Prof. Mohd Zaid Abdullah Room No:

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1 EEE 52/4 Advnced Digital Signal and Image Processing Tuesday, hrs, Data Com. Lab. Friday, hrs, Data Com. Lab Prof. Mohd Zaid Abdullah Room No: 5 mza@usm.my

Electromagnetic Wave Wavelength () = C: speed of light 8 c 2.

2 Electromagnetic Wave Wavelength () = C: speed of light 8 c m/s Speed (C) Frequency (f) Energy (E) = hf h: Planck s constant h Js

3 Electromagnetic Spectrum

5 Biological Image Acuisition the human eye

6 Electronic Image Acuisition Camera Scanner Video camera Photocopying machine

7 Image Acquisition System Video signal Programma ble acquisition gain A/D converter Look-up table Image buffer Host 32- bit PCI bus PCI bus interface Image buffer control

8 Charge Couple Devices Select Column bus FET transistor Light Active mode Capacitor Photodiode Select Reset FET transistors Column bus V DD Light Passive mode Capacitor Photodiode

9 CCD Architectures CCD elements CCD cells Shift register Linear Integratio n area Sh ift re gis te r Sh ift re gis te r Sh ift re gis te r Sh ift re gis te r Storage area Frame transfer Shift register Interline Shift register

10 Digital Image Formation i (x,y) r (x,y) f (x,y) i (x,y): incident component r (x,y): reflected component f (x,y): image component

11 Sampling f t f 2 t 2 f2 f

12 Frequency Response f s f Nyquist Undersampled f s f Nyquist Nyquist rate f s f Nyquist Oversampled

13 Time domain Fourier Transform Spectrum Cosine Gaussian Impulse Impulses

14 Sampling and Quantization Continuous Scan line A-B Sampling Quantization

15 Sampling and Quantization Continuous Sampled

16 Igital Image Processing

17 Coordinate Convention System

18 Spatial and Gray Level Resolution l 0,255 Down sampling

28 x 28 64 x 64 32 x 32 Spatial and Gray Level Resolution Fixed gray level

19 28 x x x 32 Spatial and Gray Level Resolution Fixed gray level resolution - 8 bit Varying spatial resolution l 0, x x x 256

20 4 bits l = [0,5] 3 bits l = [0,7] 2 bits l = [0,3] bit l = [0,] Spatial and Gray Level Resolution Varying gray level resolution Fixed spatial resolution 8 bits l = [0,255] 7 bits l = [0,27] 6 bits l = [0,65] 5 bits l = [0,3]

21 Image Enhancement in the Spatial Domain

22 Gray Level Transformation

23 Histogram Processing

24 Transformation Function

25 Histogram Equalization

26 Transformation Functions

27 Histogram Matching

28 Histogram Equalization vs Histogram matching

29 Histogram Equalization

30 Histogram Matching

31 Spatial Filtering

32 3 x 3 Spatial Mask

33 Smoothing or averaging masks

34 Results of smoothing by filter mask of different sizes

35 Results of smoothing by filter

36 First and second order derivatives f (x) noise ramp thin line x

37 Isotropic filters

38 original Laplacian Laplacian scaled Enhanced using (5)

39 Gradient filters

40 Sobel filters original filtered

41 Image Enhancement in the Frequency Domain the Fourier discovery f f 2 f 3 f 4 f > f 2 > f 3 > f 4 f + f 2 + f 3 + f 4

42 Inverse relation

43 Fourier spectrum representations low high high low frequencies low high high high frequencies high high standard low low frequencies high high low high low low high high frequencies low low low frequencies low low optical high high frequencies low low high

44 Fourier spectrum of 20x40 white block (52 x 52 image)

45 SEM image of damaged IC

46 Notch filtering

47 Low pass filtering (LPF) and high pass filtering (HPF) LPF HPF

48 pass Ideal Low pass filter (ILPF) pass H(u,v) - D(u,v) - D o +D o + D(u,v)

