(m2). O(log 2m) multiplica tions are required for the DFT and DCT.
Applications of KL Transforms [1] :
(i) Clustering Analysis : Used to determine a new coordinate system for
sample data where the largest variance of a projection of the data lies on
the first axis, the next largest variance on the second axis, and so on.
(ii) Image Compression : It is heavily utilised for performance evaluation
of compression algorithms since it has been proven to be the optimal
transform for the compression of an image sequence in the sense that the
KL spectrum contains the largest number of zero -valued coefficients.
Example) Perform KL transform for the following matrix:

Step 1 - Formation of vectors from the given matrix
The given matrix is a 2×2 matrix; hence two vectors can be extracted from
the given matrix. Let it be
x0 and x1.

Step 2 Determination of covariance matrix
The formula to compute covariance of the matrix is
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119 In the formula for covariance matrix, x denotes the mean of the input
matrix. The formula to compute
the mean of the giv en matrix is given below:

where M is the number of vectors in x.

The mean value is calculated as

Now multiplying the mean value with its transpose yields

xxT To find the E

In our case, M = 2 hence

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120 Step 3 Determination of eigen values of the covariance matrix
To find the eigen values λ, we solve the characteristic equation,


λ2 – λ - 4 = 0
From the last equation, we have to find the eigen values λ 0, λ1. Solving
above equation,

Step 4 - Determination of eigen vectors of the covariance matrix
The first eigen vector φ 0 is found from the equation,
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121



Step 5 - Normalisation of the eigen vectors
The normalisation formula to normalise the eigen vector φ 0 is,

Similarly, the normalisation of the eigen vector φ 1 is given by

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122 From the normalised eigen vector, we have to form the transformation
matrix.



Step 7 - KL transformation of the input matrix
To find the KL transform of the input matrix, the formula used is Y =
T[x].

The final transform matrix

Step 8 - Reconstruction of input values from the transformed coefficients
From the transform matrix, we have to reconstruct value of the given
sample matrix X using the formula X = TTY.
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123 5.5 SUMMARY
Different transform -based compression approaches have been tested with
and compared to find a viable image transformation methodology for
medical images of various sizes and modalities.
Image classification is a complicated process that relies on several f actors.
Some of the presented solutions, difficulties and more picture order
potential are discussed here. The focus should be on cutting -edge
classification algorithms for improving characterization precision.
5.6 REFERENCES
1] S. Jayaraman Digital Image Processing TMH (McGraw Hill)
publication, ISBN - 13:978 -0-07- 0144798
2] John G. Proakis, Digital Signal Processing: Principles, Algorithms,
And Applications, 4/E
3] Gonzalez, Woods & Steven, Digital Image Processing using MATLAB,
Pearson Education, ISBN -13:978 -0130085191
4] https://www.robots.ox.ac.uk/~sjrob/Teaching/SP/l7.pdf
5.7 UNIT END EXERCISES
1. Compute the discrete cosine transform (DCT) matrix for N = 4.
2. Generate one Haar Basis for N = 2.
3. Compute the Haar basis for N = 8.
4. Compute the basis of the KL transform for the input data x1 =, (4, 4,
5)T, x2 = (3, 2, 5)T, x3 = (5, 7, 6)T and x4 = (6, 7, 7 )T.
5. Compute the 2D DFT of the 4 × 4 grayscale image given below.

6. . State and prove separability property of 2D -DFT.
7. Let ( , ) denote a digital image of size 256 × 256. In order to
compress this image, we take its Discrete Cosine Transform ( , ), , =
0, … ,255 and keep only the Discrete Cosine Transform coefficients for ,
= 0, … , with 0 ≤ < 255. The percentage of total energy of the
original image that is preserved in that case is given by the formula +
+ 85 with , constants. Furthermore, the energy that is preserved if = 0
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124 8. Image transforms are needed for
______________ __________________ __________________ .
(a) conversion information form spatial to frequency
(b) spatial domain
(c) time domain
(d) both b & c
Answer : a
9. The walsh and hadamard transforms are ___________in nature
(a) sinusoidal
(b) cosine
(c) non-sinusoidal
(d) cosine a nd sine
Answer : c
10. Unsampling is a process of ____________the spatial resolution of the
image
(a) decreasing
(b) increasing
(c) averaging
(d) doubling
Answer : b

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125 Module IV
Image Restoration and Image Segmentation :
6
IMAGE DEGRADATION
Unit Structure
6.0 Image degradation
6.1 Classification of Image restoration Techniques
6.2 Image restoration model
6.3 Image blur
6.4 Noise model
6.4.1 Exponential
6.4.2 Unifo rm
6.4.3 Salt and Pepper

6.0 IMAGE DEGRADATION
Image degradation is the deterioration of image quality for a variety of
reasons. Image degradation occurs when the information stored with a
particular image is lost by either digitization or conversion (that is,
algorithmic manipulation), resulting in poor visual quality.
Image d egradation model
The operator H acts on the input image f (x, y) with an additive noise term
to model the image degradation when the degraded image g (x, y) is
generated. The pu rpose of the restore is to get an estimate of the original
image fˆ (x, y) and it should be as close as possible to the original image f
(x, y). The degraded image is given in the spatial domain by
g(x, y) =(h f )(x, y)+η(x, y)
Where
 η (x, y) is the spatial representation of the degradation function.
 “” indicates convolution.
Frequency domain is G(u,v) = H(u,v) F(u,v) + N(u,v) .
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126

6.1 CLASSIFICATION OF IMAGE RESTORATION
TECHNIQUES

 Deterministic Method: - Prior knowl edge about degradation is
known.
 Stochastic Method: - Prior knowledge about degradation is not
known.
6.2 IMAGE RESTORATION MODEL
Is the process of recovering an image that has been degraded by some
knowledge of degradation function H and the additive noi se term η(x, y).
Restoration is a process where degradation is modeled and its inverse
process is applied to recover the original image.
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127 6.3 IMAGE BLUR
This is the process of smoothing an image with no visible edges. If all
edges are clearly visible, t he image will look sharper and more detailed.
Example 1: Image with a face. If you can see the eyes, ears, nose, lips,
forehead, etc. very clearly, you can see them clearly. This shape of the
object is due to its edges. Therefore, when blurring, you redu ce the edge
content and make the transition from one color to another very smooth.
The filter used for blurring is also called a “lowpass ” filter because it
allows low frequencies to penetrate and stop at high frequencies. Here,
frequency means the change in pixel value. Blurred images are smooth, so
the pixel values at the edges change rapidly. Therefore, it is necessary to
exclude high frequencies. Filters are used for blurring purposes. For
blurred images, the value of each call is 1 because the pixe l values should
be close to adjacent values. The filter divides by 9 for normalization. If
not, the pixel value will increase and the contrast will increase, but this is
not the goal.

6.4 NOISE MODEL
6.4.1 Exponential
Exponential noise is a model wher e we can use to simulate data
corruption. The most common reasons for it are low grade equipment and
environment conditions.
Example: Photos/Images captured through an old camera end up corrupted
due to lightning, temperature changes and impacts the senso rs.
The PDF of exponential noise is given by: -

where a = 0. The mean and variance of z are

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128 Exponential noise is a special case of gamma or Erlang
noise where b parameters equal to 1.

6.4.2 Uniform
The uniform noise cause by quantizing the pixels o f image to a number of
distinct levels is known as quantization noise, the level of the gray values
of the noise are uniformly distributed across a specified range. It can be
used to generate any different type of noise distribution.
The PDF of uniform noise is: -

The mean and variance of z are

and
σ2

6.4.3 Salt and Pepper
Is known as impulse noise and can be caused by sharp and sudden
disturbances in the image signal. This form of noise is caused due to
errors in data transfer.
The PDF of salt-and-pepper noise is given by: -

k - Number of bits used to represent the intensity values
Range of intensity values is [0, 2k-1]
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129 7
IMAGE RESTORATION TECHNIQUES
Unit Structure
7.1 Image restoration techniques
7.1.1 Inverse filtering
7.1.2 Average filtering
7.1.3 Median filtering
7.2 The detection of discontinuities
7.2.1 Point detection
7.2.2 Line detection
7.2.3 Edge de tections
7.3 Various methods used for edge detection
7.3.1 Prewitt Filter or Prewitt Operator
7.3.2 Sobel Filter or Sobel Operator
7.3.3 Fri-Chen Filter Hough Transform
7.4 Thresholding Region based segmentation Chain codes
7.4.1 Region -based seg mentation
7.4.2 Region -based segmentation Chain codes
7.5 Polygon approximation
7.5.1 Shape numbers
7.6 References
7.7 Moocs
7.8 Video links
7.9 Quiz
7.1 IMAGE RESTORATION TECHNIQUES
7.1.1 Inverse filtering
It is the process of receiving the inp ut of a system from its output and is
the simplest approach to restore the original image as the degradation
function is known. The simplest approach to restoration is direct inverse
filtering, where we compute an estimate,
(u,v), of the trans form of the
original image by dividing the transform of the degraded image, G(u,v),
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7.1.2 Average filtering
Is a method of ‘smoothing’ images by reducing the amount of intensity
variation between neighboring pixels.
Types:
 Arithmetic Mean Filter
 Geometric Mean Filter
 Harmonic Mean Filter
 Contraharmonic Mean Filter.
7.1.3 Median filtering
It replaces the value of a pixel by the median of the intensity levels in a
predefined neighborhood of that pixel:

where
Sxy is a subimage centered on point ( x, y).
7.2 THE DETECTION OF DISCONTINUITIES
The partitions or sub -division of an image is based on some abrupt
changes in the intensity level of images and is used for detecting three
basic types of grey -level discontinuit ies in a digital image: Points, Lines
and Edges. To identify these, 3* 3 mask operation is used.

The response of the mask at any point in the image is given by: -

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131 where
zi is gray -level of pixel associated with mask coefficient w i.
7.2.1 Point detec tion
A point is the basic type of discontinuity in a digital image. The most
common way to finding discontinuities is to run a
mask over each
point in the image. T he detection of isolated point different from constant
background image can be done using the following mask:

The point is detected at a location (x, y) in an image where the mask is
centered. If the corresponding value of R such that:
|R|
T
Where R is the response of the mask at any point in the image and T is
non-negative threshold value. It means that isolated point is detected at the
corresponding value (x, y).
The result of point detection mask is shown in Fig 4:

Fig 4: Point Detection
and
7.2.2 Line detection
It is the process of receiving the input of a sy stem from its output and is
the simplest approach to restore the original image as the degradation
function is known. The simplest approach to restoration is direct inverse
filtering, where we compute an esti mate , F (u,v), of the transform of the
original image by dividing the transform of the degraded image, G(u,v), by
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132 Line detection is the level of complexity in the direction of image
discontinuity. Consider the mask sho wn in masks. If the first mask were
moved around an image, it would respond more strongly to lines (one
pixel thick) oriented horizontally. With a constant background, the
maximum response would result when the line passed through the middle
row of the mas k and can be easily verified by sketching a simple array of
1`s with a line of a different gray level (say, 5`s) running horizontally
through the array.
Suppose R1, R2, R3, and R4 represent the mask response of the specific
mask below from left to right. Where R is given by:
.
Suppose that the four masks are run individually through an image. If, at a
certain point in the image, |Ri| > |Rjl, for all j ≠ i, that point is said to be
more likely associated with a line in the direction of mask i.


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133

7.2.3 Edge detections
Significant transitions in an image are called as edges.
Types of edges
 Horizontal edges
 Vertical Edges
 Diagonal Edges
Edge detection is the most common approach to detecting something
meaningful. Grayscale discontinuity. An edge is th e boundary between
two regions with different intensity levels. In practice, the edges of a
digital image are blurry and noisy, the degree of blurring is primarily
determined by the limitations of the focusing mechanism (such as the lens
in the case of o ptical images), and the noise level is primarily determined
by the electronic components of the imaging system. Will be decided. .. In
such situations, the edges are modeled closer, as if they had a slanted
profile. The tilt of the ramp is inversely prop ortional to the degree of
blurring of the edges. In this model, there is no single "edge point" along
the profile. Instead, an edge point now is any point contained in the ramp,
and an edge segment would then be a set of such points that are connected.
A third type of edge is the so -called roof edge , having the characteristics
illustrated in Fig below. Roof edges are models of lines through a region,
with the base (width) of the edge being determined by the thickness and
sharpness of the line.


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134 7.3 VAR IOUS METHODS USED FOR EDGE
DETECTION
Detection of edges
Most of the shape information of an image is enclosed in edges. So first
we detect these edges in an image and by using these filters and then by
enhancing those areas of image which contains edges, s harpness of the
image will increase and image will become clearer.
 Prewitt Operator
 Sobel Operator
 Robinson Compass Masks
 Krisch Compass Masks
 Laplacian Operator.
All the filters mentioned above are Lin ear filters .
7.3.1 Prew itt Filter or Prewitt Operator
It is used for edge detection in an image detecting both types of edges.
 Horizontal edges or along the x -axis.
 Vertical Edges or along the y -axis.
Prewitt Operator [X -axis] = [ -1 0 1; -1 0 1; -1 0 1]
Prewitt Operator [Y -axis] = [ -1 -1 -1; 0 0 0; 1 1 1]

Fig 6: Horizontal Direction

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135 7.3.2 Sobel Filter or Sobel Operator
Sobel Filter looks similar to Prewitt operator; it is a derivate mask used for
edge detection. Sobel operator is also used to detect two kinds of edges in
an image :
 Horizontal direction.
 Vertical direction.
Major difference is that in sobel operator the coefficients of masks are not
fixed and they can be adjusted according to our requirement unless they do
not violate any property of derivative masks.
This mask work s exactly same as the Prewitt operator vertical mask. The
only one difference it has “2” and “ -2” values in center of first and third
column. As applied on an image this mask will highlight the vertical
edges.

Fig 8: Horizontal Direction

Fig 9: Vertica l Direction
How it works
This mask enhances the horizontal edges of the image. It also works on
the basis of the mask principle above to calculate the difference in pixel
intensity for a particular edge. The center mask row consists of zeros, so it
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136 calculate the difference in pixel intensity above and below each edge.
This amplifies the sudden changes in intensity and makes the edges easier
to see. Let’s see these masks in action:
Sample Image
Following is a sample picture on which we will apply above two masks
one at time.

After applying Vertical Mask
After applying vertical mask on the above sample image, following image
will be obtained.

After applying Horizontal Mask
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137

Comparison
As you can see, in the first image to which the vertical mask is applied, all
vertical edges are easier to see than the original image. Similarly, in the
second image , all horizontal edges are shown as a result of applying the
horizontal mask.
In this way, you can see that both horizontal and vertical edges of the
image can be detected. Also, if you compare the result of the Sobel
operator with the Prewitt operator, you can see that the Sobel operator
finds more edges and makes the edges easier to see than the Prewitt
operator.
This is because the Sobel operator gave more weight to the pixel weight
of the edges.
Applying more weight to mask
Applying more weight to the mask, the more edges it will get for us. -1 0 1 -5 0 5 -1 0 1
Compare the result of this mask with of the Prewitt vertical mask, it is
apparent that this mask will give out more edges as compared to Prewitt
one just because we have allotted more weight in the mask.
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138 7.3.3 Fri-Chen Filter Hough Transform
Fri-Chen edge detector is also a first order operation Prewitt and Sobel
operator. Frei-Chen masks are unique masks, contains all the basis
vectors. This means that a 3×3 image area is represented with the
weighted sum of nine Frei -Chen masks that can be seen below: -



7.4 THRESHOLDING REGION BASED
SEGMENTATION CHAIN CODES
Pixels are categorized based on the range of values they contain. The
figure below shows the boundaries obtained by thresh olding the muscle
fiber image. Pixel values less than 128 were placed in one category and
the rest in the other.
7.4.1 Region -based segmentation algorithms algorithm works repeatedly
to group adjacent pixels with similar values and split groups of pixels w ith
different values.
7.4.2 Region -based segmentation Chain codes
Boundary represented by a connected sequence of staraight -line segments
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139

Fig 10: Region based Segmentation Chain Codes
7.5 POLYGON AP PROXIMATION
Polygon approximation is used to represent boundaries in straight lines,
and closed paths are polygons. The number of straight line segments used
determines the accuracy of the approximation. You need to use the
minimum number of sides needed to hold the required shape information
(minimum perimeter polygons). A large number of edges only adds noise
to the model. Polygon app roximation using minimum perime ter polygons:

Fig 11: Polygon approximation


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140 7.5.1 Shape numbers
As shown in the figure below, the shape number of the Freeman chain -
coded boundary based on the 4 -way code is defined as the first difference
in minimum magnitude. The order n, of a shape is defined as the number
of digits in the representation. Moreover, for closed boundaries , n is even,
and its value limits the number of different shapes possible. The first
difference in the 4 -way directional chain code is independent of rotation
(in 90 ° increments), but the coded boundaries usually depend on the on
the orientation of the gr id.
Depending on how the grid spacing is selected, the resulting shape
number order is usually equal to n, but borders with indentations
comparable to this spacing may produce shape numbers greater than n. In
this case, specify a rectangle with an order less than n and repeat the
process until the resulting shape number is nth. The order of form numbers
starts at 4, and we are using 4 connections, so we always need it.
The border is closed.

