Lecture-02_DigitalImageEnhancemnet-02.pdf

Image Enhancement

1. Dr. Muhammad Hanif

2. Image Enhancement

9. Image Enhancement

10. Histogram

11. Histogram

12. Histogram

13. Histogram

14. Histogram

15. Interpreting Histograms

16. Histogram

17. Contrast and Histogram

18. Histogram Basics
Normalized histogram ( )
: the number of pixels in the image of
size M N with intensity
k
k
k
k
n
pr
MN
n
r
=
´
Histogram ( )
is the intensity value
is the number of pixels in the image with intensity
kk
th
k
kk
hr n
rk
nr
=

19. Histogram Equalization
•A popular technique for improving the appearance of a poor image
•Goal: The histogram of the resultant image is as flat as possible
•The histogram equalization process for digital images consists of four
steps:
•1. Find the running sum of the histogram values
•2. Normalize the values from step1 by dividing by total number of pixels.
•3. Multiply the values from step2 by the maximum gray level value and round.
•4. Map the gray-level values to the results from step 3, using a one-to-one
correspondence.

20. Histogram Equalization
•Example:
•We have an image with 3 bit /pixel, so the possible range of values is
0 to 7. We have an image with the following histogram:

21. Histogram Equalization

22. Histogram Equalization

23. •Suppose that a 3-bit image (L=8) of size 64 × 64 pixels (MN = 4096) has the intensity distribution shown in following table.
•Get the histogram equalization transformation function and give the ps(sk) for each sk.
Histogram Equalization

24. 0
00
0
() 7 () 70.19 1.33
rj
j
sTr pr
=
== =´= å
1®
1
11
0
( ) 7 ( ) 7 (0.19 0.25) 3.08
rj
j
sTr pr
=
== =´+= å
3®
23
45
67
4.55 5 5.67 6
6.23 6 6.65 7
6.86 7 7.00 7
ss
ss
ss
=®=®
=®=®
=®=®
Histogram Equalization

25. Histogram Equalization

26. Histogram Equalization

27. Point Operation and Histogram

28. Color image Histogram

29. Point Operation

30. Homogenous point Operation

31. Point Operation Pseudocode

32. Non-Homogenous point operation

33. Inverting Image

34. Image Negative

35. Thresholding

36. Thresholding

37. Thresholding and Histogram

38. Basic Grey level Transforms

39. Logarithmic Transform

42. Image Processing

43. Example

45. Example

46. Noise Estimation

47. Periodic Noise

48. Periodic Noise

49. Image Restoration

50. Correlation vs Convolution
•Both are used to extract information from images
•Both have two key features: they are Time/Shift-invariant, and linear
•Time/Shift-invariant means that we perform the same operation at
every point in the image.
•Linear means that this operation is linear, that is, we replace every pixel
with a linear combination of its neighbors.

51. Cross-Correlation Vs Convolution
•Correlation is the process of moving a filter mask often referred to as
kernel over the image and computing the sum of products at each
location.
•Correlation is the function of displacement of the filter.
•This is also known as aslidingdot productorsliding inner-product
•In other words, the first value of the correlation corresponds to zero
displacement of the filter, the second value corresponds to one unit
of displacement, and so on.

52. Cross-Correlation Vs Convolution
•Correlation is the process of moving the template or subimage w
around the image area and computing the value C in that area.
•This involves multiplying each pixel in the template by the image
pixel that it overlaps and then summing the results over all the
pixels of the template.
•The maximum value of C indicates the position where w best
matches f.

53. 2D Correlation
•Given a square filter, we can compute the results of correlation by
aligning the center of the filter with a pixel. Then we multiply all
overlapping values together, and add up the result. We can write this
as:

54. Applying linear filter: Cross-Correlation

55. Cross-Correlation Vs Convolution

56. Cross-Correlation Vs Convolution

57. Cross-Correlation Vs Convolution

58. Cross-Correlation Vs Convolution

59. 2D Convolution
•Convolution is just like correlation, except that we flip over the filter
before correlating.
•In the case of 2D convolution we flip the filter both horizontally and
vertically.

60. Cross-Correlation Vs Convolution
•In Convolution operation, the kernel is first flipped by an angle of 180
degrees and is then applied to the image.
•The fundamental property of convolution is that convolving a kernel
with a discrete unit impulse yields a copy of the kernel at the location
of the impulse.

61. Cross-Correlation Vs Convolution

62. Cross-Correlation Vs Convolution

63. Enhancement Techniques

64. Image Denosing: Mean filters

65. Image Denosing: Mean filters

66. Image Denosing: Harmonic & Contra-Harmonic

67. Image Denosing: Harmonic & Contra-Harmonic

71. Cross-Correlation Vs Convolution
•Correlation is the process of moving a filter mask often referred to as
kernel over the image and computing the sum of products at each
location.
•Correlation is the function of displacement of the filter.
•This is also known as aslidingdot productorsliding inner-product
•In other words, the first value of the correlation corresponds to zero
displacement of the filter, the second value corresponds to one unit
of displacement, and so on.

72. Cross-Correlation Vs Convolution
•Correlation is the process of moving the template or subimage w
around the image area and computing the value C in that area.
•This involves multiplying each pixel in the template by the image
pixel that it overlaps and then summing the results over all the
pixels of the template.
•The maximum value of C indicates the position where w best
matches f.

73. Cross-Correlation Vs Convolution

74. Cross-Correlation Vs Convolution

75. Cross-Correlation Vs Convolution

76. Cross-Correlation Vs Convolution
•In Convolution operation, the kernel is first flipped by an angle of 180
degrees and is then applied to the image.
•The fundamental property of convolution is that convolving a kernel
with a discrete unit impulse yields a copy of the kernel at the location
of the impulse.

77. Cross-Correlation Vs Convolution

78. Cross-Correlation Vs Convolution

79. Enhancement Techniques

80. What is a Filter?

81. What Point operation Can’t Do!

82. Spatial Filter

83. Example: Mean of 3x3

84. Kernel operation

85. Kernel operation: Smoothing

86. Kernel operation: Smoothing

87. Kernel operation: Smoothing

88. Filter Matrix

89. Example
What this filter do?

90. Example 2

91. Mean Filter
Effect of filter size

92. Applying linear filter: Cross-Correlation

93. Computing Filter Operation

94. Filtering and boundary pixels
•There are a few approaches to dealing with missing edge pixels: –
•Omit missing pixels
•Only works with some filters
•Can add extra code and slow down processing
•Pad the image
• Typically with either all white or all black pixels
•Replicate border pixels
•Truncate the image
•Allow pixels wrap around the image
• Can cause some strange image artefacts

95. Filtering and boundary pixels

96. Filtering and boundary pixels

97. Filtering and boundary pixels

98. Filtering and boundary pixels

99. Image Filtering
•Filtering operation:
•Linear : a convolution operation between f(x,y) and a window
function w(x,y).
•A filtering method is linear when the output is a weighted sum
of the input pixels.
•Non-Linear: response is based on ordering (ranking) the pixels

100. Linear Filters

101. Gaussian Filter

102. Difference filter

103. Convolution: properties

104. Convolution: Properties

105. Linear Image Filtering
- Varying the weights m(i,j), results in
different type of linear neighborhood
operations (filtering).

106. Linear Image Filtering
•Example: Smoothing filter:
•average all of the pixels in a neighbourhood around a central value

107. Weighted Smoothing filter

108. Impulse (Dirac) function

109. Impulse (Dirac) function

110. Box Filter

111. Box Filter

112. Box Filter

113. Box Filter

114. Box Filter

115. References