Objective: Reduction of data redundancy. Coding redundancy Interpixel redundancy Psychovisual redundancy Fall LIST 2

Transcription

1 Image Compression

2 Objective: Reduction of data redundancy Coding redundancy Interpixel redundancy Psychovisual redundancy 20-Fall LIST 2

3 Method: Coding Redundancy Variable-Length Coding Interpixel Redundancy Run-Length Coding Predictive Coding Psychovisual Redundancy Lossly Coding 20-Fall LIST 3

4 Compression Ratio C R n n img cod n img : image sie n cod : code sie 20-Fall LIST 4

5 JPEG Joint Photographic Experts Group Image Compression Standard JPEG Lossy JPEG Lossless JPEG Fall LIST 5

6 Transformed Image Coding f Transform F Quantiation F q Lossless Coding Bit Allocation Lossless Decoding a Encoder Dequantiation F q Inverse Transform g b Decoder 20-Fall LIST 6

7 Linear Transform Energy compaction Optimal transformation Data independent basis 20-Fall LIST 7

8 Quantiation Quantiation is used only in lossy compression. Progressive quantiation Bit plane coding 20-Fall LIST 8

9 Bit Plane Coding MSB LSB 20-Fall LIST 9

10 Variable-Length Coding Higher-Probability Value Lower-Bit Code Gray Histogram Probability 20-Fall LIST 0

11 Entropy Coding Huffman code Gray Prob n cod =2*0.9+2*0.25+2*0.2+3* *0.08+5*0.06+6*0.03+6*0.02 = Fall LIST --

12 Code Gray Pixels:, 0,, 2,, 0, 2, 4, 3, 7, 6, 2, 0,... Codes : 0, 00, 0, 0, 0, 00, 0, 0, 0,, 0, 0, 00,... Code stream: Decoding: 0,00,0,0,0,00,0,0,0,, 0,0, Fall LIST -2-

13 Huffman Shift Coding p r r prefix symbol 20-Fall LIST 3

14 Arithmetic Coding Huffman coding : Symbol Code Symbol Sequence Code Stream Arithmetic Coding : Symbol Interval Symbol Sequence Subdivided real interval *0, 20-Fall LIST 4

15 Symbol Probability Subinterval a 0.2 [0.0, 0.2 a [0.2, 0.4 a [0.4, 0.8 a [0.8,.0 a a 2 a 3 a 3 a 4 a a a a a a 4 a 3 a 2 a 3 a a 3 a a 3 a a 3 a 2 a 3 a 2 a 0.2 a a a a a Fall LIST 5

16 Constant Area Coding a, a, a,..., a a, n n a : Symbol block of symbols Run-Length Coding 20-Fall LIST 6

17 D Run-Length Coding Symbol: 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 27, 27, 62, 62, 62, 62, 62, 62, 62, 62, Code: 0, 4, 5, 9, 27, 2, 62, 8 2D Run-Length Coding: Fall LIST -7-

18 JPEG Encoding and Decoding Encoding 8x8 block DCT Quantiation Matrix DC Q DPCM DC Huffman AC Zig Zag Scan AC Huffman Decoding Code books DC Huffman AC Huffman IDPCM DC AC Q - IDCT 8x8 block 20-Fall LIST 8

19 JPEG Coding Example x Block DCT coefficients Decoded image Histogram of AC coefficients 20-Fall LIST 9

20 JPEG Compression Standard DCT-based lossy compression

21 Sampling Y C C b r R G B R,G,B Y, C r, C b 20-Fall LIST 2

22 Color Image 20-Fall LIST 22

23 Red Green Blue Fall LIST 23

24 Y C b 5000 C r Fall LIST 24

25 Original image RGB down-sampled image 20-Fall LIST 25

26 original Cb Down-sampled Cb 20-Fall LIST 26

27 Original Cr Down-sampled Cr 20-Fall LIST 27

28 Original Image Down-sampled Cb,Cr 20-Fall LIST 28

29 Down-sampled RGB Down-sampled Cb,Cr 20-Fall LIST 29

30 YUV YCbCr Subsampling 4:4:4 4:2:2 [Y0dc, Y0ac], [Cbdc, Cbac], [Crdc, Crac] [Y0dc, Y0ac] [Ydc, Yac], [Cbdc, Cbac], [Crdc, Crac] 20-Fall LIST 30

31 Digital Cosine Transform 20-Fall LIST 3 DC Coefficient / AC Coefficients cos N x N u x x f u u C cos N u N u x u C u x f u N u N u N x x f C