Fig 12: Shape Numbers
7.6 REFERENCES
1. Pratt WK. Introductio n to digital image processing. CRC press; 2013
Sep 13.
2. Niblack W. An introduction to digital image processing. Strandberg
Publishing Company; 1985 Oct 1.
3. Burger W, Burge MJ, Burge MJ, Burge MJ. Principles of digital
image processing. London: Springer; 2009 . munotes.in

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141 4. Jain AK. Fundamentals of digital image processing. Prentice -Hall,
Inc.; 1989 Jan 1.
5. Dougherty ER. Digital image processing methods. CRC Press; 2020
Aug 26.
6. Gonzalez RC. Digital image processing. Pearson education india;
2009.
7. Marchand -Maillet S, Sharaiha YM. Binary digital image processing:
a discrete approach. Elsevier; 1999 Dec 1.
8. Andrews HC, Hunt BR. Digital image restoration.
9. Lagendijk RL, Biemond J. Basic methods for image restoration and
identification. InThe essential guide to image processing 2009 Jan 1
(pp. 323 -348). Academic Press.
10. Banham MR, Katsaggelos AK. Digital image restoration. IEEE
signal processing magazine. 1997 Mar;14(2):24 -41.
11. Hunt BR. Bauesian Methods in Nonkinear Digital Image Restoration.
IEEE Transactions on Computers. 1977 Mar 1; 26(3):219 -29.
12. Figueiredo MA, Nowak RD. An EM algorithm for wavelet -based
image restoration. IEEE Transactions on Image Processing. 2003
Aug 4;12(8):906 -16.
13. Digital Image Processing – Tutorialspoint.
https://www.tutorialspoint.com/dip/index.htm .
14. Types of Restoration Filters. https://www.geeksforgeeks.org/types -
of-restoration -filters/ .
7.7 MOOCS
1. Digital Image Processing.
https://onlinecourses.nptel.ac.in/noc19_ee55/preview .
2. Digital Image Processing.
https://www.my greatlearning.com/academy/learn -for-
free/courses/digital -image -processing .
3. Fundamentals of Digital Image Processing.
https://alison.com/course/fundamentals -of-digital -image -processing

4. Digital Image Processing: Operations and Applications.
https://www.udemy.com/course/digital -image-processing -operations -
and-applications/ munotes.in

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142
5. Digita l Image Processing. https://www.udemy.com/course/digital -
image -processing -made -easy/.
7.8 VIDEO LINKS
1. Digital Image Processing.
https://www.youtube.com/watch? v=sa7vO6YXBik&list=PL3rE2jS8z
xAykFjinlf6EsucLv5EA03_m .
2. Digital Image Processing - Introduction of DIP.
https://www.youtube.com/watch?v=iZmHHVwp0Ow&lis t=PL3rE2j
S8zxAykFjinlf6EsucLv5EA03_m&index=2 .
3. Digital Image Processing - Nature of Image Processing &
Applications.
https://www.youtube.com/watch?v=Uq KQ_lfDwx8&list=PL3rE2jS8
zxAykFjinlf6EsucLv5EA03_m&index=3 .
4. Digital Image Processing - Image Smoothing Spatial Filters.
https://www.youtube.com/watch? v=Dtdmm7QodO4&list=PL3rE2jS
8zxAykFjinlf6EsucLv5EA03_m&index=31 .
5. Digital Image Processing - Image Degradation (Restoration) Model.
https://www.youtube.com/watch?v=U1h0biwb8OM&t=23s .
6. Digital Im age Processing - Estimation of Degradation Function.
https://www.youtube.com/watch?v=n5dlO82SwJU .
7. Image Restoration: Estimation of Degradation Function.
https://www.youtube.com/watch?v=fkgxpXx0250 .
8. Estimating the Degradation function in Digital Image Processing |
Observation | Experimentation | Modeling.
https://www.youtube.com/watch?v=c loLOHb5F_k .
9. Digital Image Processing - Image Restoration Techniques.
https://www.youtube.com/watch?v=PBhBw5qfaq4 .
10. Estimation of Degradation Model and Restoration Techniques – I.
https://www.youtube.com/watch?v=3XQcZeNF_8k
11. Image Degradation and Restoration and Model of Image Degradation
and Restoration process in DIP.
https://www.youtube .com/watch?v=w0YNkSQxvwo . munotes.in

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143 12. Image Restoration Techniques – I.
https://www.youtube.com/watch?v=MrNafUqh860 .
13. Image degradation and restoration | Digital Image Processing.
https://www.youtube.com/watch?v=ScBBAHHxepY .
14. Degradation function.
https://www.youtube.com/watch?v=dIC53nDnwgk .
7.9 QUIZ
1. What is Digital Image Processing?
a) It’s an a pplication that alters digital videos
b) It’s a software that allows altering digital pictures
c) It’s a system that manipulates digital medias
d) It’s a machine that allows altering digital images
ANSWER: B

2. Which of the following process helps in Imag e enhancement?
a) Digital Image Processing
b) Analog Image Processing
c) Both a and b
d) None of the above
ANSWER: C

3. Among the following, functions that can be performed by digital image
processing is?
a) Fast image storage and retrieval
b) Controlled viewing
c) Image reformatting
d) All of the above
ANSWER: D

4. Which of the following is an example of Digital Image Processing?
a) Computer Graphics
b) Pixels
c) Camera Mechanism
d) All of the mentioned
ANSWER: D


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144 5. What are the categories of digital image processing?
a) Image Enhancement
b) Image Classification and Analysis
c) Image Transformation
d) All of the mentioned
ANSWER: D

6. How does picture formation in the eye vary from image formation in a
camera?
a) Fixed focal length
b) Varying distance between lens and imaging plane
c) No difference
d) Variable focal length
ANSWER: D

7. What are the names of the various colour image processing categories?
a) Pseudo -color and Multi -color processing
b) Half -color and pseudo -color processing
c) Full -color and pseudo -color processing
d) Half -color and full -color processing
ANSWER: C

8. Which characteristics are taken together in chromaticity?
a) Hue and Saturation
b) Hue and Brightness
c) Saturation, Hue, and Brightness
d) Saturation and Brightness
ANSWER: A

9. Which of the following statement describe the term pixel depth?
a) It is the number of units used to represent each pixel in RGB space
b) It is the number of mm used to represent each pixel in RGB space
c) It is the number of bytes used to represent each pixel in RGB space
d) It is the number of bits used to represent each pixel in RGB space
ANSWER: D

10. The aliasing effect on an image can be reduced using which of the
following methods?
a) By reducing the high -frequency components of image by clar ifying the
image
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145 c) By increasing the high -frequency components of image by blurring the
image
d) By reducing the high -frequency components of image by blurring the
image
ANSWE R: D

11. Which of the following is the first and foremost step in Image
Processing?
a) Image acquisition
b) Segmentation
c) Image enhancement
d) Image restoration
ANSWER: A

12. Which of the following image processing approaches is the fastest,
most accur ate, and flexible?
a) Photographic
b) Electronic
c) Digital
d) Optical
ANSWER: C

13. Which of the following is the next step in image processing after
compression?
a) Representation and description
b) Morphological processing
c) Segmentation
d) Wavelets
ANSWER: B

14. ___________ determines the quality of a digital image.
a) The discrete gray levels
b) The number of samples
c) discrete gray levels & number of samples
d) None of the mentioned
ANSWER: C

15. Image processing involves how many steps?
a) 7
b) 8
c) 13
d) 10
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146
16. Which of the following is the abbreviation of JPEG?
a) Joint Photographic Experts Group
b) Joint Photographs Expansion Group
c) Joint Photographic Expanded Group
d) Joint Photographic Expansion Group
ANSWER: A

17. Which of the following is the role played by segmentation in image
processing?
a) Deals with property in which images are subdivided successively into
smaller regions
b) Deals with partitioning an image into its constituent parts or objects
c) Deals with extracting at tributes that result in some quantitative
information of interest
d) Deals with techniques for reducing the storage required saving an
image, or the bandwidth required transmitting it
ANSWER: B

18. The digitization process, in which the digital image comp rises M rows
and N columns, necessitates choices for M, N, and the number of grey
levels per pixel, L. M and N must have which of the following values?
a) M have to be positive and N have to be negative integer
b) M have to be negative and N have to be pos itive integer
c) M and N have to be negative integer
d) M and N have to be positive integer
ANSWER: D

19. Which of the following tool is used in tasks such as zooming,
shrinking, rotating, etc.?
a) Filters
b) Sampling
c) Interpolation
d) None of the Menti oned
ANSWER: C

20. The effect caused by the use of an insufficient number of intensity
levels in smooth areas of a digital image _____________
a) False Contouring
b) Interpolation
c) Gaussian smooth
d) Contouring
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147
21. What is the procedure done on a digital image to alter the values of its
individual pixels known as?
a) Geometric Spacial Transformation
b) Single Pixel Operation
c) Image Registration
d) Neighbourhood Operations
ANSWER: B

22. Points whose locations are known exactly in the input a nd reference
images are used in Geometric Spacial Transformation.
a) Known points
b) Key -points
c) Réseau points
d) Tie points
ANSWER: D

23. ___________ is a commercial use of Image Subtraction.
a) MRI scan
b) CT scan
c) Mask mode radiography
d) none of t he mentioned
ANSWER: C

24. Approaches to image processing that work directly on the pixels of
incoming image work in ____________
a) Spatial domain
b) Inverse transformation
c) Transform domain
d) None of the Mentioned
ANSWER: A

25. Which of the followin g in an image can be removed by using a
smoothing filter?
a) Sharp transitions of brightness levels
b) Sharp transitions of gray levels
c) Smooth transitions of gray levels
d) Smooth transitions of brightness levels
ANSWER: B


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26. Region of Interest (RO I) operations is generally known as _______
a) Masking
b) Dilation
c) Shading correction
d) None of the Mentioned
ANSWER: A

27. Which of the following comes under the application of image
blurring?
a) Image segmentation
b) Object motion
c) Object detectio n
d) Gross representation
ANSWER: D

28. Which of the following filter’s responses is based on the pixels
ranking?
a) Sharpening filters
b) Nonlinear smoothing filters
c) Geometric mean filter
d) Linear smoothing filters
ANSWER: B

29. Which of the followi ng illustrates three main types of image enhancing
functions?
a) Linear, logarithmic and power law
b) Linear, logarithmic and inverse law
c) Linear, exponential and inverse law
d) Power law, logarithmic and inverse law
ANSWER: D

30. Which of the following is the primary objective of sharpening of an
image?
a) Decrease the brightness of the image
b) Increase the brightness of the image
c) Highlight fine details in the image
d) Blurring the image
ANSWER: C


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149 31. Which of the following operation is done on t he pixels in sharpening
the image, in the spatial domain?
a) Differentiation
b) Median
c) Integration
d) Average
ANSWER: A

32. ________ is the principle objective of Sharpening, to highlight
transitions.
a) Brightness
b) Pixel density
c) Composure
d) Inte nsity
ANSWER: D

33. _________ enhance Image Differentiation?
a) Pixel Density
b) Contours
c) Edges
d) None of the mentioned
ANSWER: C

34. Which of the following fact is correct for an image?
a) An image is the multiplication of illumination and reflectan ce
component
b) An image is the subtraction of reflectance component from illumination
component
c) An image is the subtraction of illumination component from reflectance
component
d) An image is the addition of illumination and reflectance component
ANSWE R: A

35. Which of the following occurs in Unsharp Masking?
a) Subtracting blurred image from original
b) Blurring the original image
c) Adding a mask to the original image
d) All of the mentioned
ANSWER: D


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150 36. Which of the following makes an image diff icult to enhance?
a) Dynamic range of intensity levels
b) High noise
c) Narrow range of intensity levels
d) All of the mentioned
ANSWER: D

37. _________ is the process of moving a filter mask over the image and
computing the sum of products at each locati on.
a) Nonlinear spatial filtering
b) Convolution
c) Correlation
d) Linear spatial filtering
ANSWER: C

38. Which side of the greyscale is the components of the histogram
concentrated in a dark image?
a) Medium
b) Low
c) Evenly distributed
d) High
ANSWER: B

39. Which of the following is the application of Histogram Equalisation?
a) Blurring
b) Contrast adjustment
c) Image enhancement
d) None of the Mentioned
ANSWER: C

40. Which of the following is the expansion of PDF, in uniform PDF?
a) Probability Densi ty Function
b) Previously Derived Function
c) Post Derivation Function
d) Portable Document Format
ANSWER: A

41. ____________ filter is known as averaging filters.
a) Bandpass
b) Low pass
c) High pass
d) None of the Mentioned
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151 42. What is/are the resultant image of a smoothing filter?
a) Image with reduced sharp transitions in gray levels
b) Image with high sharp transitions in gray levels
c) None of the mentioned
d) All of the mentioned
ANSWER: A

43. The response for linear spatial filtering is given by the relationship
__________
a) Difference of filter coefficient’s product and corresponding image pixel
under filter mask
b) Product of filter coefficient’s product and corresponding image pixel
under filter mask
c) Sum of filter coefficient’s pro duct and corresponding image pixel under
filter mask
d) None of the mentioned
ANSWER: C

44. ___________ is/are the feature(s) of a highpass filtered image.
a) An overall sharper image
b) Have less gray -level variation in smooth areas
c) Emphasized transit ional gray -level details
d) All of the mentioned
ANSWER: D

45. The filter order of a Butterworth lowpass filter determines whether it is
a very sharp or extremely smooth filter function, or an intermediate filter
function. Which of the following filters d oes the filter approach if the
parameter value is very high?
a) Gaussian lowpass filter
b) Ideal lowpass filter
c) Gaussian & Ideal lowpass filters
d) None of the mentioned
ANSWER: B

46. Which of the following image component is characterized by a slow
spatial variation?
a) Reflectance and Illumination components
b) Reflectance component
c) Illumination component
d) None of the mentioned
ANSWER: C
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152 47. Gamma Correction is defined as __________
a) Light brightness variation
b) A Power -law response phenomeno n
c) Inverted Intensity curve
d) None of the Mentioned
ANSWER: B

48. ____________________ is known as the highlighting the contribution
made to total image by specific bits instead of highlighting intensity -level
changes.
a) Bit -plane slicing
b) Intensity Highlighting
c) Byte -Slicing
d) None of the Mentioned
ANSWER: A

49. Which gray -level transformation increases the dynamic range of gray -
level in the image?
a) Negative transformations
b) Contrast stretching
c) Power -law transformations
d) Non e of the mentioned
ANSWER: B

50. What is/are the gray -level slicing approach(es)?
a) To brighten the pixels gray -value of interest and preserve the
background
b) To give all gray level of a specific range high value and a low value to
all other gray level s
c) All of the mentioned
d) None of the mentioned
ANSWER: C



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154 Module V
8
IMAGE DATA COMPRESSION AND
MORPHOLOGICAL OPERATION
8.1 NEED FOR COMPRESSION
Image compression is one of the most important and commercially
successful technologies in the field of digital image processing. It involves
the art and science of minimizing the amount of data required to represent
an image. Image compression is a technique for reducing the amount of
data needed to represent a digital image. It's crucial for lowering storage
requirements and increasing transmission speeds.
It aims to decrease the irrelevance and redundancy of image data in order
to store or transmit data more efficiently. Its goal is to reduce the amount
of bits needed to represent an image.
Consider a black -and-white image with a resolution of 1000*1000 pixels
and an intensity of 8 bits per pixel. So total number of bits required per
image is 1000*1000*8 = 80,00,000 bits. Consider the total bits for a
video of 3 seconds with 30 frames per second of the above -mentioned
kind images: 3*(30*(8, 000, 000))=720, 000, 0 00 bits.
As we've seen, just storing a 3 -second video requires a large number of
bits. As a result, we need a technique to have a suitable representation as
well as a way to retain image information in a small number of bits
without affecting the image's c haracter. As a result, image compression
is crucial.
Unit Structure
8.1 Need for compression
8.2 Redundancy in image
8.3 Classification of Image compression schemes
8.4 Huffman coding
8.5 Arithmetic coding
8.6 Dictionary based compression
8.7 Lempel -Ziv-Welch (LZW) algorithm
8.8 Transform based compr ession
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155 8.2 REDUNDANCY IN IMAGE
Redundancy refers to "storing additional information to represent a set of
information." We know that computers store images in pixel values.
Therefore, the pixel values of the image may be duplicated, or even if
some pixel values are delet ed, the information in the actual image may
not be affected. 3-Types of Image redundancy: -
a) Coding redundancy : -

The symbols such as letters, numbers, bits, and so on are used to represe nt
a set of data or events and collection of these symbols is known as code .
Each code word's length is determined by the number of symbols it
contains. In most 2 -D intensity arrays, the 8 -bit codes used to represent the
intensities contain more bits than are required to express the intensities.

b) Spatial and temporal redundancy : -

Because most 2 -D intensity array pixels are spatially interconnected (i.e.,
each pixel is similar to or dependent on surrounding pixels), information is
duplicated in the repre sentations of the correlated pi xels unnecessarily.
Temporally interconnected pixels (those that are similar to or dependent
on pixels in surrounding frames) in a video series also duplicate
information.

c) Irrelevant information : -

Human visual system ignore most of the 2 -D intensity arrays that contain
data. If that data is not used it is considered to be as redundant.

8.3 CLASSIFICATION OF IMAGE COMPRESSION
SCHEMES
Two types of Image compression technique: -
a) Lossy image compression: - Lossy compression means to reduce the
image size while discarding some da ta from the original image file .
b) Lossless image compression: - The lossless image compression
approach involves representing an image signal with the least amount
of bits possible without losing any info rmation, resulting in faster
transmission a nd reduced storage requirement




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156 Further, these two techniques are also cla ssified as follows

Image
Compression
Lossless
Compression
Decorrelation
Entropy Coding
Lossy Compression
Transformed
Based
Non-Transformed Based
DCT Based
DWT Based
Vector
Quantization
Fractals
SPHIT ,
EZW,
EBCOT
RLC,LZW,
Huffman Coding ,
Golomb Code ,
Golomb -Rice
Code,
MQ Coder
Fast DCT ,
Integer DCT ,
Binary DCT ,
Signed DCT ,
Zonal DCT ,
Fast zonal DCT
SHPS,
Strip Based ,
Two line Based ,
Single line
Based

Fig 1: Classification of Image compression schemes
8.4 HUFFMAN CODING
The Huffman coding technique is a lossless image compression method.
Huffman coding is base d on the frequency of data item in order of their
occurrences , such as a pixel in an image, appears. These codes are variable
length code. It can be found in JPEG files.
Steps and exa mple: -
Forward Pass: -
1. Sort probabilities of each symbol.
2. Combine two probabilities having lowest probability values.
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157

Fig 2: Forward Pass
Backward Pass
 Assign code symbols going backwards.

Fig 3: Bac kward Pass
So, average length of this code: -


8.5 ARITHMETIC CODING

Arithmetic coding is a lossless image compression technique. Arithmetic
coding generates non -block. A single arithmetic code word is assigned to a
complete sequence of source symbols (or m essage). The code word itself
designates a range of actual numbers from 0 to 1. Each symbol in the
message shrinks the interval in proportion to its occurrence probability.
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158 Steps and example: -
Figure 1 illustrates the basic arithmetic coding process. A five-symbol
sequence or message, a1a2a3a3a4, is coded here from a four -symbol
source. The message is supposed to occupy the entire half -open interval
[0, 1] at the start of the coding procedure. This interval is initially
partitioned into four sections depe nding on the probabilities of each source
symbol, as shown in Table below, for example, symbol a1 is related with
Subinterval [0, 0.2]. The message interval is initially limited to [0, 0.2]
because it is the first symbol of the message being coded.

The range [0, 0.2] is enlarged to the full height of the figure, with the
values of the narrowed range labeling its end points. The narrower range is
then subdivided according with probabilities of the original source
symbol, and the process is repeated for th e next message symbol. Symbols
a2 and a3 narrow the subinterval to [0.04, 0.08], 0.056, 0.072, and so on.
The range is narrowed to [0.06752, 0.0688) when the last message sign is
used as a specific end -of-message indicator. Of fact, the message can be
represented by any number within this subinterval, such as 0.068.

Fig 4: Encoding Sequence
8.6 DICTIONARY BASED COMPRESSION
This method is not statistically based. The characteristic of this strategy is
that it is fast and adaptable. The dictionary based compres sion replaces
input strings with a code to an entry in a dictionary. The Lempel -Ziv-
Welch (LZW) algorithm is the most well -known dictionary -based
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159 8.7 LEMPEL -ZIV-WELCH (LZW) ALGORITHM
Lempel -Ziv-Welch (LZW) is an error -free compression approach. T his
technique assigns fixed -length code words to variable length sequences of
source symbols. LZW coding is distinguished by the fact that it does not
require prior information of the probability of occurrence of the symbols
to be encoded. GIF, TIFF, and P DF are just a few of the popular image file
formats that have LZW compression built in.
For Example:
The grey values 0, 1, 2,..., and 255 are assigned to the first 256 words in
the diction ary for 8 -bit monochrome images . As the encoder sequentially
examine s the image's pixels, gray - level sequences that are not in the
dictionary are placed in algorithmically determined (e.g., the next unused)
locations. If the first two pixels of the image are white, for instance,
sequence ―255 - 255 might be assigned to lo cation 256, the address
following the locations reserved for gray levels 0 through 255. The next
time that two consecutive white pixels are encountered, code word 256,
the address of the location containing sequence 255 -255, is used to
represent them. If a 9-bit, 512 -word dictionary is employed in the coding
process, the original (8 + 8) bits that were used to represent the two pixels
are replaced by a single 9 -bit code word.
Consider the following 4 x 4, 8 -bit image of a vertical edge: -

Figure 5 detail s the steps involved in coding its 16 pixels. A 512 -word
dictionary with the following starting content is assumed:


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160 Locations 256 through 511 are initially unused. The image is encoded by
processing its pixels in a left -to-right, top -to-bottom manner. Each
successive gray -level value is concatenated with a variable —column 1 of
Figure 6 called the "currently recognized sequence." As can be seen, this
variable is initially null or empty. The dictionary is searched for each
concatenated sequence and if found, as was the case in the first row of the
table, is replaced by the newly concatenated and recognized (i.e., located
in the dictionary) sequence. This was done in column 1 of row 2.

