This document provides an introduction to digital image processing. It discusses key topics like image representation as matrices, image digitization which involves sampling and quantization, and the basic steps in digital image processing such as image acquisition, preprocessing, segmentation, feature extraction, recognition and interpretation. Importance of image processing is highlighted for applications like remote sensing, machine vision, and medical imaging. Common techniques like noise filtering, contrast enhancement, compression and their importance are also summarized.

1. CHAPTER1
INTRODUCTION
Dr. Varun Kumar Ojha
and
Prof. (Dr.) Paramartha Dutta
Visva Bharati University
Santiniketan, West Bengal, India

2. Introduction
 Introduction to Digital Image Processing
 Importance of Image Processing
 Image Representation
 Steps in Digital Image Processing
 Image Digitization
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3. Introduction to Digital Image
Processing
 “A digital Image Processing is processing of
image which is digital in nature”

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5. Importance of Image
Processing
 Enhancing Pictorial Information
 Improving the pictorial information for human
interpretation
 Noise Filtering
 Content Enhancements
 Contrast Enhancement (Low contrast to High
contrast)
 Deblurring ( Hazy image to clear image)
 Remote Sensing (Enhancing Satellite image)

6. Noise Filtering
Noisy Image Filtered Image

7. Content Enhancement
 Contrast Enhancement
Low contrast Image High contrast Image

8. Content Enhancement Cont..
 Deblurring

9. Remote Sensing
 Weather forecasting
 Atmospheric Study
 Astronomy
Ozone Hole GalaxyHurricane

10. Machine Vision Application
 Image processing for autonomous machine
application ( Medical, Mechanical Engg. Etc.)
 Industrial Machine Vision for Product Assembly &
Inspection
 Automated Target Detection & Tracking
 Fingerprint Recognition
 Satellite Image for weather forecasting
 Movement Detection

11. Automated Inspection
Middle bottle can be rejected
after inspection

12. Image Compression
 Image compression is needed for efficient storage and
transmission of an image
 An image contains lot of redundancy that can be
exploited to achieve compression
 Pixel Redundancy
 Coding Redundancy
 Psycho visual Redundancy
 Image contain two entity “Information” and
“Redundancy”. In image compression we try to keep
information content intact and we are removing the
redundancy

13. Image Compression Cont..
Original Image with
256 gray level
Image with 8 gray
level
Image represented
using binary dots

14.  Lossless Image Compression
 Only the redundancy is removed. The information
remains intact
 In case of medicine science we can not afford to
loss any information
 Lossy Compression
 Loss of information can be compromised for
some cases so we can afford to do lossy
compression ( in case of photographic image
some information loss can not affect the quality of
the image)
Image Compression Cont..

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16. Image Representation
 An image is a 2D light intensity
function f(x,y)
 A digital image f(x,y) is
dicretized both in spatial
coordinate and brightness
 It can be considered as a
matrix whose row , column
indices specify a point in the
image and the element value
identify gray level value at that
point
 These elements are referred to
as pixel or pel
Y
X
f(x,y) = r(x,y) * i(x,y)
f(x,y) → Intensity function
r(x,y) → reflectivity of the
corresponding image point
i(x,y) → Intensity of incident
light at particular point

17. Image Representation Cont..
 Spatial discretization by grid
 Intensity discretization by quantization

18. Image Representation Cont..
 An image I can be represented as matrix
 An image size can be a matrix of size 256 x 256
, 512 x512, 1024 x 1024 etc
 Quantization bit : 8 bit for b/w image
: 24 bit for colour image ( 8 bit
for

19. Image Representation Cont..

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21. Steps In Digital Image
Processing
1. Image Acquisition
 The capability to digitize the signal produced
by an image capturing sensor
1. Preprocessing
 Enhancing the image quality by filtering,
contrast enhancement etc.
1. Segmentation
 Partitioning an image into constituent part of
object

22. Steps In Digital Image
Processing
4. Description/Feature Selection
 Extract description of image objet suitable for further
preocess
4. Recognition & Interpretation
 Assigning a label to the object based on the
information provided by its descriptor.
 Interpretation assign meaning to a set of labeled
object
4. Knowledge Base
 Helps for efficient processing as well as inter module
cooperation

23. Steps In Digital Image
Processing
Knowledge
Base
Preprocessing
Segmentation
Description
&
Feature
Selection
Recognition
&
Interpretatio
n
Image
Acquisition
Problem
domain
Results
Block Diagram: Image Processing

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25. Image Digitization
 Why do we need Digitization?
 What is Image Digitization?
 How to Digitize an Image

26. Why Digitization
No of pixel along x axis 0 ≤ x ≤ H
No of pixel along y axis 0 ≤ y ≤ L
Intensity at f(x,y)
Imin ≤ f(x,y) ≤ Imax
Imin → minimum intensity value
Imax → maximum intensity value
Plotting intensity value against
pixel along y axis
Intensity along the yellow line in
the figure can vary from Imin to
Imax.
H
L
x
y
f(x,y)
I min
I max

27. Why Digitization
 Real Number Theory: Between any two points there
are infinite number of points.
 Between 0 to H and 0 to L there are infinite possible
points
 Between Imin to Imax there are infinite possible
intensity value
 So the problem is an image can have infinite points
and each point can have intensity value (colour
value) from infinite range
 So it is not possible to represent an image in
computer that’s why we need to digitize an image