49 Ideal Low pass filtering with different cut-off frequencies R=80, =98% R=5, =94.6% R=5, =92% R=230, =99.5% R=30, =96.4%

50 Ideal Low pass filtering, is total power removed R=30 =3.6% R=80, =2% R=230, =0.5% original R=5, =8% R=5, = 5.4%

51 H(u,v), R=5 Ideal Low pass filtering h(x,y) H(u,v) (x,y) g(x,y) (x,y) h(x,y)

52 Mini project groupings Group Group 2 Group 3 PROJECT 4 PROJECT 2 PROJECT 6 Group 4 Group 5 Group 6 PROJECT 5 PROJECT 3 PROJECT

53 Butterworth Low pass filter (BLPF)

54 2 nd order BLP filtering original R=5 R=5 R=30 R=80 R=230

55 BLPFs of different orders st 2 nd 3 rd 4 th

56 Gaussian Low pass filter (GLPF)

57 GLP filtering original R=5 R=5 R=30 R=80 R=230

58 High pass filters (HPFs) Ideal Butterworth Gaussian

59 Spatial representations Ideal Butterworth Gausssian

60 Ideal high pass filtering original D 0 =5 D 0 =30 D 0 =80

61 Butterworth high pass filtering, n=2 original D 0 =5 D 0 =30 D 0 =80

62 Gaussian high pass filtering, n=2 original D 0 =5 D 0 =30 D 0 =80

63 Homomorphic filtering original filtered L = 0.5 H = 2.0

64 Noise models Gaussian Rayleigh Gamma Exponential Uniform Impulse

65 Noise free test pattern black near white gray

66 Noisy images and histograms Gaussian Rayleigh Gamma

67 Noisy images and histograms Exponential Uniform Salt & pepper

68 Experimentation Impulse Degraded Impulse

69 Turbulence model H 2 2 k u v u, v e 5/ 6 Original Severe k = Mild k = 0.00 Low k =

70 Inverse filtering Original (M=N=480) Full Cut-off 40 Cut-off 70 Cut-off 85 Radially limited)

71 Wiener filtering Original Full inverse Radially limited inverse Weiner Iteratively chosen

72 Motion blurring N - g(x,y) = H(u,v) F(u,v) N M M Original, f(x,y) M = N = 400 H u, v i t = 40 i t u sin i M u sin M t e ju M i t

73 Inverse filtering Original Blurred Filtered F F for G( u, v) H ( u, v) u, v for u 0,20,30,..., 39 u v G u, v and F u, v G u, v, 2 2 u 0,20,30,...,39

74 Wiener filtering Original Blurred Filtered = 0.00

75 Inverse Inverse vs Wiener filtering Wiener Original Blurred

76 Inverse Noisy restoration Weiner Original Original + gaussian noise Blurred = 0.00

77 M = N = 8 First one First two 0 Fourier basis images (real) First three 2 First four All 6 7

78 M = N = 8 Fourier basis images (imaginary) First one First two 0 First three 2 First four All 6 7

Test image M = N = 8 255 255 255 255 255 255 255 255 255 0 0 0 0 0 0 255 255 0 255 255 255 255 0 255 255 0 255 50

79 Test image M = N =

80 Fourier reconstruction First five, E=539.5 First six, E=370.9 First seven, E=248.6 All, E=0 Original First one, E=895.7 First two, E=885.0 First three, E=785.2 First four, E=539.5

81 M = N = 8 First one 0 Harr basis images First two First three 2 First four All 6 7

82 Harr reconstruction First five, E=65.0 First six, E=603.7 First seven, E=587.5 All, E=0 Original First one, E=895.7 First two, E=895.7 First three, E=879.0 First four, E=832.7