Fig 6: Currently recognized sequence
8.8 TRANSFORM BASED COMPRESSION
Transform coding is performed by taking an image and breaking it down
into sub -image (block) of size nxn. The transform is then applied to each
sub-image (block) and the resulting transform coefficients are quantized
and ent ropy coded, divides an image into small non -overlapping blocks of
equal size (e.g., 8 * 8) and and using 2 -D transform it processes the block
of image independently. To map each block of images into a set of
transform coefficients the block transform codin g uses linear transform. A
significant number of coefficients with small magnitudes can be quantized
for most images.
Typical blocks transform coding system

Fig 7: Typical blocks transform coding system
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161
9
IMAGE COMPRESSION STANDARDS
9.1 JPEG (JOINT PHOTOGRAPH EXPERT GROUP)
JPEG is a lossy image compression standard, which means that some
details may be lost when the image is restored from the compressed data.
JPEG is designed for full -color or grayscale imag es of natural scenes. It
works very well with photographic images. JPEG does not work as well
on images with sharp edges or artificial scenes such as graphical drawings,
text documents, or cartoon pictures. A product or system must support the
basic system in order make JPEG compatible. The precision in baseline of
the input and output data is limited to 8 bits, while the quantized DCT
values are limited to 11 bits. The compression method involves three steps
first one DCT computation second being Quantizat ion and final is
variable -length code assignment. The image is firstly segmented into 8 -bit
pixel blocks, which are processed from left to right and top to bottom.
Working of JPEG compression
Steps and Example: -
First step is to divide an image into bloc ks with each having dimensions of
8 x8. Unit Structure
9.1 JPEG (Joint Photograph Expert Group)
9.2 MPEG (Moving Picture Expert Group)
9.3 Vector Quantization
9.4 Wavelet based image compression
9.5 Morphological Operation
9.6 References
9.7 Moocs
9.8 Video links
9.9 Quiz
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162

Fig 8: Working of JPEG Compression
Let’s for the record, say that this 8x8 image contains the following values.

The range of the pixels intensities now are from 0 to 255. In order to
change the range from -128 to 127, it is required to subtract 128 from each
pixel value, we got the following results.


Now we will compute using this formula.

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163

The result comes from this is stored in let’s say A(j,k) matrix.
This matrix is given b elow: -

Applying the following formula

We got this result after applying.

Now ZIG -ZAG movement is performed on above matrix, whose sequence
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164


9.2 MPEG (MOVING PICTURE EXPERT GROUP)
MPE G is a method for video compression, which involves the
compression of digital images and sound, as well as synchronization of the
two. It also compress the sound track associated with the video. Algorithm
used for MPEG compress the data into small bits fo r easy transmission
and decompression and using “Discrete Cosine Transform” it can be
encoded. MPEG simply store the change that has been made to the
frames, so MPEG has high compression rate.
There currently are several MPEG standards: -
 MPEG -1 is design ed for moderate data speed of up to 1.5 megabits per
second.
 MPEG -2 is designed for high data speed of up to 10 Mbit/sec approx.
 MPEG -3 is designed for HDTV compression, but turned out to be
redundant and integrated with MPEG2.
 MPEG -4 is designed for very low data rates less than 64 Kbit/sec.
i. A video is a temporal combination of frames, and a frame is a spatial
combination of pixels..
ii. Compressing video, then, means spatially compressing each frame and
temporally compressing a set off names.
iii. Spat ial Compression: The spatial compression of each frame achieved
with JPEG. Each frame can be independently compressed.
iv. Temporal Compression: In this type of compression, redundant frames
are removed.
v. In temporally compress data, the first of all fra mes are divided into
three categories by MPEG method
vi. I-frames, P -frames, and B -frames. Figure1 shows a sample sequence
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165 vii. Figure2 shows how I -, P-, and B -frames are constructed from a
series of seven frames.

Fig 9: MPEG frames

Fig 10: MPEG frame construction
I-frames : An inter frame (I -frame) is an independent frame i.e. different
from other frame. This frame must appear handle some sudden change in
the frame occasionally. A viewer can tune at any instance of time
whenever a vi deo is relayed. In case viewer tunes late, the viewer will not
receive a complete picture at beginning of the broadcast.
P-frames: A predicted frame (P -frame) is related to the preceding I -frame
or P-frame. In other words, each P -frame contains only the ch anges from
the preceding frame. Previous I - or P -frames are only used to construct P -
frames. As compared to other frame P -frame contains very much less
information and even fewer bits after compression.
B-frames: A bidirectional frame (B -frame) is related to the preceding and
following I -frame or P -frame. Note that a B -frame is different from
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166  The entire movie is designated a video sequence as per MPEG
standard, and each picture has three components: one luminance
component and two chrominan ce components (y, u & v).
 The luminance component contains the gray scale picture & the
chrominance components provide the color, hue & saturation.
 The MPEG decoder has three parts, audio layer, video layer, system
layer.
 The basic building block of an MPE G picture is the macro block as
shown:

Fig 11: Basic Building Block of an MPEG
 The macro block consist of 16×16 block of luminance gray scale
samples divided into four 8×8 blocks of chrominance samples.
 A macro block's MPEG compression consists of passin g each of the °6
blocks through a JPEG -like DCT quantization and entropy encoding
process.
 The MPEG standard defines a quantization stage having values (1, 31).
Quantization for intra coding is:

Where,
Q = Quantization
DCT = Discrete cosine transform

Quantization rule for encoding,
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167  The quantized numbers Q_(DCT )are encoded using non adaptive
Huffman method.
9.3 VECTOR QUANTIZATION
Vector quantization being a non -transformed compression technique, is a
powerful and efficient tool for lossy image compre ssion. The idea of
Vector Quantization (VQ) is to identify the frequently occurring blocks in
a image and to represent them as representative vector and the set of
representative vectors is known as Code Book and it is then used for
image.

Traning Set
Mapping Function M
Coding Vector
Code Book

Fig 12: Vecto r Optimization

The goal of quantization usually is to produce a more compact
representation of the data while maintaining its usefulness for a certain
purpose. For example, to store color intensities you can quantize floating -
point values in the range [0 .0, 1.0] to integer values in the range 0 -255,
representing them with 8 bits, which is considered a sufficient resolution
for many applications dealing with color. In this example, the spacing of
possible values is the same over the entire discrete set, so we speak of
uniform quantization; often, a non -uniform spacing is more appropriate
when better resolution is needed over some parts of the range of values.
Floating -point number representation is an example of non -uniform
quantization —you have the as many possible FP values between 0.1 and
1 as you have between 10 and 100.
Both these are examples of scalar quantization —the input and output
values are scalars, or single numbers. You can do vector quantization
(VQ) too, replacing vectors from a continuous (o r dense discrete) input
set with vectors from a much sparser set (note that here by vector we
mean an ordered set of N numbers, not just the special case of points in
3D space). For example, if we have the colors of the pixels in an image
represented by tr iples of red, green, and blue intensities in the [0.0, 1.0]
range, we could quantize them uniformly by quantizing each of the three
intensities to an 8 -bit number; this leads us to the traditional 24 -bit
representation.
By quantizing each component of the vector for itself, we gain nothing
over standard scalar quantization; however, if we quantize the entire
vectors, replacing them with vectors from a carefully chosen sparse non -
uniform set and storing just indices into that set, we can get a much more
comp act representation of the image. This is nothing but the familiar
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168 possible quantized values for the vectors is called a "codebook," because
you need it to "decode" the indices int o actual vector values.
Figure 13 shows the result of this procedure applied to a grayscale
version of the famous "Lena", a traditional benchmark for image -
compression algorithms.

Fig 13: Grey Scale Version
The diagonal line along which the density of th e input vectors is
concentrated is the x = y line; the reason for this clustering is that "Lena,"
like most photographic images, consists predominantly of smooth
gradients. Adjacent pixels from a smooth gradient have similar values,
and the corresponding d ot on the diagram is close to the x = y line. The
areas on the diagram which would represent abrupt intensity changes
from one pixel to the next are sparsely populated.

Fig 14: Distribution of pairs of adjacent pixels from gray scale
If we decide to re duce this image to 2 bits/pixel via scalar quantization,
this would mean reducing the pixels to four possible values. If we
interpret this as VQ on the 2D vector distribution diagram, we get a
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169

Fig 15: Scalar quantization to 2 bit s/pixel interpreted as 2D VQ.
The big red dots on the figure represent the 16 evenly spaced possible
values of pairs of pixels. Every pair from the input image would be
mapped to one of these dots during the quantization. The red lines delimit
the "zones o f influence," or cells of the vectors —all vectors inside a cell
would get quantized to the same codebook vector.
Now we see why this quantization is very inefficient: Two of the cells are
completely empty and four other cells are very sparsely populated. T he
codebook vectors in the six cells adjacent to the x = y diagonal are shifted
away from the density maxima in their cells, which means that the
average quantization error in these cells will be unnecessarily high. In
other words, six of the 16 possible p airs of pixel values are wasted, six
more are not used efficiently and only four are O.K.
Let's perform an equivalent (in terms of size of resulting quantized
image) vector quantization. Instead of 2 bits/pixel, we'll allocate 4 bits per
2D vector, but now we can take the freedom to place the 16 vectors of the
codebook anywhere in the diagram. To minimize the mean quantization
error, we'll place all of these vectors inside the dense cloud around the x =
y diagonal.

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170 Figure 16 shows how things look with VQ. As in Figure 3, the codebook
vectors are represented as big red dots, and the red lines delimit their
zones of influence. (This partitioning of a vector space into cells around a
predefined set of "speci al" vectors, such as for all vectors inside a cell the
same "special" vector is closest to them, is called a Voronoi diagram; the
cells are called Voronoi cells. You can find a lot of resources on Voronoi
diagrams on the Internet, since they have some inte resting properties
besides being a good illustration of the merits of VQ.)
You can see that in the case of VQ the cells are smaller (that is, the
quantization introduces smaller errors) where it matters the most —in the
areas of the vector space where the i nput vectors are dense. No codebook
vectors are wasted on unpopulated regions, and inside each cell the
codebook vector is optimally spaced with regard to the local input vector
density.
When you go to higher dimensions (for example, taking 4 -tuples of pix els
instead of pairs), VQ gets more and more efficient —up to a certain point.
How to determine the optimal vector size for a given set of input data is a
rather complicated question beyond the scope of this article; basically, to
answer it, you need to stu dy the autocorrelation properties of the data. It
suffices to say that for images of the type and resolution commonly used
in games, four is a good choice for the vector size. For other applications,
such as voice compression, vectors of size 40 -50 are use d.
9.4 WAVELET BASED IMAGE COMPRESSION
Wavelet compression is a form of data compression well suited for image
compression (sometimes also video compression and audio compression).
Notable implementations are JPEG 2000, DjVu and ECW for still images,
Cine Form, and the BBC's Dirac. The goal is to store image data in as little
space as possible in a file. Wavelet compression can be either lossless or
lossy. Using a wavelet transform, the wavelet compression methods are
adequate for representing transients, s uch as percussion sounds in audio,
or high -frequency components in two -dimensional images, for example an
image of stars on a night sky. This means that the transient elements of a
data signal can be represented by a smaller amount of information than
woul d be the case if some other transform, such as the more widespread
discrete cosine transform, had been used.
Figure 17 shows a typical wavelet coding system. The various parameter
such as an analyzing wavelet, c, and minimum decomposition level, J - P,
are selected in order to encode a 2J 2J image. It is suitable to use fast
wavelet transform, if the wavelet has a complementary scaling function w.
In any of the case, a large portion of the original image is converted to
vertical, horizontal, and diagona l decomposition by this transform. Many
of the calculated coefficients contain very little visual information and can
be quantized and coded to minimize redundancy. Moreover, to exploit any
positional correlation across the P decomposition levels the quant ization
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Fig 17: shows a typical wavelet coding system
9.5 MORPHOLOGICAL OPERATION
Morphological image processing is a collection of non -linear operations
related to the shape or morphology of features in an image. Morphological
operations r ely only on the relative ordering of pixel values, not on their
numerical values, and therefore are especially suited to the processing of
binary images. Morphological operations can also be applied to grey scale
images such that their light transfer funct ions are unknown and therefore
their absolute pixel values are of no or minor interest.

Morphological techniques probe an image with a small shape or template
called a structuring element . The structuring element is positioned at all
possible locations i n the image and it is compared with the corresponding
neighborhood of pixels. Some operations test whether the element "fits"
within the neighborhood, while others test whether it "hits" or intersects
the neighborhood:



Fig 18: Structurin g Element

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172 Dilation: -
Dilation expands the image pixels for given element A by applying
structuring element B. The equation of this operator is defined as

A= Object to be dilated.
B=Structuring element.
Steps to perform
a) Fully match = 1
b) Some match = 1
c) No match = 0
Example
Given image A

Structuring element B

Output

Erosion
Erosion shrinks the image pixels for shrinking an element A by applying
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173

A= Object to be Eroded. B=Structuring element.
Steps to perform
a) Fully match = 1
b) Some match = 0
c) No match = 0
For Example
Given image A

Structuring element B

Output

Opening
Opening generally smoothes the contour of an object, breaks narrow
isthm uses, and eliminates thin protrusions.
The opening of set A by structuring element B, denoted by A
B, is defined
as: -
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174 So, here an erosion followed by a dilation.
For Example
Set A

Structuring Element B

Output

Closing
Closing tends to smooth sections of contours but it generates fuses narrow
breaks and long thin gulfs, eliminates small holes, and fills gaps in the
contour.
The closing of set A by structuring element B, denoted by A
B, is defined
as: -

So, here dilation followed by a erosion.
For Example
Set A
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175 Structuring Element B

Output

9.6 REFERENCES
1. Pratt WK. Introduction to digital image processing. CRC press; 2013
Sep 13.
2. Niblack W. An introduction to digi tal image processing. Strandberg
Publishing Company; 1985 Oct 1.
3. Burger W, Burge MJ, Burge MJ, Burge MJ. Principles of digital image
processing. London: Springer; 2009.
4. Jain AK. Fundamentals of digital image processing. Prentice -Hall,
Inc.; 1989 Jan 1.
5. Dougherty ER. Digital image processing methods. CRC Press; 2020
Aug 26.
6. Gonzalez RC. Digital image processing. Pearson education india;
2009.
7. Marchand -Maillet S, Sharaiha YM. Binary digital image processing: a
discrete approach. Elsevier; 1999 Dec 1.
8. Andrews HC, Hunt BR. Digital image restoration.
9. Lagendijk RL, Biemond J. Basic methods for image restoration and
identification. InThe essential guide to image processing 2009 Jan 1
(pp. 323 -348). Academic Press.
10. Banham MR, Katsaggelos AK. Digital image restoratio n. IEEE signal
processing magazine. 1997 Mar;14(2):24 -41. munotes.in

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176 11. Hunt BR. Bauesian Methods in Nonkinear Digital Image Restoration.
IEEE Transactions on Computers. 1977 Mar 1;26(3):219 -29.
12. Figueiredo MA, Nowak RD. An EM algorithm for wavelet -based
image restoratio n. IEEE Transactions on Image Processing. 2003 Aug
4;12(8):906 -16.
13. Digital Image Processing – Tutorialspoint.
https://www.tutorialspoint.com/dip/index.htm .
14. Types of Restoration Filters. https://www.geeksforgeeks.org/types -of-
restoration -filters/ .
9.7 MOOCS
1. Fundamentals of Digital Image and Video Processing. Coursera.
https://www.coursera.org/lecture/digital/mpeg -4-qYxK2
2. Moving Pictures Expert Group (MPEG) Video. SCTE.
https://www.scte.org/edu cation/course -offerings/course -
catalog/moving -pictures -expert -group -mpeg -video/
3. Huffman Coding. Coursera.
https://www.coursera.org/lecture/digital/huffman -coding -0CZoy
4. Morphology . Udemy. https://www.udemy.com/course/morphology/
9.8 VIDEO LINKS
 Fundamentals of Digital Image and Video Processing with Aggelos
Katsaggelos.
https://www.youtube.com/watch?v=6dJ6pitbuXE&list=PL3vl1rb9fAc
LA7F38Qd9cqTuBNA20HclY
 Huffman Coding (Easy Example) | Image Compression | Digital Image
Processing. https://www.youtube.com/watch?v=acEaM2W -Mfw
 Arithmetic encoding Digital Image Processing.
https://www.youtube.com/watch?v= -vvgd87antk
 Image Compression Models | Digital Image Processing.
https://www.youtube.com/watch?v=K807Ezea_GY
 LZW Coding | Digital Image Processing.
https://www.youtube.com/watch?v=2FjOJMelZe0 .
 How Image Co mpression Works.
https://www.youtube.com/watch?v=Ba89cI9eIg8

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177 9.9 QUIZ
1. Compressed image can be recover back by
(A) Image contrast
(B) Image enhancement
(C) Image equalization
(D) Image decomposition
Answer: D

2. What is the meaning of information ?
(A) Data
(B) Raw data
(C) Meaningful data
(D) None of these
Answer: C

3. Sequence of digital video is
(A) Frames
(B) Pixels
(C) Coordinates
(D) Matrix
Answer: A

4. What would you use compression for
(A) Making an image file smaller
(B) Modifying an image
(C) Both
(D) None of the above
Answer: A

5. Which of the following algorithms is the best approach for solving
Huffman codes?
(A) Brute force algorithm
(B) Greedy algorithm
(C) Exhaustive search
(D) Divide and conquer algorithm
Answer: B

6. What is the runn ing time of the Huffman encoding algorithm?
(A) O(log C)
(B) O(C)
(C) O(C log C)
(D) O(N log C)
Answer: C

7. Digitizing the image intensity amplitude is called
(A) Framing
(B) Sampling
(C) Quantization
(D) None of the above
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178 8. Image compression comprised of
(A) Encoder
(B) Decoder
(C) Frames
(D) Both A and B
Answer: D

9. What is the full form of RLE ?
(A) Run line encoder
(B) Run length electrode
(C) Run length encoding
(D) None of the above
Answer: C

10. Which bitmap file format support the R un length encoding ?
(A) BMP
(B) PCX
(C) TIF
(D) All of the above
Answer: D

11. In Huffman coding, data in a tree always occur?
(A) Roots
(B) Leaves
(C) Left sub trees
(D) Right sub trees
Answer: B

12. Which of the following of a boundary is defined as t he line
perpendicular to the major axis?
(A) Minor axis
(B) Median axis
(C) Equidistant axis
(D) Equilateral axis
Answer: C

13. The order of shape number for a closed boundary is:
(A) Even
(B) Odd
(C) 1
(D) Any positive value
Answer: A

14. Which of the f ollowing techniques of boundary descriptions have the
physical interpretation of boundary shape
(A) Laplace transform
(B) Fourier transform
(C) Statistical moments
(D) Curvature
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179
15. What does the total number of pixels in the region defines?
(A) Area
(B) Intensity
(C) Brightness
(D) None of the above
Answer: A

16. For which of the following regions, compactness is minimal?
(A) Square
(B) Irregular
(C) Disk
(D) Rectangle
Answer: C

17. On which of the following operation of an image, the topology of the
region changes?
(A) Rotation
(B) Folding
(C) Stretching
(D) Change in distance measure
Answer: B

18. Which of the following techniques is based on the Fourier transform?
(A) Spectral
(B) Structural
(C) Topological
(D) Statistical
Answer: A

19. Ba sed on the 4 -directional code, the first difference of smallest
magnitude is called as:
(A) Chain number
(B) Difference
(C) Difference number
(D) Shape number
Answer: D

20. What is the unit of compactness of a region?:
(A) Meter
(B) Meter2
(C) Meter -1
(D) No units
Answer: D

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180 Module VI
10
APPLICATIONS OF IMAGE PROCESSING
10.1 CASE STUDY ON DIGITAL WATERMARKING
Digital watermarking is a technology that embeds data into digital
multimedia content, verifying content reliability and is used to reco gnize
owner ID [1].
Digital watermarks hide copyright information in digital data through
specific algorithms. The secrecy information embedded is some text,
author number, company logo, especially important photos. This secret
information is embedded in digital dat a (image, audio, and video) to
ensure security, data authentication, owner identification, and copyright
protection. The watermark is either display or visible to digital data. You
need to apply good water sharing technology to strongly embed th e
watermark . Fig 1. shows Digital Watermark embedding process and Fig.
2. shows watermark detection process.

