# IMAGE COMPRESSION. October 7, ICSY Lab, University of Kaiserslautern, Germany

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1 Lossless Compression Multimedia File Formats Lossy Compression IMAGE COMPRESSION 69

2 Basic Encoding Steps 70

3 JPEG (Overview) Image preparation and coding (baseline system) 71

4 JPEG (Enoding) 1) select color space 2) color-subsampling 3) DCT 4) quantization 5) coding The following example shows an 8x8 pixel image section 8-bit numbers represent greyscales color space greyscale RGB YC b C r 72

5 JPEG (Encoding) 1) select color space 2) color-subsampling 3) DCT 4) quantization 5) coding Assuming a given 16x16 block with C b or C r The eye can sense local differences only poorly Averaged values of 2x2 sections 73

6 JPEG (Encoding) 1) select color space 2) color-subsampling 3) DCT 4) quantization 5) coding 8x8 block with 8-bit values thus P=8; left shift of all items corresponds to -128 this is the source matrix X DCT 1) normalize values 2) enforce NxN blocks 3) apply 2-D DCT 74

7 JPEG (Encoding) 1) select color space 2) color-subsampling 3) DCT 4) quantization 5) coding DCT 1) normalize values 2) enforce NxN blocks 3) apply 2-D DCT 8x8 block contains only values between -128 and 127 Application of the 2-D DCT leads to the transformed matrix D = A X A T 75

8 JPEG (Encoding) 1) select color space 2) color-subsampling 3) DCT 4) quantization 5) coding Quantization select table Q quantify DCT-coefficients select a quantization table Q with items q ij according to JPEG recommendation quantify according to stated formula and obtain table L with quantified DCT-coefficients store results in L 76

9 JPEG (Encoding) 1) select color space 2) color-subsampling 3) DCT 4) quantization 5) coding Coding DC-coefficient AC-coefficients DC-coefficient coding table: 16 categories with increasing number of entries code difference to preceding DCcoefficient: here: 3 3 is in group 2 and is on position 4 there (thus bitword 11) assuming Huffman-Code for group 2 is 2-bit long (e.g. 01) resulting sequence for DC:

10 JPEG (Encoding) 1) select color space 2) color-subsampling 3) DCT 4) quantization 5) coding AC-coefficients are traversed in zick-zack and coded absolutely Coding DC-coefficient AC-coefficients The (Z,C) table contains Huffman codes for AC-sequences Z: number of preceding zeros C: category of the AC coefficient For the example the results are: 1 -> (0,1) -> 00 1 (2nd position in 1st category) -9 -> (0,4) -> > (0,2) -> > (0,0) ->

11 JPEG (Encoding) 8x8 section coded with 23 bit i.e. in average 23/64 instead of 8 bit per pixel the reconstructed block has only small errors [values in %] 79

12 JPEG (Example, Comparision) Playing with JPEG ImageTrans Comparison JPEG & PNG 3,164 bytes 810 bytes 3,564 bytes 19,047 bytes 80

13 Wavelets (Introduction) Wavelets in practice JPEG 2000 Preprocessing DWT Quantizer Tier 1 / Tier 2 coding Comparison of JPEG 2000 with JPEG 81

14 JPEG 2000 (Overview) 82

15 JPEG 2000 (Example) 83

16 JPEG 2000 (RGB) 84

17 JPEG 2000 (YCrCb) 85

18 JPEG 2000 (Subsampling) 86

19 JPEG 2000 (Subsampling) 87

20 JPEG 2000 (Subsampling) 88

21 JPEG 2000 (Subsampling) 89

22 JPEG 2000 (Subsampling) 90

23 JPEG 2000 (Subsampling) 91

24 JPEG 2000 (DWT) 92

25 1-D two-band DWT 93

26 2-D wavelet decomposition 94

27 Lena original 95

28 Lena horizontal high-pass 96

29 Lena horizontal low-pass 97

30 Lena low + high-pass subsampled 98

31 1-level 2-D wavelet decomposition 99

32 2-level 2-D wavelet decomposition 100

33 3-level 2-D wavelet decomposition 101

34 JPEG 2000 (Quantization) 102

35 JPEG 2000 (Quantization) 103

36 JPEG 2000 (Quantization) Bit-plane coding 104

37 JPEG 2000 (Tier-1 Coding) 105

38 Entropy Coding JPEG 2000 (Tier-1 Coding) 106

39 JPEG 2000 (Tier-1 Coding) Entropy coder blocks 107

40 JPEG 2000 (Tier-1 Coding) 108

41 JPEG 2000 (Tier-1 Coding) 109

42 JPEG 2000 (Tier-1 Coding) 110

43 JPEG 2000 (Tier-1 Coding) 111

44 JPEG 2000 (Tier-1 Coding) 112

45 JPEG 2000 (Tier-1 Coding) 113

46 JPEG 2000 (Tier-1 Coding) 114

47 JPEG 2000 (Tier-1 Coding) 115

48 JPEG 2000 (Tier-1 Coding) 116

49 JPEG 2000 (Tier-1 Coding) 117

50 JPEG 2000 (Tier-1 Coding) 118

51 JPEG 2000 (Tier-2 Coding) 119

52 JPEG vs. JPEG 2000 original JPEG 2000 (43:1) JPEG (43:1) 120

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