83 Hadamard matrices Core 2 H 2 nd order 2 H H H 2 = H 2

84 Hadamard matrices 3 rd order 2 3 H H H H 3

85 Hadamard matrix, H 3 8 H 3 Sequency Not sequency order

86 Walsh- Hadamard matrix, H 3 8 H 3 Sequency Sequency order

87 M = N = 8 First one 0 Walsh-Hadamard basis images First two First three 2 First four All 6 7

88 W-H reconstruction First five, E=674. First six, E=674. First seven, E=0 Original First one, E=895.7 First two, E=895.7 First three, E=832.7 First four, E=832.7

89 E (%) Error in reconstruction Fourier Harr W-H First First 2First 3First 4First 5First 6First 7First 8 No. of basis images

90 Harr scaling functions 0,0 x x 2 2 x x 0, x 2 2x,0 x 2 2x,

91 Expansion x 0.5 x x 0. x f,0, 25, 4

92 Decomposition 0,0 x,0 2, 2

93 Harr wavelett functions 0, x x 0 Mother wavelett 2 x x 2 0,2 Child 2 x 2 2x,0 Child

94 Wavelett expansion f x = f x fa 0,0 0,2 f d 0,0 0,

95 Wavelett Series Expansion f x c j x j, k x d j k j, k x k 0 0 j j 0 k d j c j 0 : arbitrary starting scale j 0 k x x : approximation or scaling coefficients : detail or wavelet coefficients : scaling function : wavelet function c x f x, x f x x j j k j, k d 0 0, 0 x f x, x f x x j j, k j, k dx dx

96 Wavelett series expansion 2 y x

97 Given f Discrete Wavelet Transform x f x xx for x 0,,2,, M 0 j, k f x j k x W 0 0, M x j, k f x j k x W, M x Inverse DWT let j0 0 and M 2 j 0,,2,, J j k 0,,2,,2 J f M x W j0, k j k x W j k j k x 0,,, k M j j 0 k

98 Fast Wavelet Transform (D) HPF h n 2 W j, n W j, n h n LPF 2 W j, n

99 Fast Wavelet Transform (D) 2-stage/2-scale FWT h n 2 W J, n f n J,n h n 2 W J 2, n h n 2 W J, n h n 2 W J 2, n

100 Fast Wavelet Transform (D) Single stage synthesis W j, n 2 h n W j, n W j, n 2 h n

101 Fast Wavelet Transform (D) 2-stage synthesis W J, n J 2,n 2 2 h n h n 2 h n n J f W, n J 2,n 2 h n

102 Filter bank analysis h m 2 W D j, m, n h n 2 row, m j, m, n column, n h m h m 2 W V j, m, n row, m 2 W H j, m, n h n 2 row, m column, n h m 2 W j, m, n row, m

103 Decomposition W j, m, n j, m n W H j, m, n W, j, m nw D j, m, n W V,

104 Synthesis filter bank D j, m, n 2 h m V H j, m, n j, m, n row, m 2 row, m 2 h h m m 2 column, n h n W j, m, n j, m, n row, m 2 h m 2 column, n h n row, m

105 Sample image 52 x 52

106 Filter bank analysis first scale W j, m, n 256 x 256 W H j, m, n 256 x 256 W V j, m, n 256 x 256 W D j, m, n 256 x 256

107 Synthesis filter bank using (first-scale) W H D V j m, n, W j, m, n andw j, m, n, Original Reconstructed

108 Filter bank analysis Second-scale W H j, m, n 256 x 256 W V j, m, n 256 x 256 W D j, m, n 256 x 256

109 Synthesis filter bank using (two-scale) W j, m, n Original Reconstructed

Digital Image Processing. Chapter 4: Image Enhancement in the Frequency Domain

Digital Image Processing. Chapter 4: Image Enhancement in the Frequency Domain Digital Image Processing Chapter 4: Image Enhancement in the Frequency Domain Image Enhancement in Frequency Domain Objective: To understand the Fourier Transform and frequency domain and how to apply