Fig 1: Watermarking embedding process [2]
Unit Structure
10.1 Case Study on Digital Watermarking
10.2 Digital watermarking techniques: A case study in fingerprints
and faces
10.3 Vehicle Registration Number Plate Detection and Recognition
using Ima ge Processi ng Techniques
10.4 Object Detection using Correlation Principle

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181

Fig 2: Watermark Detection Process [2]
Digital watermarking process (Life cycle) [3]:
The process co nsists of 3 main parts:
1. Embed
2. Attack
3. Protection
Embed : Embedded with the digital watermark.
Attack : Any change in the transmitted content, it becomes a threat and is
called an attack to the watermarking system.
Protection : The detection of the watermark f rom the noi sy signal which
might have altered media is called Protection.
Types of Watermarks [3]:
1. Visible Watermarks
2. Invisible Watermarks
3. Public Watermarks
4. Fragile Watermarks
Visible Watermarks: These are visible in nature.
Invisible Watermarks: These are invisible but are embedded in the
media and use steganography technique.
Public Watermarks: These can be modified using certain algorithms by
anyone and are not secure.
Fragile Watermarks: These are said to be destroyed as data manipulation
occurs, need t o use a sys tem as to detect the changes occurred to the data,
if fragile watermarks are used.

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182 Digital watermarking is used for numerous purposes including [1 -2]:
 Broadcast Monitoring
 Ownership Assertion
 Transaction Tracking
 Content Authentication
 Copy C ontrol and Fingerprinting

Types of digital watermarking [1]:
 Visible Digital Watermarking
 Invisible Digital Watermarking

Visible Digital Watermarking: It is embedded as the watermark and can
be used as a logo or as a text representing the owner [1].

Invisible Dig ital Watermarking: The data embedded is invisible.
Example 1: Audio is inaudible in case of an invisible audio content.
Example 2: Image/text is not visible in the case of an invisible text/image/
multimedia content.


Fig 3: (a) Original fi ngerprint i mage (b) Watermarked fingerprint image

10. 2 DIGITAL WATERMARKING TECHNIQUES: A
CASE STUDY IN FINGERPRINTS AND FACES

The purpose of watermarks is two -fold:
(i) Used to determine ownership, and
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183
There are essential char acteristics that a watermark must have and must be
detectable. To determine ownership, it is required to be able to retrieve the
watermark. There are basically two mechanisms by which a watermark
can be retrieved. The incomplete watermark can only be resto red if the
original image is present. The full watermark can be retrieved
independently. Full watermarks are more desirable as they apply to more
applications. When watermarking large files or a large number of files in a
database, full watermarks are pref erred becau se they avoid storing
multiple copies of the original file. Second, the watermark should be
robust to many different types of signal processing. If the watermark is not
strong, it will be useless as the assets will be lost during processing.
Having some bu ilt-in fragile features can sometimes be helpful. If fragile
watermarks are used and the data is altered, the watermark can identify
areas that have been altered. Fragile watermarks can detect minor changes
or tampering of data. On the other han d, strong w atermarks are useful for
detecting large -scale attacks on data.

Various watermark schemes have been developed. One of the first
watermarking algorithms was to manipulate the least significant bit (LSB)
of pixels in the spatial domain [6]. The re are many ways to apply LSB
schemes where all LSBs can be changed or a random set of LSBs can be
changed. These diets are especially helpful because of their fragility. If a
person modifies an image, it is more likely that the LSB will also be
modified. Unfortunate ly, it is this fragility that can cause a host of other
problems. It deletes all watermarks. If enough LSB is changed, the
watermark will be unrecoverable. Furthermore, it is possible to modify the
image without changing the LSB. If this is done , the water mark is
essentially useless, as it cannot be used for tampering detection.

In general, spatial (pixel) domain schemas are too fragile to withstand an
attack. Resulting in the development of solutions in the frequency domain.
There are two gener al algorith ms in the frequency domain, a spreading
method and a block method. Basically, the DCT of the entire image is
captured and a watermark is applied to the preselected frequencies. If the
DCT image is represented by V(j,k) and the watermark is W(j,k ), then the
watermark is V*(j,k) = V(j,k) + αW(j,k) , where W(j, k) is normally
distributed and α is a scale parameter. In the simplified version of the
method, the value of alpha is fixed at 0.1. For better results, α can be
inferred from the JND (just a notable di fference) matrix. The JND matrix
containing the mean can be added to each pixel without causing noticeable
perceptual changes in image.

DCT block method is another method used. It is similar to the spectral
spectrum method, but instead of taking the DCT o f the entire image, the
DCT is taken for 8x8 blocks (or 16x16). This method allows the position
of the fuzzy. It also has the advantage because it is compatible with
relevant compression techniques such as MPEG. It can be built directly in
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184 separately for each image segment; It's easier to remove this type of
watermark.

With the popularity of JPEG format, the development of strong
compression watermarks is a major concern. There are some po werful
filigree algorithms with compression. In these modes, watermarks are
often inserted into the frequency field of compressed images. When the
watermark is placed in uncompressed images, the watermark can be
broken during the compression process. In fa ct, it can be so damaged that
it's unrecognizable. But by inserting the watermark into the compressed
frequency domain, the compression will have little effect on the
watermark. By placing multiple watermarks in the same image, the ability
to determine if the image has been tampered with and where the image has
been tampered with increases. Usually, two watermarks are placed in one
image. One of the watermarks has powerful image processing capabilities,
and the other watermark accurately detects small chang es in the image
(i.e. fragility). In previous studies, a watermark was inserted into the
frequency domain (watermark) as well as in the Pixel field (Watermark
fragile). There are a number of disadvantages for this type of diagram,
because two odds are ins erted, there is no maximum value possible at its
maximum value. Required is their intensity at scale. Also, when inserting
watermarks, it is essential to first insert Filigree powerful. If the fragile
fuzz is inserted first, then as soon as the watermark is definitely inserted,
the fragile watermark will detect Alleviant change!

Proposed Technique

A number of different watermarking schemes are in use today, for each
there is a simple mechanism to detect fraud and determine ownership.
There are times whe n an image owner wants to pass an image on to
someone else. In this case, how can the recipient ensure that the received
image is not corrupted? It is clear that some keys must be used. At the
most basic level, you can use a watermark or an original image as a key.
But either way would be a bad choice. A watermark is similar to a PIN or
password. Granting access to others can be detrimental as they can take
ownership of your images and remove them. Sending the original image
itself defeats the purpose of th e watermark. This is because the recipient
can now transfer ownership by watermarking another watermark on the
original image. Ideally, the key used should be unique for each image.
This will prevent smart hackers from attacking you. An idea that comes to
mind is block characterization of the image. One potential key you can use
is the regional mean matrix. The local average of the transferred images is
computed as a 5x5 block and can be used as a key. The receiver can
compare the key to a set of local aver ages computed over the received
images. This makes it easy to verify the authenticity of an image. This key
is attractive in that it is a fraction of the size of the original image,
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185

Fig 4: Wat ermarking Technique

The local average technique was used to detect image tampering in
different scenarios:
(i) smudging,
(ii) compression, and
(iii) Wiener filtering for a number of images.
An executable was passed to allow the receiver to generate a key for the
image and compare it with the real key. The keys are essentially an
exaggerated version of the local 5x5 average block. Magnification makes
it easy to detect small differences, allowing activities such as compression
to be detected. A threshold must be establ ished that must be a function of
the key's magnification. Smudging is a type of image damage that has
been investigated. It is easily detected in fingerprints and faces using a
local mean -based key. Looking at the actual key and the key generated, it's
almost clear where the change happened. But if he is not convinced, the
user can compare the keys numerically and locate the modified image and
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Fig 5: Detecting smudging in a fingerprint image. Figure (c) shows a
magnified version of the area that was smudged. The original can be
seen in figure (a). Figures (b) and (d) show the keys for figures (a) and
(b), respectively

Conclusion
Watermarking biometric information may be a still a comparatively new
issue, however it's of growing importance as a l ot of sturdy strategies of
verification and authentication are being used. Biometrics give the
mandatory distinctive characteristics but their validity should be ensured.
A receiver can't perpetually confirm whether or not or not she has received
the right data while not the sender giving her access to important data like
watermark. The key projected here is one amongst several potential
methods. The native average theme creates a semi -unique key for every
data set transmitted and so is tougher to tamper wi th. It conjointly has the
flexibility to pin -point wherever meddling has occurred up to a small pixel
window and information security will be assured in databases similarly as
in transmission. However, it's solely a semi -unique key. It’s do able to
change the image however retain constant key, because the average isn't
perpetually the simplest tool for characterizing data. A non -linear
mechanism may well be more sensitive to small changes and are a few
things that might be investigated. One major flaw in ou r methodology is
its inability to notice whether or not the alterations within the image are
because of channel distortions and noise or actual tampering by an
individual. Generally the transmission noise may be a perform of the
encryption theme employed, and at alternative times it's a function of the
channel itself. However, having how to work out whether or not the
“tampering” is that the results of noise or a malicious attack would be
useful. As for the noise to be seen as tampering, it should be sturdy
enough to start out disrupting the image and from that time on that may be
understood as an accidental attack. Another potential drawback is the
“disgruntled worker” attack. If a discontented employee has access to the
executable, then it is straightforwa rd to form the possible perpetually
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187 Similarly, the executable may be altered in order that it provides
systematically negative responses. a technique to try and do thus would be
to intro duce a random perform that operates in conjunction with the
executable, so that for example, a 5x5 native average key's not the sole
possibility.

10.3 VEHICLE REGISTRATION NUMBER PLATE
DETECTION AND RECOGNITION USING IMAGE
PROCESSING TECHNIQUES [6]
The ob jective of the proposed work is the application of new techniques of
image segmentation and other processing techniques in the context of the
identification and production of license plates. The prerequisite is that the
plates are in the following format: TS 16 EX 5679, where the first two
characters indicate the registration State of the vehicle. First, the license
plate region (the region of interest) must be located and extracted from the
larger image of the acquired vehicle.
In this work, different i mage processing techniques are used in the pre -
processing phase, namely morphological transformation, Gaussian
smoothing, Gaussian threshold. Then, for plate segmentation, the outlines
are applied following the edge and the outlines are filtered based on font
size and location space. Finally, after the region of interest filtering and
straightening area, the Knearest neighborhood algorithm is used for
character recognition.The main contributions of this work are the design
of an Indian vehicle license pla te detection and recognition system using
an image processing system to address the following challenges:Dealing
with varying illuminated images.
 Dealing with bright and dark objects
 Dealing with noisy images.
 Dealing with non -standard number plates
 Dealin g with cross -angled or skewed number plates
 Dealing with partially worn our number plates.

Methodology

The proposed methodology consisting of three major phase’s viz., pre -
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188

Fig 6: The propos ed number plate recognition system

PRE -PROCESSING
The input can be an image or a video. Video is considered as a series of
frames/frames, before starting license plate detection, the image source
must be matched for further processing. Figure 7(a) is th e example input
image used to show the process. Here is the order in which the image
processing techniques are applied:Image Under -Sampling
 RGB to HSV Conversion
 Grayscale extraction
 Morphological transformations
 Gaussian Smoothing
 Inverted Adaptive Gaussi an Thresholding
At the end of the previous stage of image pre -processing, Inverted
Adaptive Gaussian Thresholding, returns a binarized image, with values of
either 0 or 255.

Training the model
The K Nearest Neighbors (KNN) algorithm was used to train the model.
Many other models like Decision Tree, Gradient Boosting have been
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189 hyper -parameters for the model, a random search was used. Randomized
search is an optimized version of param eter sweep or grid search, in which
a rigorous search is performed from a manually formed space of a subset
of hyper -parameters belonging to the learning algorithm. Performance
metrics are used in the guidance of grid search such as, cross -validation of
the training -set or evaluation of the validation -set. The parameter space
explored by grid search and random search is the same. Setting the
parameters is quite similar; however the execution time in case of
randomized search is much shorter.
Before savin g the given character/font, it is transformed to a standard size
of 20 x 30 pixels. This ensures the consistency of model inputs. Figure
7(a) shows the characters used and Figure 7(b) depicts the extracted
images for the specified character 'P'.

Fig. 7. (a) Fonts used for training; (b) Extracted images for a the letter
‘P’
Results and discussion
The experiments were conducted on a Windows 10 machine with 8 GB of RAM
and an i5 processor running at 2.4 GHz frequency. The OpenCV Python
library is used to imp lement image processing tools. System testing was
performed with photos and videos. All of the above cases, such as
irregularly illuminated plates, stylized fonts, close -up plates, far away
plates are considered part of the testing including images with di fferent
environmental conditions. Figure 8 (a) shows an image for testing the
case of irregular and small number plates. Figure 8 (b) shows a case of
partially worn -out and a standard number plate.
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190

Fig. 8. (a) Irregular illumination and small number pl ate; (b) A
partially worn out number plate; (c) standard number plate

CONCLUSION

The job involves detecting number plates and recognizing the number
plate, involving the number of Indian vehicles or number plates. The main
contributions of this work inc lude: taking into account difficult situations
such as light changes, blur, asymmetrical, noisy, no standard images and
partial worn plates. In this job, first, some image processing techniques,
morphological changes, Gaussian smoothing, the Gaussian thres hold is
used in the pre -handling period. Then, for the segment of the number
plate, the borders are applied at the next boundary and the contours are
filtered according to the size of the character and space location. Finally,
after filtering and transform ing areas of interest, neighborhood algorithms
are used to recognize the characters.

10.4 OBJECT DETECTION USING CORRELATION
PRINCIPLE [7]

The problem definition of object detection is to determine where objects
are located in a given image and which cat egory each object belongs to.
So the pipeline of traditional object detection models can be mainly
divided into three stages:
 Informative region selection,
 Feature extraction and
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191

Fig 9: The application domains of object detection [7].

Deep Neural Networks (DNNs), more profitable to introduce regions with
CNN (RCNN) functions. DNNs, or most typical CNNs, operate quite
differently from traditional approaches. They have deeper architectures
with the ability to learn more complex feature s than shallower ones. In
addition, expressiveness and powerful training algorithms make it possible
to learn information object representations without manually designing
features.
Deep learning has been popular since 2006 with a breakthrough in speech
recognition. The recovery of deep learning can be attributed to the
following factors.
1. The emergence of large -scale annotated training data, such as
ImageNet, to fully demonstrate its enormous learning capacity;
2. The rapid development of high -perfor mance parallel computing
systems, such as GPU clusters;
3. ignificant advances in the design of network structures and training
strategies. With unsupervised and layer wise pre -training guided by
Auto -Encoder (AE) or Restricted Boltzmann Machine (RBM), a good
initialization is provided.
CNN advantages against traditional methods are summarized as follows.
Hierarchical feature representation, which is the multilevel representations
from pixel to high -level semantic features learned by a hierarchical multi -
stage structure, can be learned from data automatically and hidden factors
of input data can be disentangled through multi -level nonlinear mappings.
Compared with traditional shallow models, a deeper architecture provides
an exponentially increased expres sive capability.
The CNN architecture provides an opportunity to optimize numerous
related tasks jointly. munotes.in

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192 Benefitting from the large learning capacity of deep CNNs, some classical
computer vision challenges can be recast as high -dimensional data
transform problems and solved from a different viewpoint.
Due to these advantages, CNN has been widely applied into many
research fields, such as image super -resolution, reconstruction, image
classification, image retrieval, face recognition, pedestrian detection and
video analysis.
Region Proposal Based Framework
Region -proposal -based framework, a two -step process, corresponding to
some degree for the human brain's attention mechanism, which first
provides a rough analysis set about the entire scenario, then focu s on
regions of interest. Among the works related to the earlier, the most
typical is Overfeat. This model inserts CNN into the sliding window
method, which predicts the bounding boxes directly from the top positions
of the feature map after obtaining the confidants of confidences of
underlying object categories.
RCNN: It is important to improve the quality of candidate bounding boxes
and apply a deep architecture to extract high -level functionality. To
address these issues, RCNN was proposed by Ross Girshi ck in 2014 and
achieved a mean average accuracy (mAP) of 53.3% with an improvement
of more than 30% over the previous best. (DPM HSC) on PASCAL VOC
2012. Figure 10 shows the flowchart of the RCNN, which can be divided
into three phases as follows.
Region p roposal generation
The RCNN uses a selective search to generate approximately 2,000 region
proposals for each image. The selective search method relies on simple
bottom -up clustering and salience indices to quickly provide more
accurate candidate boxes of arbitrary size and to reduce the search space in
object detection. feature extraction. At this point, each proposed region is
warped or cropped to a fixed resolution and the CNN module is used to
extract a 4096 dimensional feature as the final representa tion. Due to the
high learning capacity, dominant expressive power and hierarchical
structure of CNNs, it is possible to obtain a high -level, semantic and
robust representation of the features of each proposed region.
Classification and localization
With pre -trained linear category -specific SVMs for multiple classes, the
different region proposals are evaluated against a set of positive regions
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Processing
193

Fig 10: R -CNN – Regions with CNN features
Face detection is essential for many facial applications and serves as an
important pre -processing procedure for face recognition, face synthesis
and facial expression analysis.Unlike general object detection, this task
involves recognizing and locating regions of the face that cover a v ery
wide range of scales (30,300 points versus 101,000 points). ; impose great
challenges in real applications. The most famous facial detector proposed
by Viola and Jones trains cascade classifiers with HaarLike and AdaBoost
features, achieving good perf ormance with real -time efficiency. In contrast
to this cascading structure, Felzenszwalb et al. proposed a deformable part
model (DPM) for face detection. However, for these traditional face
detection methods, high computational costs and large amounts of
annotations are required to achieve a reasonable result. Moreover, their
performance is severely limited by hand -designed features and surface
architecture.
Despite rapid development and promising advances in object detection,
there are still many open q uestions for future work. The first is the
detection of small objects as done in the COCO dataset in the face
detection activity. To improve the localization accuracy on small objects
in case of partial occlusions, it is necessary to modify the network
architectures of the following aspects.
 Multi -task joint optimization and multi -modal information fusion.
 Scale adaption
 Spatial correlations and contextual modeling
The second one is to release the burden on manual labor and accomplish
real-time object det ection, with the emergence of large -scale image and
video data. The following three aspects can be taken into account.
Unsupervised and weakly supervised learning
The third one is to extend typical methods for 2D object detection to adapt
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194 from autonomous driving, intelligent transportation and intelligent
surveillance.
 3D object detection
 Video object detection
CONCLUSION
Due to its powerful learning ability and advantages in dealing w ith
occlusion, scale transformation and background switches, deep learning
based object detection has been a research hotspot in recent years. Review
starts with generic object detection pipelines which provide base
architectures for other related tasks. T hen, three other common tasks,
namely salient object detection, face detection and pedestrian detection,
are also briefly reviewed. Finally, several promising future directions to
gain a thorough understanding of the object detection landscape have been
expressed. This section is meaningful for the developments in neural
networks and related learning systems, providing valuable insights and
guidelines for future progress.