32 MCU: Minimum coded unit 20-Fall LIST 32

33 DCT Basic Functions 20-Fall LIST 33

34 8x8 2D DCT Basic Functions 20-Fall LIST 34

35 Quantiation F q u,v = Fu,v/Q uv Quantiation Table scale factor % 5000 Q 200 2* Q Q Q 99 Q Fall LIST 35

36 Encoding DC Difference Coding AC RLE, Huffman Encoding 20-Fall LIST 36

37 DC Y, Cb, Cr: difference encoding SIZE, AMPLITUDE SSSS DIFF 20-Fall LIST 37

38 20-Fall LIST 38

39 20-Fall LIST 39

40 20-Fall LIST 40

41 AC Y, C b, C r : Run-Length Encoding Cnt of 0 Bits Value 4 4 RRRR SSSS 20-Fall LIST 4

42 20-Fall LIST 42

43 20-Fall LIST 43

44 Fall LIST 44

45 Fall LIST 45

46 20-Fall LIST 46

47 20-Fall LIST 47

48 DCT DWT 20-Fall LIST 48

49 Crochiere et al in 976 Subband Coding Simple and powerful technique Subband Coding Signal Subband 2 Coding Subband n Coding 20-Fall LIST 49

50 Fourier basis functions exact frequency spatially no precise Subband basis frequency concentration spacially compact 20-Fall LIST 50

51 Band Splitting octave bands 20-Fall LIST 5

52 Aliasing distortion 20-Fall LIST 52

53 2-band encoder/decoder 20-Fall LIST 53

54 Lowpass subband 20-Fall LIST 54

55 Highpass subband 20-Fall LIST 55

56 Cancellation of aliasing Y G Y G Y Fall LIST 56

57 20-Fall LIST X H X H Y 2 X H X H Y 0 0 Y G Y G Y X G H G H X G H G H Y

58 20-Fall LIST G H G H 0 H G 0 H G X H H H H Y 0 H H P 2 X P P Y

59 20-Fall LIST 59 m P P 2 if X Y m m n x n y e.g P

60 20-Fall LIST H H P H H H H

61 decomposition Wavelet transform X w a, b x t a, b t dt basis function: mother wavelet a, b t a, b t a t b a 20-Fall LIST 6

62 a, b t a t b a,0, b 2,0 0.5, 0 20-Fall LIST 62

63 20-Fall LIST 63

64 Scaling Wavelet Small scale -Rapidly changing details, -Like high frequency Large scale -Slowly changing details -Like low frequency 20-Fall LIST 64

65 Discrete wavelet transform DWT discretiation: x t X a, b m a a0 w a 0, m :integer a bandwidth bsampling for a 0 2, b 0 b nb a m 0 0 t m, nm, n m n x t m, n x t m, n t 20-Fall LIST 65

66 Multiresolution representation orthonormal set t n multireslution expansion n x t c t n n m/ 2 m m x t 2 c 2 t n m n n 20-Fall LIST 66

67 Harr wavelet: t 0 n c n n t 22t n 0 t scaling function: t otherwise c n 2 0 n 0, otherwise t 2t 2t t 0 2 t 2 t 20-Fall LIST 67

68 Harr scaling function Harr wavelet A x t 0 A x A j x t : approximationof x t at D j x t A x t j A j x t : detail t resolution of x t at j resolution j 20-Fall LIST 68

69 Wavelet transform and filter banks 20-Fall LIST 69 n n n n n t c t function synthesis scaling n t c t function analysisscaling 2 2 : 2 2 : n n n n n t d t synthesis wavelet n t d t analysiswavelet 2 2 : 2 2 :

70 analysis synthesis 20-Fall LIST 70

71 Wavelet filter design 20-Fall LIST 7 2 Q P n e.g , Q n P H H

72 Multidimensional wavelet transform 20-Fall LIST 72

73 2-D Example LIST Lec4 Wavelet Coding [73]

74 JPEG 2000

75 20-Fall LIST 75

76 20-Fall LIST 76

77 20-Fall LIST 77

78 20-Fall LIST 78

79 20-Fall LIST 79

80 20-Fall LIST 80

81 20-Fall LIST 8

82 20-Fall LIST 82

83 20-Fall LIST 83

84 20-Fall LIST 84

85 20-Fall LIST 85

86 20-Fall LIST 86

87 20-Fall LIST 87

88 Quantiation: 20-Fall LIST 88

89 64x64, 32x32 20-Fall LIST 89

90 Embedded Block Coding encoding at bit-plane level context-based adaptive binary arithmetic coder significance propagation magnitude refinement clean-up 20-Fall LIST 90