Digital Image Processing BEC613C

Digital Image Processing

Course Code : BEC613C CIE Marks 50
Teaching/Week(L:T:P:S) 3:0:0:1 SEE Marks 50
Total Hours of Pedagogy 40 Total marks 100
Credits 3 Exam Hours 3

Module - 1
DIGITAL IMAGE FUNDAMENTALS: What is Digital Image Processing?.
Origins of Digital Image Processing, Fundamental Steps in Digital Image
Processing, Components of an Image processing system, Elements of Visual
Perception. Image Sensing and Acquisition, Image Sampling and Quantization, Some
Basic Relationships between Pixels, Module - 2
IMAGE TRANSFORMS: Introductions, Two-Dimensional Orthogonal &
Unitary Transforms, Properties of Unitary Transforms, Two Dimensional
Discrete Fourier Transform. Discrete Cosine Transform, Haar Transform

Module-3
SPATIAL DOMAIN: Some Basic Intensity Transformation Functions,
Histogram Processing, Fundamentals of Spatial Filtering, Smoothing Spatial
Filters, Sharpening Spatial Filters

Module-4
FREQUENCY DOMAIN: Basics Of Spatial Filtering in the Frequency Domain
Filters, Image Smoothing and Image Sharpening Frequency Domain Filter
Color Fundamentals. Color Models, Pseudo Color Image Processing.

Module-5
RESTORATION: Model Of Image Degradation/Restoration Process, Noise
Models, Restoration In The Presence of Noise, Only-Spatial Filtering Periodic
Noise Reduction by Frequency Domain Filtering, Linear Position-Invariant
Degradations, Inverse Filtering, Minimum Mean Square Error (Weiner) Filtering

TEXT BOOK:
1. “Digital Image Processing”, Rafael C.Gonzal and Richard E.
Woods, Pearson Education, 2001, 2nd edition.

REFERENCE BOOKS:
1. “Fundamentals of Digital Image Processing”, Anil K. Jain, Pearson Edun, 2001.
2. “Digital Image Processing and Analysis”, B. Chanda and D. Dutta
Majumdar, PHI, 2003

Dr.B B S Kumar, Associate Professor, DBIT

 Digital Image Processing BEC613C

Module-1

Introduction

1.1 What Is Digital Image Processing?

An image may be defined as a two-dimensional function, f(x, y), where x and y are
spatial (plane) coordinates, and the amplitude of f at any pair of coordinates (x, y) is
called the intensity or gray level of the image at that point. When x, y, and the amplitude
values of f are all finite, discrete quantities, we call the image a digital image. The field
of digital image processing refers to processing digital images by means of a digital
computer. Note that a digital image is composed of a finite number of elements, each of
which has a particular location and value. These elements are referred to as picture
elements, image elements, pels, and pixels. Pixel is the term most widely used to denote
the elements of a digital image.

1.2 Fundamental Steps in Digital Image Processing

It is helpful to divide the material covered in the following chapters into the two broad
categories defined in Section 1.1: methods whose input and output are images, and
methods whose inputs may be images, but whose outputs are attributes extracted from
those images..The diagram does not imply that every process is applied to an image.
Rather, the intention is to convey an idea of all the methodologies that can be applied to
images for different purposes and possibly with different objectives.
Image acquisition is the first process acquisition could be as simple as being given an
image that is already in digital form. Generally, the image acquisition stage involves
preprocessing, such as scaling.
Image enhancement is among the simplest and most appealing areas of digital image
processing. Basically, the idea behind enhancement techniques is to bring out detail that
is obscured, or simply to highlight certain features of interest in an image. A familiar
example of enhancement is when we increase the contrast of an image because “it looks

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better.” It is important to keep in mind that enhancement is a very subjective area of

image processing

Image restoration is an area that also deals with improving the appearance of an image.
However, unlike enhancement, which is subjective, image restoration is objective, in the
sense that restoration techniques tend to be based on mathematical or probabilistic
models of image degradation. Enhancement, on the other hand, is based on human
subjective preferences regarding what constitutes a “good” enhancement result.
Color image processing is an area that has been gaining in importance because of the
significant increase in the use of digital images over the Internet. fundamental concepts in
color models and basic color processing in a digital domain. Color is used also in later
chapters as the basis for extracting features of interest in an image.