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195 11
HUMAN BODY TRACKING BASED ON
DISCRETE WAVELET TRANSFORM
Unit Structure

11.1 HUMAN BODY TRACKING BASED ON
DISCRETE WAVELET TRANSFORM [8]
A novel human body tracking system based on discrete wavelet transform
is proposed based on color and spatial information. The configuration of
the proposed tracking system is very simple, consisting of a CCD camera
mounted on a rotary platform for tracking moving objects. By using the
position information o f objects in the image frame captured by the camera,
the rotary platform is controlled to position the tracking object around the
central area of images to improve tracking efficiency.
Image tracking is getting more and more popular over the past years
because of the advancements of automation technologies and is widely
applied in surveillance systems, robot localization, human computer
interaction, etc. Researches of human -body tracking are the most attractive
one although difficulties still exist because the shapes and dynamics of
humans are complicated and the backgrounds are cluttered. Over the past
years, many applications of people tracking systems such as surveillance,
human -computer interface, people counting system, etc, have been
attempted based o n a popular method of background subtraction to
segment and track moving objects in real -time surveillance. Segmentation
methods using background subtraction, however, have difficulties in
image sequences from moving camera or sequences including
instantan eous change of illumination or shadow. 11.1 Human Body Tracking Based on Discrete Wavelet Transform
11.2 Hand written and Printed Character Recognition
11.3 A Comparative Study of Text Compression Algorithms
11.4 Performance Evaluation in Content -Based Image Retrieval:
Overview and Proposals
11.5 References
11.6 Moocs
11.7 Video links
11.8 Quiz
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196 Discrete wavelet transform
Discrete Wavelet transform has been extensively applied in the areas of
image processing, image compression, edge detection, and texture
analysis. A 2 -dimensional wavelet transform decompos es an image into 4
sub-images as shown in Fig. 11, where filters are first applied in one
dimension (e.g. X axis) and then in the other (e.g. Y axis). Because down
sampling is performed at these two stages, the size of the sub -images
becomes 1/4 as large a s the original image. Observing these four sub -
images in Fig. 12, we found that the wavelet transform preserves not only
the frequency features but also spatial ones. It can be decomposed into
four different bands (LL, HL, LH, HH) via the discrete wavelet transform.
These sub -bands contain different frequency characteristics with the use of
high-pass and low -pass filters. The high -pass filter extracts the high -
frequency portions (e.g. edges of the object). On the other hand, the low -
pass filter gives the lo w-frequency information representing the most
energy of an image and rejects the noise of an image as well. The basic
idea is to use the wavelet transform to reduce the resolution of each frame
of the sequence for reducing the computational cost. Basis wav elet
transform is used due to its simplicity and speed efficiency, where only the
low-frequency part is used for processing due to the consideration of low
computing cost and noise reduction issue. The original image of 240× 320
is pre -processed via a 2 -level discrete wavelet transform to obtain a
lowest -frequency sub -image (i.e. LL2 in Fig. 12(d)) for further processing
in the proposed tracking system. As a result, the image size of the sub -
image LL2 has been reduced to 60×80 , which represents 1/6 of the size of
the original image.

Fig 11: Two -dimensional discrete wavelet transform
The proposed human body tracking system
The objective of tracking is to closely follow objects in each frame of a
video stream such that the object position as well as other information is
always known. To overcome difficulties in achieving realtime tracking
and improving tracking efficiency, a novel colour -image real -time human
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197 camera is mounted on a rotary platform for tracking moving objects.
Procedures in tracking moving objects via the proposed approach can be
illustrated via a flowchart shown in Fig. 13.

Fig 12: (a) Original image (b) first -level DWT (c) second -level DWT
(d) sub -bands of second -level DWT

Fig 13: Flowchart of the tracking procedures
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198 Experimental results
Proposed tracking system is implemented in Windows XP PC with
Pentium 2.0G CPU, 1024MB RAM under Borland C++ builder 5 software
environment as the implementation platform. The resolu tion of each color
images is 320x240 pixels. We can achieve real -time processing at about
25 frames per second. As demonstrated satisfactory performances have
been achieved via the proposed approach.
Conclusions
With the aim at single human -body tracking, a novel colour image real -
time human body tracking system based on discrete wavelet transform is
proposed for identifying the target based on color and spatial information.
To improve tracking performances, discrete wavelet transform is used to
pre-proces s the image for reducing computations required and achieving
real-time tracking. The experiments results have shown that the proposed
tracking system is capable of realtime tracking human objects in about 25
frames per second.
11.2 HANDWRITTEN AND PRINTED CHARACTER
RECOGNITION
Indian script is collection of scripts used in the sub -continent namely
Devanagari, Bangla, Hindi, Gurmukhi, Kannada and etc. The researchers
used data that was already in an isolated form in order to avoid the
segmentation phase and are based on statistical and structural algorithms.
The results of Devanagari scripts were found to be better than English
numerals. Devanagari had a recognition rate of 89% with 4.5 confusion
rate, while English numerals had a recognition rate of 78% with confusion
rate of 18%. A modular neural network was used for script identification
while a two -stage feature extraction system was developed, first to dilate
the document image and second to find average pixel distribution in the
resulting images. The res earchers used 64 directional features based on
chain code histogram for feature recognition. The proposed scheme
resulted in 98.86% and 80.36% accuracy in recognizing Devanagari
characters and numeral, respectively. Five -fold cross -validation was used
for the computation of results. Perwej and Chaturvedi used
backpropagation based neural network for the recognition of handwritten
characters and the results showed that the highest recognition rate of
98.5% was achieved. Obaidullah et al. proposed Handwritten Numeral
Script Identification or HNSI framework based on four indices scripts,
namely, Bangla, Devanagari, Roman and Urdu. The researchers used
different classifiers, namely NBTree, PART, Random Forest, SMO,
Simple Logistic and MLP and evaluated the perfo rmance against the true
positive rate. Performance of MLP was found to be better than the rest.
Research on Indian scripts is very diverse, and a number of researchers are
involved in research on multiple scripts. This is the reason why a number
of researc h articles on character recognition of Indian scripts are growing
each year. researchers have used techniques like Tesseract OCR and
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199 Belief Network with the distributed average of gradients f eature, Modified
Neural Network with the aid of elephant herding optimization, VGG
(Visual Geometry Group) and SVM classifier with the polynomial and
linear kernel.
CEDAR
CEDAR, was developed by the researchers at the University of Buffalo in
2002 and is considered among the first few large databases of handwritten
characters. In CEDAR, the images were scanned at 300 dpi as shown in
Figure 14.

Fig 14: CEDAR dataset
CHARS74K
Chars74k dataset was introduced by researchers at the University of
Surrey in 20 09 which contains 74,000 images of English and Kannada
(Indian) scripts. Segmentation of individual characters was done manually,
and results were presented in bounding box segmentation. Bag of visual
words technique was used for object categorization, and eventually, 62
different classes were created for English and 657 classes for Kannada. A
number of researchers have used CHARS74k dataset for recognition of
Kannada script. It is to be noted that Kannada is one of many Indian
scripts we have included in t his research. There are various datasets for
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Fig 15: Sample image from CHARS74K dataset
CONCLUSION
1) Optical character recognition has been around for the last eight (8)
decades. Development of machine learning and deep learning has
enabled individual researchers to develop algorithms and
techniques, which can recognize handwritten manuscripts with
greater accuracy.
2) Systematically extracted and analyzed research publications on six
widely spoken languages. We explored that some techniques
perform better on one script than on another, e.g. multilayer
perceptron classifier gave better accuracy on Devanagri, and
Bangla numerals and gave average results for other languages.
3) Most of the publ ished research studies propose a solution for one
language or even a subset of a language.
4) It is observed that researchers are increasingly using Convolution
Neural Networks (CNN) for the recognition of handwritten and
machine -printed characters. This i s due to the fact that CNN based
architectures are well suited for recognition tasks where input is an
image.
11.3 A COMPARATIVE STUDY OF TEXT
COMPRESSION ALGORITHMS [9]
Data Compression is the science and art of representing information in a
compact form . For decades, Data compression has been one of the critical
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201 are lots of data compression algorithms which are available to compress
files of different formats. Experimental results and comparisons of the
lossless compression algorithms using Statistical compression techniques
and Dictionary based compression techniques were performed on text
data. Statistical coding techniques the algorithms such as Shannon -Fano
Coding, Huffman codi ng, Adaptive Huffman coding, Run Length
Encoding and Arithmetic coding are considered. Lempel Ziv scheme
which is a dictionary based technique is divided into two families: those
derived from LZ77 (LZ77, LZSS, LZH and LZB) and those derived from
LZ78 (LZ78 , LZW and LZFG).
The size of data is reduced by removing the excessive information. The
goal of data compression is to represent a source in digital form with as
few bits as possible while meeting the minimum requirement of
reconstruction of the original. Data compression can be lossless, only if it
is possible to exactly reconstruct the original data from the compressed
version. Examples of such lossless data are medical images, text and
images preserved for legal reason, some computer executable files, e tc.
Another family of compression algorithms is called lossy as these
algorithms irreversibly remove some parts of data and only an
approximation of the original data can be reconstructed. Multimedia
images, video and audio are more easily compressed by lo ssy compression
techniques. Lossy algorithms achieve better compression effectiveness
than lossless algorithms, but lossy compression is limited to audio,
images, and video, where some loss is acceptable. This session examines
the performance of statistica l compression techniques such as Shannon -
Fano Coding, Huffman coding, Adaptive Huffman coding, Run Length
Encoding and Arithmetic coding. The Dictionary based compression
technique Lempel -Ziv scheme is divided into two families: those derived
from LZ77 (L Z77, LZSS, LZH and LZB) and those derived from LZ78
(LZ78, LZW and LZFG).
STATISTICAL COMPRESSION TECHNIQUES
a) SHANNON FANO CODING
The algorithm is as follows:
Step 1. For a given list of symbols, develop a frequency or probability
table.
Step 2. Sort the table according to the frequency, with the most frequently
occurring symbol at the top.
Step 3. Divide the table into two halves with the total frequency count of
the upper half being as close to the total frequency count of the bottom
half as possible.
Step 4. Assign the upper half of the list a binary digit ‘0’ and the lower
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202 Step 5. Recursively apply the steps 3 and 4 to each of the two halves,
subdividing groups and adding bits to the codes until each symbol has
become a corresponding lea f on the tree.
b) HUFFMAN CODING
The Huffman algorithm is simple and can be described in terms of
creating a Huffman code tree. The procedure for building this tree is:
Step 1. Start with a list of free nodes, where each node corresponds to a
symbol in the a lphabet.
Step 2. Select two free nodes with the lowest weight from the list.
Step 3. Create a parent node for these two nodes selected and the weight is
equal to the weight of the sum of two child nodes.
Step 4. Remove the two child nodes from the list and the parent node is
added to the list of free nodes.
Step 5. Repeat the process starting from step -2 until only a single tree
remains.
c) ADAPTIVE HUFFMAN CODING
The basic Huffman algorithm suffers from the drawback that to generate
Huffman codes it requi res the probability distribution of the input set
which is often not available. The Adaptive Huffman coding technique was
developed based on Huffman coding first by Newton Faller and by Robert
G. Gallager and then improved by Donald Knuth and Jefferey S. V itter.
Both sender and receiver maintain dynamically changing Huffman code
trees whose leaves represent characters seen so far. Initially the tree
contains only the 0 -node, a special node representing messages that have
yet to be seen. Huffman tree include s a counter for each symbol and the
counter is updated every time when a corresponding input symbol is
coded. Huffman tree under construction is still a Huffman tree if it is
ensured by checking whether the sibling property is retained. If the sibling
property is violated, the tree has to be restructured to ensure this property.
Storing Huffman tree along with the Huffman codes for symbols with the
Huffman tree is not needed here. It is superior to Static Huffman coding in
two aspects: It requires only one pass through the input and it adds little or
no overhead to the output.
d) ARITHMETIC CODING
Huffman and Shannon -Fano coding techniques suffer from the fact that an
integral value of bits is needed to code a character. Arithmetic coding
completely bypasses the idea of replacing every input symbol with a
codeword. Instead it replaces a stream of input symbols with a single
floating point number as output. The basic concept of arithmetic coding
was developed by Elias in the early 1960’s and further developed l argely
by Pasco, Rissanen and Langdon. The main aim of Arithmetic coding is to
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203 assigned to this interval. The algorithm starts with an interval of 0.0 and
1.0. After each input symbol fr om the alphabet is read, the interval is
subdivided into a smaller interval in proportion to the input symbol’s
probability. This subinterval then becomes the new interval and is divided
into parts according to probability of symbols from the input alphabe t.
This is repeated for each and every input symbol. And, at the end, any
floating point number from the final interval uniquely determines the input
data.
e) LEMPEL ZIV ALGORITHMS
The Lempel Ziv Algorithm is an algorithm for lossless data compression.
It is not a single algorithm, but a whole family of algorithms, stemming
from the two algorithms proposed by Jacob Ziv and Abraham Lempel in
their landmark papers in 1977 and 1978.

Fig 16: LEMPEL ZIV ALGORITHMS
Jacob Ziv and Abraham Lempel have presented thei r dictionary -based
scheme in 1977 for lossless data compression. LZ77 exploits the fact that
words and phrases within a text file are likely to be repeated. When there
is repetition, they can be encoded as a pointer to an earlier occurrence,
with the point er accompanied by the number of characters to be matched.
It is a very simple adaptive scheme that requires no prior knowledge of the
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f) LZ78
In 1978 Jacob Ziv and Abraham Lempel presented their dictionary based
scheme, which is known as LZ78. This dictionary has to be built both at
the encoding and decoding side and they must follow the same rules to
ensure that they use an identical dictionary. The codewords output by the
algorithm consists of two elements where ‘i’ is an index referring to the
longest matching dictionary entry and the first non -matching symbol.
When a symbol that is not yet found in the dictionary, the codeword has
the index value 0 and it is added to the dictionary as well. The algorithm
gradually builds up a dictionary with this method. The algorithm for LZ78
is given below:

LZ78 algorithm has the ability to capture patterns and hold them
indefinitely but it also has a serious drawback. There are variou s methods
to limit dictionary size, the easiest being to stop adding entries and
continue like a static dictionary coder or to throw the dictionary away and
start from scratch after a certain number of entries has been reached. The
encoding done by LZ78 is fast, compared to LZ77, and that is the main
advantage of dictionary based compression. The decompression in LZ78 is
faster compared to the process of compression.
EXPERIMENTAL RESULTS
In this section we compare the performance of various Statistical
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205 Huffman coding, Adaptive Huffman coding and Arithmetic coding), LZ77
family algorithms (LZ77, LZSS, LZH and LZB) and LZ78 family
algorithms (LZ78, LZW and LZFG). Research works done to evaluate the
efficiency of any compression algorithm are carried out having two
important parameters. Tested several times the practical performance of
the above mentioned techniques on files of Canterbury corpus and have
found out the results of various Statistic al coding techniques and Lempel -
Ziv techniques selected for this study.
CONCLUSION
Statistical compression techniques and Lempel Ziv algorithms were taken
up to examine the performance in compression. In the Statistical
compression techniques, Arithmetic coding technique outperforms the rest
with an improvement of 1.15% over Adaptive Huffman coding, 2.28%
over Huffman coding, 6.36% over Shannon -Fano coding and 35.06% over
Run Length Encoding technique. LZB outperforms LZ77, LZSS and LZH
to show a marked c ompression, which is 19.85% improvement over LZ77,
6.33% improvement over LZSS and 3.42% improvement over LZH,
amongst the LZ77 family. LZFG shows a significant result in the average
BPC compared to LZ78 and LZW. From the result it is evident that LZFG
has outperformed the other two with an improvement of 32.16% over
LZ78 and 41.02% over LZW.
11.4 PERFORMANCE EVALUATION IN CONTENT -
BASED IMAGE RETRIEVAL: OVERVIEW AND
PROPOSALS [10]
Abstract
Evaluation of retrieval performance is a crucial problem in content -based
image retrieval (CBIR). Many different methods for measuring the
performance of a system have been created and used by researchers. This
article discusses the advantages and disadvantages of the performance
measures currently used. Problems such as a common image database for
performance comparisons and a means of getting relevance judgments (or
ground truth) for queries are explained. The relationship between CBIR
and information retrieval (IR) is made clear, since IR researchers have
decades of expe rience with the evaluation problem. Many of their
solutions can be used for CBIR, despite the differences between the fields.
Several methods used in text retrieval are explained. Proposals for
performance measures and means of developing a standard test s uite for
CBIR, similar to that used in IR at the annual Text REtrieval Conference
(TREC), are presented.
Introduction
Early reports of the performance of CBIR systems were often restricted
simply to printing the results of one or more example queries. This is
easily tailored to give a positive impression, since developers can chooses
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206 measure, nor a means of comparing different systems. Many of the
measures used in CBIR have long been used in IR. Several other standard
IR tools have recently been imported into CBIR.
In the 1950s IR researchers were already discussing performance
evaluation, and the first concrete steps were taken with the development of
the SMART system in 1961. Other i mportant steps towards common
performance measures were made with the Craneld test. Finally, the
TREC series started in 1992, combining many efforts to provide common
performance tests. The TREC project provides a focus for these activities
and is the worl dwide standard in IR. Such novelties are included in TREC
regularly.
Information Retrieval
Although performance evaluation in IR started in the 1950s, here we focus
on newer results and especially on TREC and its achievements in the IR
community. Not only did TREC provide an evaluation scheme accepted
worldwide, but it also brought academic and commercial developers
together and thus created a new dynamic for the field.
Data Collections
The TREC collection is the main collection used in IR. Co -sponsored by
the National Institute of Standards and Technology and the Defense
Advanced Research Projects Agency, TREC has been held annually since
its inception. A large amount of training data is also provided before the
conference. Special evaluations exist for interactive systems, spoken
language, high -precision and cross -language retrieval. The collections can
grow as computing power increases, and as new research areas are added.
Relevance judgments
The determination of relevant and non -relevant documents for a given
query is one of the most important and time -consuming tasks. TREC uses
the following working definition of relevance: If you were writing a report
on the subject of the topic and would use the information contained in the
document in the report, t hen the document is relevant. Only binary
judgments are made, and a document is judged relevant if any piece of it
is.
Performance measures
The most common evaluation measures used in IR are precision and
recall, usually presented as a precision vs. recal l graph. Researchers are
familiar with PR graphs and can extract information from them without
interpretation problems.

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Basic Problems in performance evaluation in CBIR
The current status of performance evaluation in CBIR is far from that in
IR. Th ere are many different groups who are working with different sets
of specialized images. There is neither a common image collection, nor a
common way to get relevance judgments, nor a common evaluation
scheme.
Defining a common image collection
There are several problems which must be addressed in order to create a
common image collection. The greatest problem is to create a collection
with enough diversity to cater for the diverse, partly specialized domains
in CBIR such as medical images, car images, fac e recognition and
consumer photographs.
A common means of constructing an image collection is to use Corel
photo CDs, each of which usually contains 100 broadly similar images.
Most research groups use only a subset of the collection, which can result
in a collection consisting of several highly dissimilar groups of images,
with relatively high within -group similarity. This can lead to great
apparent improvements in performance: it is not too hard to distinguish
sunsets from underwater images of fish! A go od candidate for a standard
collection could be the images and videos from MPEG -7.
An alternative approach is for CBIR researchers to develop their own
collection. Such a project is underway at the the University of Washington
in Seattle and is freely ava ilable without any copyright and owners
annotated photographs of different regions and topics. It is still small
(~500 images), but several groups are contributing to enlarge the data set.
Collection size should be sufficiently high that the trade -of betwe en speed
and accuracy can be evaluated. In IR it is quite normal to have millions of
documents whereas in CBIR most systems work with a few thousand
images and some even with fewer than one hundred.
Obtaining relevance judgments
In CBIR there is not yet a common means of obtaining relevance
judgments for queries. A very common technique is to use standard image
databases with sets of different topics such as the Corel collection.
Relevance “judgments" are given by the collection itself. Grouping is not
always based on global visual similarity, but often on the contained
objects. In some studies images which are too visually different are
removed from the collection, which definitely improves results.
Image grouping
An alternative approach is for the colle ction creator or a domain expert to
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208 very often used in medical CBIR. This can be seen as real groundtruth,
because the images have a diagnosis certified by at least one medical
doctor. The se groups can then be used like the subsets discussed above.
Simulating users
Some studies simulate a user, by assuming that users' image similarity
judgments are modeled by the metric used by the CBIR system, plus
noise. Real users are very hard to mode l: Tversky (1977) has shown that
human similarity judgments seem not to obey the requirements of a
metric, and they are certainly user - and task -dependent. Such simulations
cannot replace real user studies.
Performance Evaluation Methods
User comparisons
User comparison is an interactive method. It is hard to get a large number
of such user comparisons as they are time -consuming. Users are given two
or more different results and allowed to choose the one which is preferred
or found to be most relevant to the query. This method needs a base
system or another system for comparison.
Single -valued measures
Rank of the best match Berman & Shapiro (1999) measure whether the
\most relevant" image is in either the first 50 or first 500 images retrieved.
50 repres ents the number of images returned on screen and 500 is an
estimate of the maximum number of images a user might look at when
browsing.
Error rate Hwang et al. (1999) use this measure, which is common in
object or face recognition. It is in fact a single p recision value, so it is
important to know where the value is measured.

