1. Chapter 2. Image Analysis

2. Image Analysis Domains Frequency Domain Spatial Domain

3. Image Algebra Addition  Morphing Addition  Morphing Subtraction  Segmentation Subtraction  Segmentation Multiplication by constant  brighter Multiplication by constant  brighter Division by constant  darker Division by constant  darker AND  mask AND  mask OR  mask OR  mask NOT  negative NOT  negative

8. Example

9. Image Geometry Scaling Scaling Translation Translation Rotation Rotation

10. How to enlarge an image (Scaling or Sampling) Zero-order hold (expand & duplicate) Zero-order hold (expand & duplicate) First-order hold (linear interpolation) First-order hold (linear interpolation)  Two methods 1.Expand rows, then expand columns 2.Extend with zeros, then perform convolution process (support by hardware)

12. First Method (Method I) 

13. Convolution process Kernel or Mask

14. Convolution

15. First Order (method II)

16. How to reduce # of gray levels (Quantization) Converting the lower bits to 0 via an AND operation. Converting the lower bits to 0 via an AND operation. Converting the lower bits to 1 via an OR operation. Converting the lower bits to 1 via an OR operation. Improved gray-scale (IGS) quantization Improved gray-scale (IGS) quantization  remove false contour Variable bin size quantization Variable bin size quantization

17. Example of IGS

19.  IGS Quantization recognizes the eye’s inherent sensitivity to edges and breaks them up by adding to each pixel a random number, which is generated from the low-order (Least Significant Bits) of neighboring pixels. Improved Gray-Scale (IGS) Quantization

20.  A sum is formed from the current 8-bit gray-level value and the four least significant bits of a previously generated sum. If the four most significant bits of the current value are 1111, however, 0000 is added instead. An Example

21. IGS Practice Consider an 8-pixel line of gray-scale data, {12, 12, 13, 13, 10, 13, 57, 54}, which has been uniformly quantized with 6-bit accuracy. Construct its 3-bit IGS (Improved Gray-Scale) code.

23. Smoothing Just like Integration

24. Image Filtering Linear filter Linear filter Non-linear filter Non-linear filter

25. Image Smoothing Mean Filtering Gaussian Filtering Median Filtering Smoothing uniform regions Preserve edge structure

26. Mean Filtering Example

27. Gaussian Filtering Masks

28. Properties of smoothing masks The amount of smoothing and noise reduction is proportional to the mask size. Step edges are blurred in proportion to the mask size.

29. Median Filtering Example

30. Example

31. Edge Detection Just like Differentiation

32. Detecting Edges

33. Edge Detection Masks

34. Properties of derivative masks The sum of coordinates of derivative masks is zero so that a zero response is obtained on constant regions. First derivative masks produce high absolute values at point of high contrast. Second derivative masks produce zero-crossings at points of high contrast.

35. Edge Magnitude & Orientation

37. Laplacian Of Gaussian (LOG)

38. Zero crossing detection A zero crossing at a pixel implies that the values of the two opposing neighboring pixels in some direction have different signs. There four cases to test: 1.up/down 2.left/right 3.up-left/down-right 4.up-right/down-left

39. Two equivalent methods 1.Convolve the image with a Gaussian smoothing filter and compute the Laplacian of the result. 2.Convolve the image with the linear filter that is the Laplacian of the Gaussian filter. 12

40. Gaussian Equations

41. Gaussian Plots

42. Gaussian Properties Symmetry matrix 95% of the total weight is contained within 2  of the center. In the first derivative of 1D Gaussian, extreme points are located at –  and + . In the second derivative of 1D Gaussian, zero crossings are located at –  and + . The LOG filter responds well to: 1. small blobs coinciding with the center lobe. 2. large step edges very close to the center lobe.

43. LOG Masks

44. LOG Example

45. Frei-Chen Edge Detection Represent any 3x3 subimage as a weighted sum of the nine Frei-Chen masks. Represent any 3x3 subimage as a weighted sum of the nine Frei-Chen masks. Weights are found by projecting a 3x3 subimage onto each of these masks. Weights are found by projecting a 3x3 subimage onto each of these masks. The projection is performed through convolution. The projection is performed through convolution.