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Wavelets are the foundation for representing images in various degrees of resolution. In
particular, this material is used in this book for image data compression and for
pyramidal representation, in which images are subdivided successively into smaller
regions.
Compression, as the name implies, deals with techniques for reducing the storage
required to save an image, or the bandwidth required to transmit it. Although storage
technology has improved significantly over the past decade, the same cannot be said for
transmission capacity. This is true particularly in uses of the Internet, which are
characterized by significant pictorial content. Image compression is familiar (perhaps
inadvertently) to most users of computers in the form of image file extensions, such as
the jpg file extension used in the JPEG(Joint Photographic Experts Group) image
compression standard.
Morphological processing deals with tools for extracting image components that are
useful in the representation and description of shape. The material in this chapter begins a
transition from processes that output images to processes that output image attributes,
Segmentation procedures partition an image into its constituent parts or objects. In
general, autonomous segmentation is one of the most difficult tasks in digital image
processing. A rugged segmentation procedure brings the process a long way toward
successful solution of imaging problems that require objects to be identified individually.
On the other hand, weak or erratic segmentation algorithms almost always guarantee
eventual failure. In general, the more accurate the segmentation, the more likely
recognition is to succeed.
Representation and description almost always follow the output of a segmentation stage,
which usually is raw pixel data, constituting either the boundary of a region (i.e., the set
of pixels separating one image region from another) or all the points in the region itself.
In either case, converting the data to a form suitable for computer processing is
necessary. The first decision that must be made is whether the data should be represented
as a boundary or as a complete region. Boundary representation is appropriate when the
focus is on external shape characteristics, such as corners and inflections. Regional
representation is appropriate when the focus is on internal properties, such as texture or
skeletal shape. In some applications, these representations complement each other.

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Choosing a representation is only part of the solution for transforming raw data into a
form suitable for subsequent computer processing. A method must also be specified for
describing the data so that features of interest are highlighted. Description, also called
feature selection, deals with extracting attributes that result in some quantitative
information of interest or are basic for differentiating one class of objects from another.

Recognition is the process that assigns a label (e.g., “vehicle”) to an object based on its
descriptors. As detailed in Section 1.1, we conclude our coverage of digital image
processing with the development of methods for recognition of individual objects. So far
we have said nothing about the need for prior knowledge or about the interaction between
the knowledge base and Knowledge about a problem domain is coded into an image
processing system in the form of a knowledge database. This knowledge may be as
simple as detailing regions of an image where the information of interest is known to be
located, thus limiting the search that has to be conducted in seeking that information. The
knowledge base also can be quite complex, such as an interrelated list of all major
possible defects in a materials inspection problem or an image database containing high-
resolution satellite images of a region in connection with change-detection applications.

In addition to guiding the operation of each processing module, the knowledge base also
controls the interaction between modules. This distinction is made in Fig. 1.23 by the use
of double headed arrows between the processing modules and the knowledge base, as
opposed to single-headed arrows linking the processing modules. Although we do not
discuss image display explicitly at this point, it is important to keep in mind that viewing
the results of image processing can take place at the output of any stage.

1.3 Components of an Image Processing System

Although large-scale image processing systems still are being sold for massive imaging
applications, such as processing of satellite images, the trend continues toward
miniaturizing and blending of general-purpose small computers with specialized image
processing hardware.