Retrieval efficiency
Muller & Rigoll (1999) define Retrieval efficiency as specified below. If
the number of images retrieved is lower than or equal to the number of
relevant images , this value is the precision, otherwise it is the recall of a
query. This definition can be misleading since it mixes two standard
measures.

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Human Body Tracking Based
on Discrete Wavelet Transform
209 Correct and incorrect detection
Ozer et al. (1999) use these measures in an object recognition context. The
numbers of correct and incorrect classifications are counted. When divided
by the number of retrieved images, these measures are equivalent to error
rate and precision.
Graphical representations
Precision vs. recall graphs
PR graphs are a standard evaluati on method in IR and are increasingly
used by the CBIR community. PR graphs contain a lot of information, and
their long use means that they can be ready easily by many researchers. It
is also common to present a partial PR graph (e.g. He (1997)). This can be
useful in showing a region in more detail, but it can also be misleading
since areas of poor performance can be omitted. Interpretation is also
harder, since the scaling has to be watched carefully. A partial graph
should always be used in conjunction w ith the complete graph.

Fig 17: PR graphs for four different queries both without and with
feedback.
Correctly retrieved vs. all retrieved graphs contain the same information as
recall graphs, but differently scaled. Fraction correct vs. No. images
retrieved graphs are equivalent to precision graphs. Average recognition
rate vs. No. images retrieved graphs show the average percentage of
relevant images among the first N retrievals. This is equivalent to the
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Imag e Processing
210

Fig 18: Recall vs. No. of images graph and partial precision vs. No. of
images graph
CONCLUSIONS
Current section gives an overview of existing performance evaluation
measures in CBIR. The need for standardized evaluation measures is clear,
since several measures are slight variations of the same definition. This
makes it very hard to compare the performance of systems objectively. To
overcome this problem a set of standard performance measures and a
standard image database is needed. We have proposed such a set of
measures, similar to th ose used in TREC. A frequently updated shared
image database and the regular comparison of system performances would
be of great benefit to the CBIR community.
11.5 REFERENCES
1. Digital Watermarking.
https://www.techopedia.com/definition/24927/digital -watermarking
2. Rashid A. Digital watermarking applications and techniques: a brief
review. International Journal of Computer Applications Technology and
Research. 2016;5(3):147 -50.
3. Digital Watermarking and its Types.
https://www.geeksforgeeks.org/digital -watermarking -and-its-types/.
4. Jain S. Digital watermarking techniques: a case study in fingerprints &
faces. InProc. Indian Conf. Computer Vision, Graphics, and Image
Processing 2000 Dec (pp. 139 -144).
5. Joshi, Manjunath & Joshi, Vaibhav & Raval, Mehul . (2013). Multilevel
Semi -fragile Watermarking Technique for Improving Biometric
Fingerprint System Security. Communications in Computer and
Information Science. 276. 10.1007/978 -3-642-37463 -0_25.
6. Ganta S, Svsrk P. A novel method for Indian vehicle reg istration
number plate detection and recognition using image processing
techniques. Procedia Computer Science. 2020 Jan 1;167:2623 -33. munotes.in

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Human Body Tracking Based
on Discrete Wavelet Transform
211 7. Zhao ZQ, Zheng P, Xu ST, Wu X. Object detection with deep learning:
A review. IEEE transactions on neural networks and learning systems.
2019 Jan 28;30(11):3212 -32.
8. Chang SL, Hsu CC, Lu TC, Wang TH. Human body tracking based on
discrete wavelet transform. InProceedings of the 2007 WSEAS
International Conference on Circuits, Systems, Signal and
Telecommunications 2007 J an 17 (pp. 113 -122).
9. Shanmugasundaram S, Lourdusamy R. A comparative study of text
compression algorithms. International Journal of Wisdom Based
Computing. 2011 Dec;1(3):68 -76.
10. Müller H, Müller W, Squire DM, Marchand -Maillet S, Pun T.
Performance ev aluation in content -based image retrieval: overview and
proposals. Pattern recognition letters. 2001 Apr 1;22(5):593 -601.
11.6 MOOCS
1. Watermarking Basics. https://www .coursera.org/lecture/hardware -
security/watermarking -basics -UHE3w .
2. Biometric Authentication. https://www.coursera.org/lecture/usable -
security/biometric -authentic ation -RXVog .
3. Biometrics. https://www.udemy.com/course/biometrics/ .
4. YOLO: Automatic License Plate Detection & Extract text App.
https://www.udemy.com/course/deep -learning -web-app-project -
number -plate -detection -ocr/
5. Object Detection. https://www.coursera. org/lecture/convolutional -
neural -networks/object -detection -VgyWR .
6. Introduction to Optical Character Recognition.
https://www.coursera.org/lec ture/python -project/introduction -to-
optical -character -recognition -n8be7 .
7. Introduction to Data Compression.
https://www.coursera.org/lecture/algorithms -part2/introduction -to-
data-compression -OtmHU .
11.7 VIDEO LINKS
1. INTRODUCTION TO DIGITAL WATERMARKING.
https://www.youtube.com/watch?v=WvRBKn8 -JJA
2. Digital Watermarking – Introduction.
https://www.youtube.com/watch?v=gd2W0vaKTxA
3. What is Biometric Authentication.
https://www.youtube.com/watch?v=MBtzOzPakt8 munotes.in

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Imag e Processing
212 4. Biometric authentication and it s types and methods, information
security. https://www.youtube.com/watch?v=tTnkq6Y3Hdg .
5. Vehicle License Plate Recognition.
https://www.yout ube.com/watch?v=CVDTtRiIXME
6. Vehicle Number Plate Recognition using MATLAB.
https://www.youtube.com/watch?v=p_g -g7C3uHw .
7. Handwritten and Printed Text Recognition.
https://www.youtube.com/watch?v=H64vHn_R0vg
8. OCR Explained...Handwriting Recognition!!!.
https://www.youtube.com/watch?v=i_XJa165_9I .




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See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/331095222Digital Image Restoration in Matlab: A Case Study on Inverse and WienerFilteringPreprint · February 2019DOI: 10.20944/preprints201811.0566.v2CITATIONS0READS6804 authors, including:
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Digital Image Restoration in Matlab: A Case Study
on Inverse and Wiener Filtering
Mohammad Mahmudur Rahman Khan1*, Shadman Sakib2#, Rezoana Bente Arif2@, and Md. Abu Bakr Siddique2$
1Dept. of ECE, Mississippi State University, Mississippi State, MS 39762, USA
2Dept. of EEE, International University of Business Agriculture and Technology, Bangladesh
mrk303@msstate.edu*, sakibshadman15@gmail.com#, rezoana@iubat.edu@, absiddique@iubat.edu$
Corresponding Author: absiddique@iubat.edu$
Abstract—In this paper, at first, a color image of a car is
taken. Then the image is transformed into a grayscale image.
After that, the motion blurring effect is applied to that image
according to the image degradation model described in
equation 3. The blurring effect can be controlled by a and b
components of the model. Then random noise is added in the
image via Matlab programming. Many methods can restore
the noisy and motion blurred image; particularly in this paper
Inverse filtering as well as Wiener filtering are implemented
for the restoration purpose. Consequently, both motion
blurred and noisy motion blurred images are restored via
Inverse filtering as well as Wiener filtering techniques and the
comparison is made among them.
Keywords—Color image, grayscale image, motion blurring,
random noise, inverse filtering, Wiener filtering, restoration of
an image.
I. INTRODUCTION
In digital image processing, image restoration is an
essential approach used for the retrieval of uncorrupted,
original image from the blurred and noisy image [1, 2]
because of motion blur, noise, etc. caused by environmental
effects [3] and camera misfocus. Image blur may occur for
many reasons such as motion blur which is due to the
sluggish camera shutter speed comparative to the
instantaneous motion of the targeted object [4]. The image
also may subject to several forms of noises such as Poisson
noise, Gaussian noise, etc. Poisson noise is controlled by
signal and it is associated with the low light sources owing
to photon counting statistic [4]. In contrast, the reason of
Gaussian noise is because of electronic components and
broadcast transmission effects [4]. In short, the term image
restoration is an inverse process [5] by which the
uncorrupted, original image can be recovered from the
degraded form of the actual image [6]. There are many
useful applications of digital image restoration in several
fields including the area of astronomical imaging, medical
imaging, media and filmography, security and surveillance
videotapes, law enforcement and forensic science, image
and video coding, centralized aviation assessment
procedures [7], uniformly blurred television pictures
restoration [8], etc. Several algorithmic techniques such as
Artificial Neural Network [9], Convolutional neural
Network [10], and K-nearest Neighbors [11] can also be
applied in image processing techniques such as
segmentation, thresholding and filtering. The technique used
in image restoration is known as filtering which suppresses
or removes unwanted components or features from the
images. The most popular filtering techniques are used in
image restoration in recent times are inverse filtering and
Wiener filtering [12]. Inverse filter is a handy technique for image restoration
if a proper degradation function can be modeled for the
corrupted image. The performance of the inverse filter is
quite right when the noise does not corrupt images, but in
the presence of noise in the images, performance degrades
significantly as high pass inverse filtration cannot eliminate
noise properly because noise tends to be high frequency.
Wiener filter is incorporated with low pass filter together
with high pass filter; as a result, it works actively in the
existence of additive noise within the image. It performs
deconvolution operation (high pass filtering) to invert
motion blurring and also perform compression operation i.e.
(low pass filtering) to eliminate the additive noise.
Furthermore, in the process of inverting motion blurring and
noise elimination, Wiener filter diminishes the overall mean
square inaccuracy between the original and the output image
of the filtration.
In this paper, the implementation of inverse filtering and
Wiener filtering are analyzed for image restoration. Inverse
filtering is applied into a motion blurred car image at first,
and then wiener filtering is also used to the same image.
After that, inverse and Wiener filtering are performed on the
same motion blurred car image with additive noise. Finally,
the comparison is made between inverse and Wiener
filtering regarding their performances in restoring motion
blurred images with and without additive noise.
II. LITERATURE REVIEW
Over the past two decades, the technique of image
processing has taken its place into every aspect of today's
technological society. In digital image processing, there are
a variety of essential steps involved such as image
enhancement, pre-processing of images, image
segmentation, image restoration and reconstruction of
images etc. Among them, image restoration plays a vital
role in today's world. It has several fields of applications in
the areas of astronomy, remote sensing, microscopy,
medical imaging, satellite imaging, molecular spectroscopy,
law enforcement, and digital media restoration etc. Image
restoration is very challenging as there is a lot of
interference and noise in the environment like Gaussian
noise, multiplicative noise, and impulse noise etc, inclusive
of the camera such as wide angle lens, long exposure times,
wind speed and degradation, blurring such as uniform blur,
atmospheric blur, motion blur, and Gaussian blur etc.
However, there are various methods of image restoration in
the domain of image processing, for instance, Median filter,
Wiener filtering, inverse filtering, Harmonic mean filter,
Arithmetic mean filter, Max filter, and Maximum
Likelihood (ML) method etc. Among these restoration
methods, Wiener and inverse filtering method is the Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 5 February 2019
© 2019 by the author(s). Distributed under a Creative Commons CC BY license.
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© 2019 by the author(s). Distributed under a Creative Commons CC BY license.
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simplest and advantageous method for overcoming the
current restoration challenges mentioned above.
Stephen et al. outlined the restoration and reconstruction
process from overlapping images of the multiple and same
scene which is subjected to user-defined and data
availability constraints on the support for the spatial domain
process [13]. Michael et al. proposed an approach for out-
of-focus blur and projector blur to reduce the image blur
[14]. Yu et al. introduced an algorithm for the restoration of
distorted and noisy images degraded by impulse and
Gaussian noises [15]. Restoration of digitized photographs
can be made by using multi-resolution texture synthesis and
image imprinting [16]. Image restoration based on neural
networks mainly focuses on spatial variation in terms of
changeable regularization parameter for adaptively training
the weights [17]. Moreover, the image can be restored by
using a novel adaptive k-th nearest neighbor (KNN) strategy
variant of the mean shift by knowing its neighbor [18],
unsupervised, information-theoretic, adaptive filtering
(UINTA) which improves the pixel intensities [19]. In
another approach, the image can be restored from the mixed
noise through minimization approach [20]. Recently, image
restoration based on Convolutional Neural Network (CNN)
achieved an encouraging implementation such as deep
networks which performs non-local color image denoising
[21], model-based optimization method to solve the various
inverse problems like deblurring [22]. Moreover, the image
can be restored by using the iterative method using
denoising algorithm which provides a solution for the linear
inverse problem [23].
The median filter is complex to execute as well as it’s
very time-consuming. Max filter cannot find the black or
dark colored pixel of an image. When there is a need of
sharp edges in the output, the arithmetic mean filter cannot
provide the sharp edges rather it blurs the edges. ML
method is sensitive to noise as the reversal of the imaging
equation. Moreover, for pepper noise harmonic mean filter
does not work well. After all those drawbacks of image
restoration process mentioned above, Wiener and inverse
filtering method are prominent and beneficial. The mean
square error between the uncorrupted image is minimized by
using the Wiener filter also it is not sensitive to noise.
Inverse filtering is the prominent and simplest method to
restore the image in the existence of noise and blur. In
parallel, both wiener, and inverse filtering are used to
retrieve the noisy and motion blurred images.
III. FUNDAMENTALS OF IMAGE RESTORATION
Image restoration is a restoring or recovering process of
a degraded image by utilizing some prior knowledge of
degradation method which has degraded the image. So the
image restoration process involves the estimation of the
deteriorated model as well as the relevance of the inverse
filtering to restore or retrieve the original image [24].
Although the reconstructed image may not be the exact form
of the original image, it will be the approximation of the
original image. Figure 1 below shows a fundamental model
of image degradation and restoration procedure.

Fig. 1. The fundamental outline of image degradation and restoration
procedure

In spatial domain, the degradation of the original image can
be modeled as [25]: (,)(,)*(,)(,) ...... (1)gxyhxyfxynxy 

Where, ,xy= detached pixel coordinates of the image frame. ,fxy= Original image ,gxy= Degraded image ,hxy= Image degradation function ,nxy= Ad-on noise

As convolution operation within the spatial domain
corresponds to multiplication in the frequency domain, the
equation 1 can be rewritten as:
(,) (,) (,) (,) ...... (2)GuvHuvFuvNuv 

Now, Motion blur is present when there exists comparative
motion in the midst of the recording device and the scene
(object). However, the types of blur may be in the
appearance of a translation, rotation, and scaling, or some
combinations of these. Here only the critical case of a global
translation will be considered.

Let’s pretend the scene to be recorded interprets
comparative to the camera at constant velocities a and b
along the directions of x and y during the exposure time T.
The frequency domain degradation function can be
simplified as [26]:
( ) sin(( ))(,) ...... (3)( )juavbT uavbTHuv euavb

Image restoration process can be subdivided into two
classes:

 Deterministic methods are applicable to images
with a small amount of noise and a familiar
degradation function.
 Stochastic techniques are to restore images
according to some stochastic criterion.

Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 5 February 2019 Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 5 February 2019 doi:10.20944/preprints201811.0566.v2
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A. The Basics of Inverse Filtering

Like any other unsupervised methods such as Fuzzy C-
Means [27] and ADBSCAN [28] clustering, inverse filtering
is also unsupervised. The basic image restoration model for
inverse filtering is exposed in figure 2.

Fig. 2. Image restoration model (Inverse filtering)

When the degradation function H(u,v) is identified, the
image can be returned to normal state by:
(,)ˆ(,) ...... (4)(,)GuvFuvHuv

Now, in our case, we have added noise after implementing
the motion blurring effect. Hence we have used the
following formula to restore the original image:
(,)ˆ(,) (,) ...... (5)(,)NuvFuvFuvHuv
Since, the function of N(u,v) is random whose Fourier
transform is generally unfamilier, it is impossible to retrieve
F(u,v) accurately. The impact of noise is noteworthy for
frequencies where H(u,v) has a tiny magnitude. In reality,
H(u,v) usually decreases in size much more rapidly than
N(u,v) and thus the noise effect N(u,v)/H(u,v) could take
over the entire restoration result.
B. The Basics of Wiener Filtering

The basic image restoration model for Wiener filtering is
modeled in figure 3.

Fig. 3. Image restoration model (Wiener filtering)

Wiener filter exploits the previous knowledge of the spectral
properties of the original signal and the noise and linear
time-invariant rule to produce an output as close to the
original image as feasible. In wiener filtering, it is presumed
that the signal and noise are static linear stochastic processes
with familiar spectral properties [29, 30]. Wiener filter tries
to reconstruct the degraded image by minimizing an error
function as designed by the following equation: 2ˆ[{(,) (,)}] ...... (6)MSEEfxy fxy  

Where, MSE = Mean square error .E= The expectation operation ˆ(,)fxy = Restored image
The Wiener filter is to locate an approximation (,)fxy of
the original image (,)fxy so as to the mean square error
between them is minimized. Wiener filter is represented
as(,)Luv as shown below [31, 32]:

*
2
*
2(,)(,)(,)(,) (,) (,)(,) ...... (7)(,)(,)(,)f
f n
n
fHuvSuvLuvHuvSuvSuvHuv
SuvHuvSuv




Again,
*
2
2
2(,)(,)(,)(,) (,) (,)(,) 1 ...... (8)(,)(,)f
f nHuvSuvLuvHuvSuvSuvHuv
HuvHuv K




Where,




= Power spectrum of the original image

= Noise power spectrum

Here, K is the inverse of SNR. The image and noise are
considered as arbitrary processes. The Wiener filter can
generate optimal estimate only if such stochastic processes
are stationary Gaussian. These situations are not typically
satisfied for real images. So the restored image can be
expressed as: ˆ(,) (,)(,) ...... (9)fuvLuvGuv 







(,)(,)n
fSuvKSuv(,)fSuv(,)nSuvPreprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 5 February 2019 Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 5 February 2019 doi:10.20944/preprints201811.0566.v2
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IV. RESULTS AND DISCUSSION
For this paper, the following color image of a car is used
as made known in figure 4.

Fig. 4. The color image of a car
Then the image is transformed into a grayscale image in
Matlab. The grayscale image is made known in figure 5
below.

Fig. 5. The grayscale image of figure 1


Now, the first task was to insert motion blur effect into the
image according to equation (1). After doing so, the resulted
image is represented in figure 6.