28. Digitization
 Digitization means Sampling & Quantization
 An image can be represented by a 2D matrix
which has finite no. of values in rows and
columns
 Still, the value of element in the matrix may vary
from 0 to infinity
 We need to represent values of the matrix
element from a finite range, say from 0 to 8

29. Digitization
 To display an digital image we first convert it
to analog signal
Sampling Quantization
Digital
Computer
Digital
Computer
Digital to
Analog
Converter
Display

30. Sampling
 Image representation by a 2D matrix
 A 1D analog signal can be represented as
t
X(t)
Cycle/time
X(t)
∆ts ∆ts ∆ts ∆ts
Ruther by taking value at every point
we are taking value at some interval
∆
Sampling frequency fs = 1/ ∆ts

31. Sampling Cont..
∆ts ∆ts ∆ts ∆ts
Problem is some information
can be missed when we taking
value at interval ∆t
Missed Information Solution is increasing the
sampling frequency or
decreasing the sampling
interval ∆t
Here we take interval ∆t’s = ∆t /2
Sampling frequency
f’s = 1/ ∆t’s = 2/ ∆t = 2fs
X(t)
X(t)

32. Sampling Theory
 Sampling Function: 1D array of Dirac delta
function situated at regular spacing of ∆t.
∆t

33. Sampling Theory cont..
X(t)
X(t) : Continuous function
t
Xs(t)
Xs(t) : multiplication with
comb function
t
Xs(t) = set to 1 when
comb(t:∆t) gives 1
else Xs(t) set to 0
Sampling is correct and true if and only if reconstruction of the
previous analog signal is possible from the sampled signal

34. Convolution
Multiplication of two signal in time domain
If we have two signal h(t) and x(t) in time domain then h(t) * x(t) is
the convolution of the signals is represented as
Let we have the Fourier transform of the convolution

35. Convolution Cont..
Where X(w) is Fourier transform of xs(t) and H(w) is Fourier transform of h(t)
x(t) * h(t) ≡ X(w) . H(w)
So convolution of two signal in time domain is equivalent to the multiplication
of two signal in frequency domain

36. Convolution Concept
 Let we have function h(n) which I nothing but a
comb function and a signal x(n) as
-9 0 9
0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
h(n)
-2 -1 0 1 2
2 5 7 9 3x(n)
In discrete domain the convolution of h(n) and x(n) is represented as

37. Convolution Concept
-9
0 9
0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
h(m)
3 9 7 5 2
x( - n)
x( - 11 - m)
↓ -9
0 9
0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-2 -1 0 1 2
3 9 7 5 2

38. Convolution concept
-9
0 9
0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
h(m)
3 9 7 5 2
x( - n)
x( - 10 - m)
↓ -9
0 9
0 0 2 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-2 -1 0 1 2
3 9 7 5 2

39. Convolution concept
-9
0 9
0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
h(m)
3 9 7 5 2
x( - n)
x( - 9 - m)
↓ 0 9
0 0 2 5 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-2 -1 0 1 2
3 9 7 5 2

40. Convolution concept
-9
0 9
0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
h(m)
3 9 7 5 2
x( - n)
x( - 8 - m)
↓ 0 9
0 0 2 5 7 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-2 -1 0 1 2
3 9 7 5 2

41. Convolution concept
-9
0 9
0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
h(m)
3 9 7 5 2
x( - n)
x( - 7 -m)
↓ 0 9
0 0 2 5 7 9 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-2 -1 0 1 2
3 9 7 5 2

42. Convolution concept
h(m) convolution x(n)
0 9
0 0 2 5 7 9 3 0 0 0 0 2 5 7 9 3 0 0 0 0 2 5 7 9 3 0 0
-9 0 9
0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
-2 -1 0 1 2
2 5 7 9 3

43. Aliasing
w0
w00
1/ ∆ts
-w0
-w0
w0 Highest frequency
- w0 Lowest fequency
1/ ∆ts – w0 > w0
=> 1/ ∆ts > 2w0
fs = 2w0
(nyquest frequency)

44. Aliasing
w00 -w0
If we use alow pass fillter (LPF)
for cutting out frequency fs > 2w0
the reconstruction of original
continuous signal is possible
0
Overlapping
If fs 2w0 i.e fs < 2w0
Here single spectrum can not be
taken out by using LPF. Hence
distorted image in results. This
problem of overlapping is known
as aliasing

45. Quantization
 Quantization is a mapping of a continuous
variable U to a discrete variable U’
 U’ є { r1, r2, ….., rL} i.e u’ belongs to one of
these value
 U U‘Quantization
It is only discrete in time domain and we
get analog sample value U which also
needs to be dicretized. For this we use a
mapping function which generaly a stair
case function

46. Quantization Rule
 Define a set of decision or transition level
 { tk ; k= 1, 2, ….., L +1}
 Where t1 is the minimum value
 and tL+1 is the maximum value
 U’ = rk if tk < U < tk+1

47. Staircase Quantizer
t2t1 tL +1
t1
t2
rL+1
U
U’
Input signal lies along the U
axis
And corresponding U’
represent the quantized value
Here if the i/p signal lies
between t1 and t2 then it will
take the value r1 as
quantized value

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