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The function of each component is discussed in the following paragraphs, starting with
image sensing. With reference to sensing, two elements are required to acquire digital
images. The first is a physical device that is sensitive to the energy radiated by the object
we wish to image. The second, called a digitizer, is a device for converting the output of
the physical sensing device into digital form. For instance, in a digital video camera, the
sensors produce an electrical output proportional to light intensity. The digitizer converts
these outputs to digital data.
Specialized image processing hardware usually consists of the digitizer just mentioned,
plus hardware that performs other primitive operations, such as an arithmetic logic unit
(ALU), which performs arithmetic and logical operations in parallel on entire images.
One example of how an ALU is used is in averaging images as quickly as they are
digitized, for the purpose of noise reduction. This type of hardware sometimes is called a
front-end subsystem, and its most

distinguishing characteristic is speed. In other words, this unit performs functions that
require fast data throughputs (e.g., digitizing and averaging video images at 30 frames_s)
that the typical main computer cannot handle.
The computer in an image processing system is a general-purpose computer and can
range from a PC to a supercomputer. In dedicated applications, sometimes specially
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designed computers are used to achieve a required level of performance, but our interest
here is on general-purpose image processing systems. In these systems, almost any well-
equipped PC-type machine is suitable for offline image processing tasks.

Software for image processing consists of specialized modules that perform specific
tasks. A well-designed package also includes the capability for the user to write code that,
as a minimum, utilizes the specialized modules. More sophisticated software packages
allow the integration of those modules and general- purpose software commands from at
least one computer language.

Mass storage capability is a must in image processing applications.An image of size

1024*1024 pixels, in which the intensity of each pixel is an 8-bit quantity, requires one
megabyte of storage space if the image is not compressed. When dealing with thousands,
or even millions, of images, providing adequate storage in an image processing system
can be a challenge. Digital storage for image processing applications falls into three
principal categories: (1) short term storage for use during processing, (2) on-line storage
for relatively fast recall, and (3) archival storage, characterized by infrequent access.
Storage is measured in bytes (eight bits), Kbytes (one thousand bytes), Mbytes (one
million bytes), Gbytes (meaning giga, or one billion, bytes), and T bytes (meaning tera,
or one trillion, bytes).

One method of providing short-term storage is computer memory.Another is by

specialized boards, called frame buffers, that store one or more images and can be
accessed rapidly, usually at video rates (e.g., at 30 complete images per second).The
latter method allows virtually instantaneous image zoom, as well as scroll (vertical shifts)
and pan (horizontal shifts). Frame buffers usually are housed in the specialized image
processing hardware unit. Online storage generally takes the form of magnetic disks or
optical-media storage. The key factor characterizing on-line storage is frequent access to
the stored data. Finally, archival storage is characterized by massive storage requirements
but infrequent need for access. Magnetic tapes and optical disks housed in “jukeboxes”
are the usual media for archival applications.

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Image displays in use today are mainly color (preferably flat screen) TV monitors.
Monitors are driven by the outputs of image and graphics display cards that are an
integral part of the computer system. Seldom are there requirements for image display
applications that cannot be met by display cards available commercially as part of the
computer system. In some cases, it is necessary to have stereo displays, and these are
implemented in the form of headgear containing two small displays embedded in goggles
worn by the user.

Hardcopy devices for recording images include laser printers, film cameras, heat-
sensitive devices, inkjet units, and digital units, such as optical and CD-ROM disks. Film
provides the highest possible resolution, but paper is the obvious medium of choice for
written material. For presentations, images are displayed on film transparencies or in a
digital medium if image projection equipment is used. The latter approach is gaining
acceptance as the standard for image presentations.

Networking is almost a default function in any computer system in use today. Because of
the large amount of data inherent in image processing applications, the key consideration
in image transmission is bandwidth. In dedicated networks, this typically is not a
problem, but communications with remote sites via the Internet are not always as
efficient. Fortunately, this situation is improving quickly as a result of optical fiber and
other broadband technologies.