Fig. 6. Grayscale car image with motion blur effect
The effect of the motion blur can be controlled by a and b
components of the model.
After applying the blur to the image inverse and, Wiener
filterings are implemented to restore the image.
A. The Results of Inverse Filtering
For inverse filtering, if we do not add any noise after the
motion blur, then we can restore the same image before
motion blur. The figure 7 below shows the effectiveness of
inverse filtering without any noise.
Now, if we add some random noise to the image, then the
filter performance degrades to some extent. The
consequence of noise on the performance of inverse filtering
is made known in figure 8. In figure 8, though the inverse
filter is capable of inverting the effect of motion blur, it is
not able to nullify the effect of noise. Here, a=0.0001 and
b=0.1.
Fig. 7. Restoration of motion blurred car image by inverse filtering Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 5 February 2019 Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 5 February 2019 doi:10.20944/preprints201811.0566.v2
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Fig. 8. Restoration of noisy motion blurred car image by inverse filtering

B. The Results of Wiener Filtering
The Wiener filter has a ‘K’ component which is inverse
to the SNR. Now, if the noise power is zero, which means
no noise, then the Wiener can restore the exact image which
was corrupted by motion blur effect. In the following case,
we have considered zero noise power, and figure 9 shows
the performance of the Wiener filter.

Here, the restored image is almost exactly similar to the
image before motion blur. However, if we change the k to
0.01, then there would be 1% noise added after the motion
blur effect. If then we apply wiener filter, we will get the
following result as represented in figure 10. It is observed
that the Wiener filter is reversing the effect of motion blur,
but still, there is some noise remaining in the picture.

Fig. 9. Restoration of motion blurred car image by Wiener filtering
Fig. 10. Restoration of noisy motion blurred car image by Wiener filteringPreprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 5 February 2019 Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 5 February 2019 doi:10.20944/preprints201811.0566.v2
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V. CONCLUSION
This paper presents inverse and wiener filterings’
practical implementation on some images for image
restoration. It is observed that both inverse and Wiener
filtering work quite well in the absence of noise in restoring
original image from its degraded version. But in the
existence of additive noise wiener filtering works better for
restoration purpose compared to inverse filtering. In
subsequent works of this series, some other improved
filtering techniques for image restoration will be discussed.
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Adaptive Density-Based Spatial Clustering of Applications with
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[29] R. G. Brown and P. Y. Hwang, "Introduction to random signals
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Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 5 February 2019 Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 5 February 2019 doi:10.20944/preprints201811.0566.v2
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IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 6, NO. 2, JUNE 2011 371
Restoring Degraded Face Images: A Case Study in
Matching Faxed, Printed, and Scanned Photos
Thirimachos Bourlai ,M e m b e r ,I E E E ,A r u n R o s s ,S e n i o rM e m b e r ,I E E E ,a n d A n i lK .J a i n ,F e l l o w ,I E E E
Abstract— We study the problem of restoring severely degraded
face images such as images scanned from pas sport photos or im-
ages subjected to fax compression, downscaling, and printing. The
purpose of this paper is to illust rate the complexity of face recog-
nition in such realistic scenarios and to provide a viable solution
to it. The contributions of this work are two-fold. First, a database
of face images is assembled and use dt oi l l u s t r a t et h ec h a l l e n g e s
associated with matching severe ly degraded face images. Second,
ap r e p r o c e s s i n gs c h e m ew i t hl o wc omputational complexity is de-
veloped in order to eliminate the noise present in degraded images
and restore their quality. An extensive experimental study is per-
formed to establish that the propos ed restoration scheme improves
the quality of the ensuing face images while simultaneously im-
proving the performance of face matching.
Index Terms— Face recogni tion, faxed face images, image quality
measures, image restoration, scanned face images.
I. INTRODUCTION
A. Motivation
THE past decade has seen signi ficant progress in the field
of automated face recognition as is borne out by results of
the 2006 Face Recognition Vendor Test (FRVT) organized by
NIST [2]. For example, at a false accept rate (FAR) of 0.1%, the
false reject rate (FRR) of the be st performing face recognition
system has decreased from 79% in 1993 to 1% in 2006. How-
ever, the problem of matching facial images that are severely
degraded remains to be a challenge. Typical sources of image
degradation include harsh ambient illumination conditions [3],
low quality imaging devices, image compression, down sam-
pling, out-of-focus acquisition, device or transmission noise,
and motion blur [Fig. 1(a)–(f)]. Other types of degradation that
Manuscript received March 08, 2010; revised January 10, 2011; accepted
January 11, 2011. Date of publication February 04, 2011; date of current ver-
sion May 18, 2011. This work was supported by the Center for Identi fication
Technology Research (CITeR) at World Class University (WCU). The work of
A. K. Jain was supported in part by the WCU program through the National Re-
search Foundation of Korea funded by the Ministry of Education, Science and
Technology (R31-10008). A preliminary version of this work was presented at
the First IEEE International Conference on Biometrics, Identity and Security
(BIDS), September, 2009. The associate editor coordinating the review of this
manuscript and approving it for publication was Dr. Fabio Scotti.
T. Bourlai and A. Ross are with th eL a n eD e p a r t m e n to fC o m p u t e r
Science and Electrical Engineering, West Virginia University, Morgan-
town, WV 26506 USA (e-mail: Thirimachos.Bourlai@mail.wvu.edu;
Arun.Ross@mail.wvu.edu).
A. K. Jain is with the Computer Science and Engineering Department,
Michigan State University, East Lansing, MI 48824 USA, and also with the
Department of Brain and Cognitive Engineering, Korea University, Seoul
136-713, Korea (e-mail: jain@cse.msu.edu).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identi fier 10.1109/TIFS.2011.2109951have received very little attentio ni nt h ef a c er e c o g n i t i o nl i t e r a -
ture include halftoning [Fig. 1(e)], dithering [Fig. 1(f)], and the
presence of security watermarks on documents [Fig. 1(g)–(j)].
These types of degradation are observed in face images that
are digitally acquired from printed or faxed documents. Thus,
successful face recognition in t he presence of such low quality
probe images is an open research issue.
This work concerns itself with an automated face recognition
scenario that involves compar ing degraded facial photographs
of subjects against their high-resolution counterparts (Fig. 2).
The degradation considered in this work is a consequence of
scanning, printing, or faxing face photos. The three types of
degradation considered here are: 1) fax image compression,1
2) fax compression, followed by printing, and scanning, and
3) fax compression, followed by actual fax transmission, and
scanning. These scenarios are en countered in situations where
there is a need, for example, to identify legacy face photos ac-
quired by a government agency that has been faxed to another
agency. Other examples include matching scanned face images
present in driver’s licenses, refugee documents, and visas for
the purpose of establishing or verifying a subject’s identity.
The factors impacting the qual ity of degraded face photos can
be 1) person-related ,e . g . ,v a r i a t i o n si nh a i r s t y l e ,e x p r e s s i o n ,
and pose of the individual; 2) document-related ,e . g . ,l a m i n a -
tion and security watermarks th at are often embedded on pass-
port photos, variations in image q uality, tonality across the face,
and color cast of the photographs; 3) device-related ,e . g . ,t h e
foibles of the scanner used to capture face images from docu-
ments, camera resolution, image file format, fax compression
type, lighting artifacts, document photo size, and operator vari-
ability.
B. Goals and Contributions
The goals of t his work include 1) the design of an experi-
ment to quant itatively illustrate the dif ficulty of matching de-
graded fac ep h o t o sa g a i n s th i g h - r e s o l u t i o ni m a g e s ,a n d2 )t h e
developme nt of a preprocessing methodology that can “restore”
the degra ded photographs prior to comparing them against the
gallery f ace images. In this regard, we first propose an iterative
image re storation scheme. The object ive functions employed to
guide t he restoration process are two image distortion metrics,
viz., p eak signal-to-noise ratio ( PSNR) and the Universal Image
Quali ty Index (UIQ) proposed by Wang and Bovik [5]. The
target is to generate restored images that are of higher quality
and t hat can achieve better recognition performance than their
1In this work, Fax image compression is defined as the process where data
(e.g., face images on a document) are tra nsferred via a fax machine using the
T.6data compression, which is performed by the fax software.
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372 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 6, NO. 2, JUNE 2011
Fig. 1. Degraded face images: Low-resolution probe face images due to various degradation factors. (a) Original. (b) Additive Gaussian noise. (c) JP EG com-
pressed (medium quality). (d) Resized to 10% and up-scaled to the original spatial resolution. (e) Half-toning. (f) Floyd–Steinberg dithering [4]. Mug-shots of face
images taken from passports issued by different countries: (g) Greece (issued in 2006). (h) China (issued in 2008). (i) U.S. (issued in 2008). (j) Egyp t( i s s u e di n
2005) [1].
Fig. 2. Matching a high-resolution face image (a) against its degraded coun-
terpart. The image in (b) is obtained by transmitting the document containing
image (a) via a fax machine, and digita lly scanning the resulting image.
original degraded counterparts. In order to facilitate this, a clas-
sification algorithm based on texture analysis and image quality
isfirst used to determine the nature of the degradation present
in the image. This information is then used to invoke the ap-
propriate set of parameters for the restoration routine. This en-
sures that the computational complexity of both the classi fica-
tion and denoising algorithms is low, making the proposed tech-
nique suitable in real-time operations.
Second, we demonstrate that f ace recognition system perfor-
mance improves when using the restored face image instead
of the original degraded one. For this purpose, we perform
identi fication tests on a variety of experimental scenarios, in-
cluding 1) high-quality versus hi gh-quality image comparison,
and 2) high-quality versus deg raded image comparison. In the
high-quality versus high-quality tests, we seek to establish the
baseline performance of each of the face recognition methods
employed. In the high-quality versus degraded tests, we inves-
tigate the ef ficacy of matching the degraded face photographs
(probe) against their high-resolution counterparts (gallery).
Our approach avoids optimizing f acial image representation
purely for matching. Instead, the goal is to improve the quality
of face images while at the same time boosting the matching
performance. This can potentially assist human operators in
verifying the validity of a match.
The key characteristics of the proposed face image restora-
tion methodology are the following: 1) it can be applied on im-
ages impacted by various degradation factors (e.g., halftoning,dithering, watermarks, Gaussian noise, etc.); 2) individual im-
ages can have different levels of n oise originating from a variety
of sources; 3) the classi fication algorithm can automatically rec-
ognize the three main types of degradation studied in this paper;
4) it employs a combination of l inear and nonlinear denoising
methods ( filtering and wavelets) whose parameters can be auto-
matically adjusted to remove diff erent levels of noise, and 5) the
restoration process is computationally feasible (3 s per image
in a Matlab environment) since parameter optimization is per-
formed of fline.
The proposed methodology is applicable to a wide range
of face images—from high-qu ality raw images to severely
degraded face images. To facilita te this study, initially a data-
base containing passport photos and face images of 28 live
subjects referred to as the WVU Passport Face Database was
assembled. This dataset was extended to 408 subjects by using
as u b s e to ft h eF R G C 2[ 6 ]d a t a b a s e .T h ep u r p o s ew a st o
evaluate the restoration ef ficiency of our methodology in terms
of identi fication performance on a larger dataset. Experiments
were conducted using standard face recognition algorithms,
viz., Local Binary Patterns [7], those implemented in the CSU
Face Recognition Evaluation P roject [8], and a commercial
algorithm.
Section II brie flyr e v i e w sr e l a t e dw o r ki nt h el i t e r a t u r e .
Section III presents the proposed restoration algorithm.
Section V describes the technique used to evaluate the proposed
algorithm. Section VI discusses the experiments conducted and
Section VII provides concluding remarks.
II. B ACKGROUND
The problem addressed in this paper is closely related to two
general topics in the field of image processing: 1) image restora-
tion and 2) super-resolution. The problem of restoring degraded
images has been extensively stu died [9]–[15]. However, most
of the proposed techniques make implicit assumptions about the
type of degradation present in the input image and do not nec-
essarily deal with images whose degree of degradation is as se-
vere as the images considered in this work. Furthermore, they
do not address the speci ficp r o b l e mo fr e s t o r i n g face images
where the goal is to simultaneously improve image quality andmunotes.in

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BOURLAI et al. :R E S T O R I N GD E G R A D E DF A C EI M A G E S 373
recognizability of the face. In the context of super-resolution,
the authors in [16] and [17] addressed the problem of matching
ah i g h - s p a t i a lr e s o l u t i o ng a l l e r yf a c ei m a g ea g a i n s tal o w - r e s -
olution probe. With the use of super-resolution methods [18],
high-resolution images can be produced from either a single
low-resolution image [19] or f rom a sequence of images [20].
While such techniques can compen sate for disparity in image
detail across image pairs, they cannot explicitly restore noisy
or degraded content in an image. Also, when using a single
low-resolution image to perform super-resolution, certain as-
sumptions have to be made about the image structure and con-
tent.
The problem of matching passport photos was studied in [21]
where the authors designed a Bayesian classi fier for estimating
the age difference between pairs of face images. Their focus
was on addressing the age dispar ity between face images prior
to matching them. However, their work did not address the spe-
cificp r o b l e mo fm a t c h i n gf a c ei m a g e s scanned from documents
such as passports. Staroviodov et al. [22], [23] presented an au-
tomated system for matching face images scanned from docu-
ments against those directly obtained using a camera. The au-
thors constrained their study to an earlier generation of pass-
ports (1990s) from a single country. Further, in the images con-
sidered in their work, the facial portion of the photograph was
reasonably clear and not “contaminated” by any security marks.
Therefore, the system’s ability to automatically identify the face
photograph was not severely compromised. To the best of our
knowledge, the only work reported in the literature that ad-
dresses the problem of passport facial matching using interna-
tional passports is [1].
III. F ACEIMAGE RESTORATION
Digital images acquired using cameras can be degraded due
to many factors. Image denoising [24] is, therefore, a very im-
portant processing step to restore t he structural and textural con-
tent of the image. While simple image filtering can remove spe-
cificf r e q u e n c yc o m p o n e n t so fa ni m a g e ,i ti sn o ts u f ficient for
restoring useful image content. For effective removal of noise
and subsequent image restoration, a combination of linear de-
noising (using filtering), and nonlinear denoising (using thresh-
olding) may be necessary in order to account for both noise re-
moval as well as restoration of image features.
The quality of the denoiser used can be measured using the
average mean square error,w h i c h
is the error of the restored imagewith respect to the true image.S i n c et h et r u ei m a g eis unknown, the MSE corresponds
to a theoretical measure of performance. In practice, this perfor-
mance is estimated from denoising a single realizationusing
different metrics such as the PSNR and/or UIQ:
•Signal-to-Noise Ratio (SNR): It is a measure of the mag-
nitude of the signal compared to the strength of the noise.
It is de fined (in units of decibels) as:(1)
Fig. 3. Denoising using a Wiener filter of increasing width.
This measure of performance requires knowledge of the
true signalthat might not be available in a real sce-
nario. Thus, it should only be considered as an experimen-
tation tool. Furthermore, this metric neglects global and
composite errors, and in a pract ical scenario, its use is ques-
tionable. As a result, one should observe the image visually
to judge the quality of the denoising method employed.
•Peak Signal-to-Noise Ratio (PSNR): This measure is de-
fined as the ratio between the maximum possible power of
as i g n a la n dt h ep o w e ro fc o r r u p t i n gn o i s et h a ta f f e c t st h e
fidelity of its representation. It is de fined (in units of deci-
bels) via the MSE as follows:(2)
whereis the maximum fluctuation in the input
image data type. For example, if the image has a
double-precision floating-point data type, thenis 1, whereas in the case of an 8-bit unsigned integer
data type,is 255. A higher PSNR would nor-
mally indicate that the reconstruction is of higher quality.
However, the authors in [5] illustrate some limitations
of MSE/PSNR, and thus one must be very cautious in
interpreting its outcome [25].
•Universal Image Quality Index (UIQ): The measure pro-
posed in [5] was designed to model any image distortion
via a combination of three main factors, viz., loss of cor-
relation [(3): term 1], luminance distortion [(3): term 2],
and contrast distortion [(3): term 3]. In our study, UIQ can
be de fined as follows: given a true imageand a restored
image,l e t,be the means, and,be the variances
ofand,r e s p e c t i v e l y .A l s o ,l e tbe the covariance ofand.T h e n ,U I Qc a nb ed e n o t e da sf o l l o w s :(3)
A. Linear and Nonlinear Denoising
1) Image Filtering-Based Linear Denoising: Linear methods
can be used for image denoising so that the noise that perturbs an
image is suppressed as much as possible. The filtering strength
can be controlled by the filter width:h i g h e rv a l u e so fin-
crease the blurring effect (see Fig. 3). When 2-D FIR filters are
designed and used with the windowing method technique,rep-
resents the window size of the digital filter in terms of pixels.
In this paper, several smooth window functions were tested,
viz., Hamming, Hanning, Bartl ett, Blackman, boxcar, Kaiser,
and Chebwin, with variable w indow sizes. Linear methods canmunotes.in

