Image Enhancement

1. 9/30/2023 1
Lecture 3 (2.5.07)
Image Enhancement in
Spatial Domain
Shahram Ebadollahi
DIP ELEN E4830

2. 9/30/2023 2
Today’s Lecture - Outline
 Review of Lecture 2
 Processing Images in Spatial Domain: Intro
 Image Histogram
 Point Operations
 Using Histogram for Image Enhancement
 Kernel Operations

3. 9/30/2023 3
Today’s Lecture - Outline
 Review of Lecture 2
 Processing Images in Spatial Domain: Intro
 Image Histogram
 Point Operations
 Using Histogram for Image Enhancement
 Kernel Operations

4. 9/30/2023 4
Today’s Lecture - Outline
 Review of Lecture 2
 Processing Images in Spatial Domain: Intro
 Image Histogram
 Point Operations
 Using Histogram for Image Enhancement
 Kernel Operations

5. 9/30/2023 5
Processing Images in Spatial Domain:
Introduction
)
(
(.)
f
T
g
f N
T



 

N
y
M
x
y
x
f 


 1
,
1
,
)
,
( N
y
M
x
y
x
g 


 1
,
1
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)
,
(
(.)
N
T : Spatial operator defined on a neighborhood N of a given pixel
)
,
(
0 y
x
N )
,
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4 y
x
N )
,
(
8 y
x
N
point processing mask processing

6. 9/30/2023 6
Mask (filter, kernel, window, template)
processing
x
y
(0,0)
x
y
(0,0)
)
,
( y
x
f )
,
( y
x
g

7. 9/30/2023 7
Today’s Lecture - Outline
 Review of Lecture 2
 Processing Images in Spatial Domain: Intro
 Image Histogram
 Point Operations
 Using Histogram for Image Enhancement
 Kernel Operations

8. 9/30/2023 8
Image Histogram
 
MxN
r
n
m
f
MxN
n
k
h
L
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k
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h
h
H
r
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, 1
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


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
histogram
histogram
bi-level image
Pixel values linearly
increasing from 0 to
255 with increasing
column index
normalized
256x256
256x256
r
H
r
H
255
255
0
0.5
0
1/256

9. 9/30/2023 9
Image Histogram: example

10. 9/30/2023 10
Today’s Lecture - Outline
 Review of Lecture 2
 Processing Images in Spatial Domain: Intro
 Image Histogram
 Point Operations
 Using Histogram for Image Enhancement
 Kernel Operations

11. 9/30/2023 11
Point Processing:
Thresholding
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Input gray-level value Output gray-level value

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(
 T

0

2


12. 9/30/2023 12
Point Processing:
Gamma Correction

cr
s 

13. 9/30/2023 13
Point Processing:
Contrast Stretching
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L-1

14. 9/30/2023 14
Point Processing:
Clipping & Thresholding
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s
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clipping
thresholding
clip
g
thresh
g

15. 9/30/2023 15
Point Processing:
Gray-level Slicing
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(
 T

2

1

0 L-1

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(
 T

2

1

0 L-1

16. 9/30/2023 16
Point Processing:
Bit-plane Slicing
0
1
2
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1
1 2
2
2
2 a
a
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f n
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f
e.g.
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 n
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n i
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a






 n
n
f
i
2
where,
lsb
msb

17. 9/30/2023 17
Point Processing:
Bit-plane Slicing (example)







0
,
0
1
,
n
n
a
a
L
g
f
Point operation for
obtaining n-th bit-plane:
n=7 n=6 n=5 n=4
Bi-level image

18. 9/30/2023 18
Today’s Lecture - Outline
 Review of Lecture 2
 Processing Images in Spatial Domain: Intro
 Image Histogram
 Point Operations
 Using Histogram for Image Enhancement
 Kernel Operations