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Recommended Questions

1. What is digital image processing? Explain the fundamental steps in digital image
processing.
2. Briefly explain the components of an image processing system.
3. How is image formed in an eye? Explain with examples the perceived brightness is
not a simple function of intensity.
4. Explain the importance of brightness adaption and discrimination in image
processing.
5. Define spatial and gray level resolution. Briefly discuss the effects resulting from a
reduction in number of pixels and gray levels.
6. What are the elements of visual perception?

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1. Elements of Visual Perception

1.1Elements Of Human Visual Systems

• The following figure shows the anatomy of the human eye in cross section

-3 membrane Cornea & Sclera outer layer, Choroid and Retina –average diameter 20mm
Cornea-tough and transparent issue
Sclera- Opaque membrane
Choroid- Iris and Ciliary body
• There are two types of receptors in the retina
– The rods are long slender receptors
– The cones are generally shorter and thicker in structure- 7-8 million helps at dim light night/bright light,
sensitive to color.
• The rods and cones are not distributed evenly around the retina.
• Rods and cones operate differently
– Rods are more sensitive to light than cones. 75 to 150 million

– At low levels of illumination the rods provide a visual response called scotopic vision(to see dim light at
night)
– Cones respond to higher levels of illumination; their response is called photopic vision
• Rods are more sensitive to light than the cones.
-Pupil varies diameter 2to 8mm, Iris-control of light, front of iris visible pigment and black pigment
-Lens contains 60 to 70% water, 6% fat, and protein, UV & IR observed by lens, over excessive
damages the lens

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• There are three basic types of cones in the retina

• These cones have different absorption characteristics as a function of

wavelength with peak absorptions in the red, green, and blue regions of the
optical spectrum.

• is blue, b is green, and g is red

Most of the cones are at the fovea. Rods are spread just about everywhere except the
fovea 2024-25

 There is a relatively low sensitivity to blue light. There is a lot of overlap

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1.1 Image Formation In The Eye

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1.2 Contrast Sensitivity

• The response of the eye to changes in the intensity of illumination is nonlinear

• Consider a patch of light of intensity i+dI surrounded by a background

intensity I as shown in the following figure

• Over a wide range of intensities, it is found that the ratio dI/I, called the
Weber fraction, is nearly constant at a value of about 0.02.

• This does not hold at very low or very high intensities

• Furthermore, contrast sensitivity is dependent on the intensity of the

surround. Consider the second panel of the previous figure.

1.3 Logarithmic Response of Cones and Rods

• The response of the cones and rods to light is nonlinear. In fact many image
processing systems assume that the eye's response is logarithmic instead of
linear with respect to intensity.

• To test the hypothesis that the response of the cones and rods are
logarithmic, we examine the following two cases:
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• If the intensity response of the receptors to intensity is linear, then the

derivative of the response with respect to intensity should be a constant. This
is not the case as seen in the next figure.

• To show that the response to intensity is logarithmic, we take the logarithm of

the intensity response and then take the derivative with respect to intensity.
This derivative is nearly a constant proving that intensity response of cones
and rods can be modeled as a logarithmic response.

• Another way to see this is the following, note that the differential of the
logarithm of intensity is d(log(I)) = dI/I. Figure 2.3-1 shows the plot of dI/I for
the intensity response of the human visual system.

• Since this plot is nearly constant in the middle frequencies, we again conclude
that the intensity response of cones and rods can be modeled as a logarithmic
response.

2.1 Image Sensing and Acquisition

The types of images in which we are interested are generated by the combination of an
“illumination” source and the reflection or absorption of energy from that source by the
elements of the “scene” being imaged. We enclose illumination and scene in quotes to
emphasize the fact that they are considerably more general than the familiar situation in
which a visible light source illuminates a common everyday 3-D (three-dimensional)
scene. For example, the illumination may originate from a source of electromagnetic
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energy such as radar, infrared, or X-ray energy. But, as noted earlier, it could originate
from less traditional sources, such as ultrasound or even a computer-generated
illumination pattern. Similarly, the scene elements could be familiar objects, but they
can just as easily be molecules, buried rock formations, or a human brain. We could
even image a source, such as acquiring images of the sun.