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374 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 6, NO. 2, JUNE 2011
cause image blurring. Therefore, these filters are ef ficient in de-
noising smooth images but not images with several discontinu-
ities.
2) Thresholding-Based Nonlinear Denoising: When
wavelets are used to deal with the problem of image denoising
[24], the necessary steps invol ved are the following: 1) Apply
discrete wavelet transform (DWT) to the noisy image by using
aw a v e l e tf u n c t i o n( e . g . ,D a u b u c h i e s ,S y m l e t ,e t c . ) .2 )A p p l y
at h r e s h o l d i n ge s t i m a t o rt ot h er e s u l t i n gc o e f ficients thereby
suppressing those coef ficients smaller than a certain amplitude.
3) Reconstruct the denoised image from the estimated wavelet
coefficients by applying the inverse d iscrete wavelet transform
(IDWT).
The idea of using a thresholding estimator for denoising was
systematically explored for the first time in [26]. An important
consideration here is the choice of the thresholding estimator
and threshold value used since they impact the effectiveness
of denoising. Different estimat ors exist that are based on dif-
ferent threshold value quantizat ion methods, viz., hard, soft, or
semisoft thresholding.
Each estimator removes redundant coef ficients using a non-
linear thresholding based on (4), whereis the noisy obser-
vation,is the mother wavelet function,(is
the scale andis the position of the wavelet basis),is the
thresholding estimator,is the thresholding type, andis the
threshold used.
Ifis an input signal, then the estimators used in this paper
are de fined based on (5)–(7), whereis a parameter greater
than 1, and the superscripts,,a n ddenote hard, soft, and
semisoft thresholdi ng, respectively.
In nonlinear thresholding-based denoising methods [see (4)],
translation invariance means that the basisis
translation invariant,w h e r eis a lattice ofandfor an image signal. While the Fourier basis is translation
invariant, the orthogonal wavelet basisis not (in either the
continuous or dis crete settings)(4)ifif(5)ifif(6)ififif,o t h e r w i s e .(7)
Image denoising using the traditional orthogonal wavelet
transforms may result in visual artifacts. Some of these can be
attributed to the lack of translation invariance of the wavelet
basis. One method to suppress suc ha r t i f a c t si st o“ a v e r a g eo u t ”
the translation dependence, i.e., through “cycle spinning” as
proposed by Coifman [27](8)where,.T h i si sc a l l e d cycle
spinning denoising. If we have an-sample data, then pixel
precision translation invariance is achieved by havingwavelet translation transforms (vectors) or.
Similar to cycle spinning de noising, thresholding-based
translation invariant denoising can be de fined as(9)
The bene fito ft r a n s l a t i o ni n v a r i a n c eo v e ro r t h o g o n a lt h r e s h -
olding is the SNR improvement afforded by the former. The
problem with orthogonal thresholding is that it introduces oscil-
lating artifacts that occur at random locations whenchanges.
However, translation invariance signi ficantly reduces these arti-
facts by the averaging process. A further improvement in SNR
can be obtained by proper selection of the thresholding esti-
mator.
IV. F ACEIMAGE RESTORATION METHODOLOGY
The proposed restoration met hodology is composed of an on-
lineand an offlineprocess (see Fig. 4). The online process has
two steps. First, each input face im age is automatically classi-
fied into one of three degradatio nc a t e g o r i e sc o n s i d e r e di nt h i s
work: 1) class 1: fax compression, 2) class 2: fax compression,
followed by printing and scanning, and 3) class 3: fax compres-
sion, followed by fax transmission and scanning. In actual im-
plementation, the system will not know whether the input face
image is degraded or not. If the input face image is the orig-
inal (good quality) image, it is assigned a fourth category, i.e.,
4) class 4: good quality. Based on this classi fication, a restora-
tion algorithm with a prede fined meta-parameter set associated
with the nature of degradation of the input image, is invoked.
Each meta-parameter set is deduced during the offline process .
A. Of fline Process
Noniterative denoising methods (as those described above,
viz., filtering and wavelet denoising with thresholding) de-
rive a solution through an explicit numerical manipulation
applied directly to the image in a single step. The advantages
of noniterative methods are prim arily ease of implementation
and faster computation. Unfortunately, noise ampli fication is
hard to control. Thus, when applied to degraded face images,
they do not result in an accepta ble solution. However, when
they are applied iteratively and evaluated through a quality
metric-based objective function, image reconstruction can be
performed by optimizing this function. In our study, we employ
such a scheme. At each step the system meta-parameters,
i.e., 2-D FIR filter type/size, wavelet/thresholding type, and
thresholding level, change incrementally within a prede fined
interval until the image quality of the reconstructed image is
optimized in terms of some image distortion metric.
Mathematically, this can be expressed as follows. In each
iterationof the algorithm, letbe the noisy observation of a
true 2-D image,a n d,be the estimated image
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BOURLAI et al. :R E S T O R I N GD E G R A D E DF A C EI M A G E S 375
Fig. 4. Overview of the face image restoration methodology.
wheredenotes the set of linear denoising param-
eters, i.e., filter type and window size, andis the set of nonlinear parameters, i.e., wavelet type, thresh-
olding type and level, r espectively. Then,,w h e r erepresents a dataset ofdegraded images, given a finite
domainthat represents the parameters employed
(discrete or real numbers) and a quality metric functionsuch
that,t h ep r o p o s e dr e c o n s t r u c t i o nm e t h o dw o r k s
byfinding the parameter setinthat maximizeswhere the terms involved correspond to filtering (noted as),
nonlinear denoising (noted as), and their combination (noted
as).
This procedure is iterated until convergence (i.e., stability of
the maximum quality) by altering the constrained parameters
(window/wavelet/thresholding type) and updating the window
size and threshold level in an incremental way. The maximum
number of iterations is empirically set. For instance, a threshold
value of more than 60 results in removing too much information
content. The application of thi sp r o c e s st oad e g r a d e dt r a i n i n g
dataset results in an estimated parameter set for each image. The
optimum meta-parameter set for each degraded training dataset
is obtained by averaging. The der ived meta-parameter sets are
utilized in the online restoration process.
B. Online Process
In the online process (see Fig. 4 ), the degradation type of each
input image is recognized by using a texture- and quality-based
classi fication algorithm. First, the classi fier utilizes the gray-
tone spatial-dependence matrix, or cooccurrence matrix (COM)[28], which is the statistical relationship of a pixel’s intensity to
the intensity of its neighborin gp i x e l s .T h eC O Mm e a s u r e st h e
probability that a pixel of a parti cular gray level occurs at a spec-
ified direction and distance from its neighboring pixels. In this
study, the main textural features extracted are inertia, correla-
tion, energy, and homogeneity:
•Inertia is a measure of local variation in an image. A high
inertia value indicates a high degree of local variation.
•Correlation measures the joint probability occurrence of
the speci fied pixel pairs.
•Energy provides the sum of squared elements in the COM.
•Homogeneity measures the closeness of the distribution of
elements in the COM to the COM diagonal.
These features are calculated from the cooccurrence matrix
where pairs of pixels separated by a distance ranging from 1
to 40 in the horizontal direction are considered resulting in
at o t a lo f1 6 0f e a t u r e sp e ri m a g e( 4m a i nt e x t u r a lf e a t u r e sa t
40 different offsets).
Apart from these textural feat ures, image graininess is used
as an additional image quality f eature. Graininess is measured
by the percentage change in image contrast of the original
image before and after blurring is applied.2The identi fication
of the degradation type of an input image is done by using the-Nearest Neighbor (-NN) method [29], [30] with.
The online process restores the input image by employing the
associated meta-parameter set (deduced in the of fline process).
C. Computation Time
Theonline restoration process when using MATLAB on a
Windows Vista 32-bit system with 4-GB RAM and Intel Core
Duo CPU T9300 at 2.5 GHz, requires about 0.08 s for the-NN
classi fication and about 2.5 s for image denoising, i.e., a total
time of less than 3 s per image.
2Available: http://www.clear.rice.edu/elec301/Projects02/artSpy/graini-
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376 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 6, NO. 2, JUNE 2011
Fig. 5. Sample images of subjects in the three datasets of PassportDB.
V. D EGRADED FACEIMAGE DATABASES
In this section, we will describe the hardware used for 1) the
acquisition of the high-quality f ace images, and 2) for printing,
scanning, and faxing the face images (along with the associated
software). We will also describe the live subject-capture setup
used during the data collection process and the three degraded
face image databases used in this paper.
1) Hardware and Subject-Capture Setup: AN I K O NC o o l p i x
P-80 digital camera was used fo rt h ea c q u i s i t i o no ft h eh i g h -
quality face images (36482736) and an HP Of fice jet Pro
L7780 system was used for printing and scanning images. The
fax machine used was a Konica Minolta bizhub 501, in which
the fax resolution was set to 600600 dpi, the data compres-
sion method was MH/MR/MMR/JBIG, and transmission stan-
dard used for the fax communication line was super G3. The
Essential Fax software was used to convert the scanned docu-
ment of the initial nondegraded face photos into a PDF docu-
ment with the fax resolution set to 203196 dpi.
Our live subject-capture se tup was based on the one sug-
gested by the U.S. State Department, Bureau of Consular
Affairs [31]. For the passport-capture setup we used the P-80
camera and the L7780 system. We acquired data from 28 sub-
jects bearing passports from di fferent countries, i.e., 4 from
Europe, 14 from the United States, 5 from India, 2 from Middle
East, and 3 from China; the age distribution of these partici-
pants was as follows: 20–25 (12 subjects), 25–35 (10 subjects),
and over 35 (6 subjects). The database was collected over
2s e s s i o n ss p a n n i n ga p p r o x i m a t e l y1 0d a y s .I nt h eb e g i n n i n g
of the first session, the subjects w ere briefed about the data
collection process after which they signed a consent document.
During data collection, each subject was asked to sit4f e e t
away from the camera. The data c ollection process resulted in
the generation of three datasets, i.e., the NIKON Face Dataset
(NFaceD) containing high-resol ution face photographs from
live subjects, the NIKON Passport Face Dataset (NPassFaceD)
containing images of passport photos, and the HP ScannedPassport Face Dataset (HPassFaceD) containing face images
scanned from the photo page of passports (see Fig. 5).
2) Experimental Protocol: Three databases were used in this
paper (Fig. 6).
Passport Database: As stated above, th ed a t ac o l l e c t i o n
process resulted in the generation of the Passport Database
(PassportDB) composed of three datasets: 1) the NFaceD
dataset that contains high-resolution face photographs from
live subjects, 2) the NPassFaceD da taset that contains passport
face images of the subjects acq uired by using the P-80 camera,
and 3) the HPassFaceD dataset that contains the passport face
images of the subjects acquire db yu s i n gt h es c a n n i n gm o d eo f
the L7780 machine.
In the case of NPassFaceD, three samples of the photo page
of the passport were acquired for each subject. In the case of
HPassFaceD, one scan (per subject) was suf ficient to capture a
reasonable quality mug-shot from the passport (Fig. 5).
Passport-Fax Database: This database was created from
thePassport Database (Fig. 7). First, images in the Passport
database were passed through four fax-related degradation
scenarios. This resulted in the g eneration of four fax-passport
datasets that demonstrate the different degradation stages of the
faxing process when applied to the original passport photos: –
Dataset 1 :E a c hf a c ei m a g ei nt h eN P a s s F a c e D / H P a s s F a c e D
datasets was placed in a Microsoft PowerPoint document. This
document was then processed by the fax software producing
am u l t i p a g eP D Fd o c u m e n tw i t h fax compressed face images.
Each page of the document was then resized to150%. Then,
each face image was captured at a resolution of 600600 dpi
by using a screen capture utilit ys o f t w a r e( S n a g I tv 8 . 2 . 3 ) . –
Dataset 2 :S a m ea s Dataset 1 ,b u tt h i st i m ee a c hp a g eo ft h e
PowerPoint document was resized to100%. Then each face
image was captured at a resolution of 400400 dpi. The pur-
pose of employing this scenario was to study the effect of lower
resolution of the passport face images on system performance.
–D a t a s e t3 :F o l l o w i n gt h es a m ei n i t i a ls t e p so f Dataset 1 ,a
multipage PDF document was pr oduced with degraded imagesmunotes.in

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BOURLAI et al. :R E S T O R I N GD E G R A D E DF A C EI M A G E S 377
Fig. 6. Description of the experimental protocol.
due to fax compression. The document was then printed and
scanned at a resolution of 600600 dpi. –D a t a s e t4 :A g a i n ,
we followed the same initial steps of Dataset 1 .I nt h i sc a s e ,t h e
PDF document produced was sent via an actual fax machine
and each of the resulting faxed pages was then scanned at a
resolution of 600600 dpi.
FRGC2-Passport F AX Database: The primary goal of the
Face Recognition Grand Challenge (FRGC) Database project
was to evaluate the face recognition technology. In this work,
we combined the FRGC dataset that has 380 subjects with our
NFacePass dataset that consists of another 28 subjects. The ex-
tended dataset is composed of 408 subjects with eight samples
per subject, i.e., 3264 high-quality facial images. The purpose
was to create a larger dataset of high-quality f ace images that
can be used to evaluate the restoration ef ficiency of our method-
ology in terms of identi fication performance, i.e., to investigate
whether the restored face imag es can be matched with the cor-
rect identity in the augmented database. Following the process
described for the previous database, four datasets were created
and used in our experiments.
A. Face Image Matching Methodology
The salient stages of the proposed method are described
below:
1)Face Detection :T h eV i o l a&J o n e sf a c ed e t e c t i o na l g o -
rithm [32] is used to localize t he spatial extent of the face
and determine its boundary.
2)Channel Selection :T h ei m a g e sa r ea c q u i r e di nt h eR G B
color domain. Empirically, it was determined that in the
majority of passports, the Green channel (RGB color
space) and the Value channel (HSV color space) are less
sensitive to the effects of watermarking and re flections
from the lamination. These t wo channels are selected and
then added, resulting in a new single-channel image. This
step is bene ficial when using the Passport data. With thefax data this step is not employed since the color images
are converted to grayscale by the faxing process.
3)Normalization :I nt h en e x ts t e p ,ag e o m e t r i cn o r m a l i z a -
tion scheme is applied to the original and degraded im-
ages after detection. The normalization scheme compen-
sates for slight perturbations in the frontal pose. Geometric
normalization is composed of two main steps: eye detec-
tion and af fine transformation. Eye detection is based on a
template matching algorithm. Initially, the algorithm cre-
ates a global eye from all subjects in the training set and
then uses it for eye detection b ased on a cross correlation
score between the global and the test image. Based on the
eye coordinates obtained by eye detection, the canonical
faces are constructed by applying an af fine transformation
as shown in Fig. 4. These faces are warped to a size of
300300. The photometric normalization applied to the
passport images before restoration is a combination of ho-
momorphic filtering and histogram equalization. The same
process is used for the fax compressed images before they
are sent to the fax machine.
4)Image Restoration :T h em e t h o d o l o g yd i s c u s s e di n
Section IV is used. By employing this algorithm, we
process the datasets described in Section V and create
their reconstructed versions th at are later used for quality
evaluation and identity authen tication. Fig. 8 illustrates
the effect of applying the restoration algorithm on some
of the Passport Datasets (1, 3, and 4), i.e., passport faces
a) subjected to T.6 compressi on (FAX SW) and restored;
b) subjected to T.6 compressi on, printed, scanned, and
restored; and c) subjected to T. 6c o m p r e s s i o n ,s e n tv i af a x
machine, then scanned and finally restored. Note that in
Fig. 8, the degraded faces in the left column are the images
obtained after face detection and before normalization.
5)Face Recognition Systems :B o t hc o m m e r c i a la n da c a -
demic software were emp loyed to perform the face
recognition experiments: 1) Commercial software Identitymunotes.in

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378 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 6, NO. 2, JUNE 2011
Fig. 7. Overview of the generation of the Passport FAX Database.
Fig. 8. Illustration of the effect of the proposed restoration algorithm. The input consists of (a) images subjected to fax compression and then captu red at
600600 dpi resolution; (b) images subjected to fax compression and then captured at 400400 dpi resolution; (c) images subjected to fax compression then
printed and scanned.
Tools G8 provided by L1 Systems;32) standard face
recognition methods provided by the CSU Face Iden-
tification Evaluation System [8], including Principle
Components Analysis (PCA) [33]–[35], ac o m b i n e dP r i n -
ciple Components Analysis and Linear Discriminant
Analysis algorithm (PCA+LDA) [36], the Bayesian In-
trapersonal/Extra-personal Classi fier(BIC) using either
the Maximum likelihood (ML) or the Maximum ap o s t e -
riori (MAP) hypothesis [37] and the Elastic Bunch Graph
3Available: www.l1id.comMatching (EBGM) method [38]; and (3) Local Binary
Pattern (LBP) method [39].
VI. E MPIRICAL EVA LUAT ION
The experimental scenarios investigated in this paper are the
following: 1) evaluation of image restoration in terms of image
quality metrics; 2) evaluation o ft h et e x t u r ea n dq u a l i t yb a s e d
classi fication scheme; and 3) identi fication performance before
and after image restoration.munotes.in

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BOURLAI et al. :R E S T O R I N GD E G R A D E DF A C EI M A G E S 379
Fig. 9. Improvement in image quality as assessed by the PSNR and UIQ metrics. These metrics are computed by using the high-quality counterpart of each i mage
as the “clean image.”
A. Image Restoration Evaluation
In this experiment, we demonstrate that the combination of
filtering and TI-denoising is essential for improving the quality
of restoration. Due to the absence of the ground truth passport
data (digital version of the face images before they are printed
and placed on the passport), we c ompare the high-quality live
face images of each subject agains tt h e i rd e g r a d e dv e r s i o n( d u e
to fax compression) in terms of the PSNR and UIQ metrics.
We investigate whether 1) linear filtering (2-D finite impulse
response (FIR) filters that used the windowing method), 2) de-
noising, or 3) their combination is a favorable choice for restora-
tion.
In the first experiment ,w et e s t e ds e v e nw i n d o w s ,i . e . ,b o x c a r ,
Hamming, Hanning, Bartlett, Blackman, Kaiser, and Chebwin,
and varied the window size from 3 to 60 in increments of 2.
When PSNR is used, in the majority of the cases (75%), the
most ef ficient window for image restoration was Hamming.
This is illustrated in Fig. 9(a). The same trend in results is
observed when using the UIQ metric; however, in a majority
of the cases (72%), the most ef ficient window for image
restoration was Hanning [Fig. 9(b)]. The main conclusion from
this experiment is that image filtering does improve the quality
of the degraded fax images.In the second experiment ,w ed e t e r m i n e dt h eT I - w a v e l e t
parameter set that could offer the best tradeoff between image
restoration (in terms of PSNR and UIQ) and computational
complexity. Thus, in this experiment, we examined the use of
different filters (Daubechies and Symlets), thresholding type
(hard, soft, semisoft), and level of thresholding (from 5 to 75
in increments of 5). The Daubechies filters are minimal phase
filters that generate wavelets which have a minimal support
for a given number of vanishing moments. Symlets are also
wavelets within a minimum size support for a given number
of vanishing moments. However, they are as symmetrical as
possible in contrast to the Daubechies filters which are highly
asymmetrical. Experimental results show that in terms of the
average metric (PSNR/UIQ) for all subjects, the best option
is to employ Symlet wavelets with hard thresholding [see
Fig. 9(a), (b)].
In the third experiment ,w ei n v e s t i g a t et h ee f f e c to fc o m -
bining filtering with denoising. Fig. 9(a) and (b) shows that,
overall, the best option is to combine Hanning Filtering with
Symlets (hard thresholding). We can see that in the baseline
case, the quality of the degraded fax images before restoration
is very low (almost zero in some cases). By using filtering, de-
noising, or both and employing the proposed iterative approach,
the average image quality signi ficantly improves. In the “best”munotes.in

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380 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 6, NO. 2, JUNE 2011
Fig. 10. Comparison of degraded images and their r econstructed counterparts after employing the proposed restoration method using PSNR/UIQ as qual ity met-
rics. UIQ appears to result in, at least visually, better images.
Fig. 11. (a) Clustering results when using textural features. (b) Importance of
graininess in identifying the degraded datasets. BFAXFax Compression
(not sent via Fax machine). AFAXsent via Fax machine.
option, we achieve an average q uality improvement of about
54% (PSNR), or approximately 7 times in terms of UIQ.
We note that the PSNR method does not provide as crisp
ar e s u l ta sU I Ql e a d i n gu st ot h ef o l l o w i n gq u e s t i o n :w h i c h
metric should be trusted? We know that PSNR (as well as mean
squared error) is one of the most widely used objective image
quality/distortion metric, but is widely criticized as well, for not
correlating well with perceived quality measurement. There are
many other image quality measurements proposed in the litera-
ture, but most of them share a common error-sensitivity-based
philosophy (motivated from psychological vision science re-
search), i.e., human visual error sensitivities and masking ef-
fects vary in different spatial fre quency, temporal frequency, and
directional channels.
In our experiments, UIQ appears to be more robust in the se-
lection of the best reconstructed image. Even though both PSNR
and UIQ lead to the same conclusion (that the combination of
image filtering and TI denoising is pr eferable), they converge
Fig. 12. Box plot of degradation classi fication performance results when using
a combination of features. Note that the central mark (red line) is the median
classi fication result over 10 runs, the edges of the box (blue) are the 25th and
75th percentiles, the whiskers (black lines) extend to the most extreme data
points not considered outliers, and outliers (red crosses) are plotted individu-
ally.Inertia;Homogeneity;Energy;Contrast (Image
Graininess); andno usage of Contrast.
to a different filtering window size and level of thresholding,
and ultimately image restoration quality. Fig. 10 illustrates some
cases where the reconstructed images based on PSNR were not
as good as those that were based on UIQ. This is a general con-
clusion based on the results fo und across all degradation sce-
narios investigated in this paper.
Based on the results obtained in this set of experiments, we
applied the iterative TI-wavelet restoration algorithm that com-
bines Hanning filtering and Symlets with hard thresholding to
both passport and passport-fax d atabases. The quality of the
restoration was then tested by using the commercial face recog-
nition software provided by L1 Systems.4
B. Evaluation of the Degradation Classi fication Algorithm
Thesecond experimental scenario illustrates the ef ficiency of
the degradation classi fication algorithm, i.e., the capability of
identifying the degradation t ype of an input image. For each de-
graded dataset generated from the FRGC2-Passport F AX Data-
base (Section V), a subset (approximately 22.5% of the training
set that was used for the identi fication experiments) is used to
extract the textural features as well as image graininess. Out of
all the features considered here, the optimal ones in terms of per-
formance are energy, homogeneity, and graininess. In Fig. 11(a),
we see the clustering of these f eature sets based on the nature
of degradation of the input image. It is important to see that
images in datasets 1 and 2 are within the same cluster. In con-
trast, datasets 3 and 4 form their own clusters. In addition, image
graininess can be used to separate datasets (1,2) from (3,4).
4Available: http://www.l1id.com/munotes.in