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”
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)
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
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..
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
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
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
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
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