Depending on the nature of the source, illumination energy is reflected from, or

transmitted through, objects. An example in the first category is light reflected from a
planar surface. An example in the second category is when X-rays pass through a
patient’s body for the purpose of generating a diagnostic X-ray film. In some
applications, the reflected or transmitted energy is focused onto a photo converter (e.g.,
a phosphor screen), which converts the energy into visible light. Electron microscopy
and some applications of gamma imaging use this approach.
The idea is simple: Incoming energy is transformed into a voltage by the combination of
input electrical power and sensor material that is responsive to the particular type of
energy being detected.

The output voltage waveform is the response of the sensor(s), and a digital quantity is
obtained from each sensor by digitizing its response. In this section, we look at the
principal modalities for image sensing and generation.

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2.1.1 Image Acquisition Using a Single Sensor

The components of a single sensor. Perhaps the most familiar sensor of this type is the
photodiode, which is constructed of silicon materials and whose output voltage
waveform is proportional to light. The use of a filter in front of a sensor improves
selectivity. For example, a green (pass) filter in front of a light sensor favors light in the
green band of the color spectrum. As a consequence, the sensor output will be stronger
for green light than for other components in the visible spectrum. In order to generate a
2-D image using a single sensor, there has to be relative displacements in both the x- and
y-directions between the sensor and the area to be imaged. Figure 2.13 shows an
arrangement used in high-precision scanning, where a film negative is mounted onto a
drum whose mechanical rotation provides displacement in one dimension. The single
sensor is mounted on a lead screw that provides motion in the perpendicular direction.
Since mechanical motion can be controlled with high precision, this method is an
inexpensive (but slow) way to obtain high-resolution images. Other similar mechanical
arrangements use a flat bed, with the sensor moving in two linear directions. These types
of mechanical digitizers sometimes are referred to as microdensitometers.

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2.1.2 Image Acquisition Using Sensor Strips

A geometry that is used much more frequently than single sensors consists of an in-line
arrangement of sensors in the form of a sensor strip, shows. The strip provides imaging
elements in one direction. Motion perpendicular to the strip provides imaging in the
other direction. This is the type of arrangement used in most flat bed scanners. Sensing
devices with 4000 or more in-line sensors are possible. In-line sensors are used routinely
in airborne imaging applications, in which the imaging system is mounted on an aircraft
that flies at a constant altitude and speed over the geographical area to be imaged. One-
dimensional imaging sensor strips that respond to various bands of the electromagnetic
spectrum are mounted perpendicular to the direction of flight. The imaging strip gives
one line of an image at a time, and the motion of the strip completes the other dimension
of a two-dimensional image. Lenses or other focusing schemes are used to project area
to be scanned onto the sensors.

Sensor strips mounted in a ring configuration are used in medical and industrial imaging
to obtain cross-sectional (“slice”) images of 3-D objects\

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2.1.3 Image Acquisition Using Sensor Arrays

The individual sensors arranged in the form of a 2-D array. Numerous electromagnetic
and some ultrasonic sensing devices frequently are arranged in an array format. This is
also the predominant arrangement found in digital cameras. A typical sensor for these
cameras is a CCD array, which can be manufactured with a broad range of sensing
properties and can be packaged in rugged arrays of elements or more. CCD sensors are
used widely in digital cameras and other light sensing instruments. The response of each
sensor is proportional to the integral of the light energy projected onto the surface of the
sensor, a property that is used in astronomical and other applications requiring low noise
images. Noise reduction is achieved by letting the sensor integrate the input light signal
over minutes or even hours. The two dimensional, its key advantage is that a complete
image can be obtained by focusing the energy pattern onto the surface of the array.
Motion obviously is not necessary, as is the case with the sensor arrangements

This figure shows the energy from an illumination source being reflected from a scene
element, but, as mentioned at the beginning of this section, the energy also could be
transmitted through the scene elements. The first function performed by the imaging
system is to collect the incoming energy and focus it onto an image plane. If the
illumination is light, the front end of the imaging system is a lens, which projects the
viewed scene onto the lens focal plane. The sensor array, which is coincident with the
focal plane, produces outputs proportional to the integral of the light received at each
sensor. Digital and analog circuitry sweep these outputs and convert them to a video
signal, which is then digitized by another section of the imaging system.