19. 9/30/2023 19
Histogram Modification
 Apply a transform to an image such that the resulting
image has desired histogram.
 Histogram Equalization (linearization)
 Histogram Specification (matching)
 Non-adaptive vs. Adaptive Histogram Modification
 Global histogram
 Local histogram

20. 9/30/2023 20
Histogram Equalization
Source
image
Equalized
Image
Corresponding
Histograms

21. 9/30/2023 21
Histogram Equalization
 Often images poorly use the full range of the
gray scale
 Solution:
Transform image such that its histogram is spread
out more evenly in gray scale
 Rather than guessing the parameters and the
form of the transformation use original gray-
scale distribution as the cue

22. 9/30/2023 22
Histogram Equalization
Histogram
Equalization
r s
r
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MxN
n
r
p
r
T
s
0
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)
(
)
(
# pixels with the
j-th gray-level
image size
Point operation for
equalizing histogram
for the example image
(.)
T

23. 9/30/2023 23
Histogram Matching
 Transform image such that resulting image has
specified histogram



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r du
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Histogram
Matching
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

24. 9/30/2023 24
Histogram Matching




k
j
j
r
k
k r
p
r
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(
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1
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0 
 L
k 

25. 9/30/2023 25
Adaptive Histogram Equalization
Note: local
structure revealed
x
y
(0,0)
)
,
( y
x
f
)
,
( y
x
H
Histogram
Equalization

26. 9/30/2023 26
Today’s Lecture - Outline
 Review of Lecture 2
 Processing Images in Spatial Domain: Intro
 Image Histogram
 Point Operations
 Using Histogram for Image Enhancement
 Kernel Operations

27. 9/30/2023 27
Kernel Operator: Intro
Note: need to handle
borders of the image

28. 9/30/2023 28
Kernel Operator: Intro
Spatial
Filtering
f g
(.)
(.) w
TN 
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,
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(
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 n
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n
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f
w
n
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f
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n
m
f
w
n
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a
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N
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
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
1
1 kernel

29. 9/30/2023 29
FT
FT
Low-pass filter
Smoothing: Image Averaging
* Image edges
are softened

30. 9/30/2023 30
Smoothing: Averaging (example)
3x3
5x5
15x15
9x9
35x35
original
Noise effect is gone,
but image edges are
heavily blurred also

31. 9/30/2023 31
Order Statistics Filter
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{
max
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s
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,
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,
(
t
s
f
y
x
g
y
x
W
t
s 

original

32. 9/30/2023 32
Image Derivative

33. 9/30/2023 33
Image Sharpening: 1-st derivative

























y
f
x
f
G
G
f
y
x
Image gradient: y
x G
G
f 


Robert’s
operator
Sobel’s
operator
Sobel filter in
frequency
domain

34. 9/30/2023 34
Image Sharpening: 2-nd derivative
2
2
2
2
2
y
f
x
f
f







Image Laplacian:
)
,
(
2
)
,
1
(
)
,
1
(
2
2
y
x
f
y
x
f
y
x
f
x
f







)
,
(
2
)
1
,
(
)
1
,
(
2
2
y
x
f
y
x
f
y
x
f
y
f

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
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(
4
)
1
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(
)
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1
(
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(
2
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x
f
y
x
f
y
x
f
y
x
f
y
x
f
f


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







35. 9/30/2023 35
Image Sharpening: 2-nd derivative
* +
Laplacian filter in
frequency
domain

36. 9/30/2023 36
High-boost Filtering
Avg.
+
+
-
)
,
(
)
,
(
)
,
( y
x
f
y
x
Af
y
x
f lp
hb 

Unsharp mask:
high-boost with A=1

37. 9/30/2023 37
Recap
 Point operations vs. Kernel Operations
 Image Histogram
 Image Enhancement using Point Operators
 Contrast Stretching
 Gamma Correction
 Using Image Histogram for Enhancement
 Histogram Equalization
 Histogram Matching
 Image Enhancement using Kernel Operators
 Low-pass filtering (averaging)
 High-pass filtering (sharpening)