46. Frei- Chen Masks

47. Projection of vectors Since f 1, f 2, …, f 9 are nine 9D orthonormal vectors

48. Errors in Edge Detection

49. Pratt Figure of Merit Rating Factor I N = maximum(I I, I F ) I N = maximum(I I, I F ) I I = # of ideal edge points I I = # of ideal edge points I F = # of found edge points I F = # of found edge points α = a scaling constant to adjust the penalty for offset edges α = a scaling constant to adjust the penalty for offset edges d i = the distance of a found edge point to an ideal edge point d i = the distance of a found edge point to an ideal edge point

50. Noise Removal

51. Pepper & Salt Noise Reduction Change a pixel from 0 to 1 if all neighborhood pixels of the pixel is 1 Change a pixel from 1 to 0 if all neighborhood pixels of the pixel is 0

52. Expanding & Shrinking

53. Example 1

54. Example 2

55. Image Segmentation Region Based Clustering Region Growing Edge based Boundary Detection

56. Space of Clustering Histogram space  Thresholding Histogram space  Thresholding Color space  K-Means Clustering Color space  K-Means Clustering Spatial space  Region Growing Spatial space  Region Growing

57. Histogram & Thresholding

58. P-Tile Thresholding

59. Mode Thresholding

60. Mode Algorithm

61. Iterative Thresholding

62. Adaptive Thresholding Example

63. Adaptive Thresholding

64. Variable Thresholding Example

65. Double Thresholding Method

66. Double Thresholding Example

67. Recursive Histogram Clustering

68. Clustering

69. Iterative K-Means Clustering

70. Example of Region Growing

71. Region Growing (Split & Merge Algorithm) 1.Split the image into equally sized regions. 2.Calculate the gray level variance for each region 3.If the gray level variance is larger than a threshold, then split the region. Otherwise, an effort is made to merge the region with its neighbors. 4.Repeat Step 2 & 3. Gray level variance :

72. Boundary Detection 1.Canny Edge Detector 2.Hough Transform

73. Canney Edge Detector

74. Canny Edge Detector Example

75. Hough Transform

76. Accumulator array for Hough Transform

77. Hough Transform for Accumulating Straight Lines

78. Hough Transform Example

79. Hough Transform for Extracting Straight Lines

80. Example of Hough Transform

81. Morphological Filter

83. Example

84. Example

85. Closing & Opening

86. Opening Example

87. Morphological Filter Example 1

88. Structure Element Example 1

89. Morpho- logical Filter Example 2

90. Structure Element Example 2

91. Conditional Dilation

92. Conditional Dilation Example

93. Image Transform

94. Basis Vectors

95. Transform Coefficients

96. Fourier Transform 1.Remove high frequency noise 2.Extract texture features 3.Image compression

97. Discrete Fourier Transform

98. Magnitude & Phase of Discrete Fourier Transform

99. Separability of Fourier Transform

100. Properties of Fourier Transform Translation Brightness Scaling Rotation

101. Discrete Cosine Transform

102. Discrete Cosine Transform Basis Images

103. Walsh-Hadamard Transform

104. Walsh- Hadamard Basis Images

105. Construction of Walsh-Hadamard Basis Images

106. Frequency Domain Image Filtering

107. Bandpass Filtering

108. Symmetry of the Fourier Transform

109. Symmetry of the Discrete Cosine Transform

110. Ideal Lowpass Filter

111. Nonideal Lowpass Filter

112. Highpass Filter

113. Bandpass & Bandreject Filter

115. Convolution Theorem 1.Fourier transform the image g(x,y) to obtain its frequency representation G(u,v) 2.Fourier transform the mask h(x,y) to obtain its frequency representation H(u,v) 3.Multiply G(u,v) and H(u,v) pointwise 4.Apply the inverse Fourier transform to obtain the filtered image