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2.2 Image Sampling and Quantization

To create a digital image, we need to convert the continuous sensed data into digital
form. This involves two processes: sampling and quantization. A continuous image, f(x,
y), that we want to convert to digital form. An image may be continuous with respect to
the x- and y-coordinates, and also in amplitude. To convert it to digital form, we have to
sample the function in both coordinates and in amplitude. Digitizing the coordinate
values is called sampling. Digitizing the amplitude values is called quantization.

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The one-dimensional function shown in Fig. 2.16(b) is a plot of amplitude (gray level)
values of the continuous image along the line segment AB. The random variations are
due to image noise. To sample this function, we take equally spaced samples along line
AB, The location of each sample is given by a vertical tick mark in the bottom part of
the figure. The samples are shown as small white squares superimposed on the function.
The set of these discrete locations gives the sampled function. However, the values of
the samples still span (vertically) a continuous range of gray-level values. In order to
form a digital function, the gray-level values also must be converted (quantized) into
discrete quantities. The right side gray-level scale divided into eight discrete levels,
ranging from black to white. The vertical tick marks indicate the specific value assigned
to each of the eight gray levels. The continuous gray levels are quantized simply by
assigning one of the eight discrete gray levels 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.

2.3 Some Basic Relationships Between Pixels

In this section, we consider several important relationships between pixels in a digital

image.As mentioned before, an image is denoted by f(x, y).When referring in this
section to a particular pixel, we use lowercase letters, such as p and q.

Neighbors of a Pixel
A pixel p at coordinates (x, y) has four horizontal and vertical neighbors whose
coordinates are given by
(x+1, y), (x-1, y), (x, y+1), (x, y-1)
This set of pixels, called the 4-neighbors of p, is denoted by N4(p). Each pixel is a unit
distance from (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 (x+1, y+1), (x+1, y-1), (x-1, y+1), (x-
1, y-1)

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and are denoted by ND(p). These points, together with the 4-

neighbors, are called the 8- neighbors of p, denoted by N8(p). As
before, some of the points in ND(p) and N8(p) fall outside the image
if (x, y) is on the border of the image.

Adjacency, Connectivity, Regions, and Boundaries

Connectivity between pixels is a fundamental concept that

simplifies the definition of numerous digital image concepts, such
as regions and boundaries. To establish if two pixels are connected,
it must be determined if they are neighbors and if their gray levels
satisfy a specified criterion of similarity (say, if their gray levels are
equal).For instance, in a binary image with values 0 and 1, two
pixels may be 4-neighbors, but they are said to be connected only if
they have the same value.
Let V be the set of gray-level values used to define adjacency. In a
binary image, V={1} if we are referring to adjacency of pixels with
value 1. In a grayscale image, the idea is the same, but set V
typically contains more elements. For example, in the adjacency of
pixels with a range of possible gray-level values 0 to 255, set V
could be any subset of these 256 values. We consider three types of
adjacency:

(a) 4-adjacency. Two pixels p and q with values from V are 4-adjacent if q
is in the set
N4(p).
(b) 8-adjacency. Two pixels p and q with values from V are 8-adjacent if q
is in the set
N8(p).
(c) m-adjacency (mixed adjacency).Two pixels p and q with
values from V are m- adjacent if
(i) q is in N4(p), or

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(ii) q is in ND(p) and the set has no pixels whose values are from V.

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