Basic encoding steps:

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1 5.8. Hybrid Coding Steps for Images, Video, and Audio Basic encoding steps: 1

2 Image Compression - JPEG (1) Image preparation and coding: (baseline system) select color space, color-subsampling, DCT, quantization, coding 2

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

4 Image Compression - JPEG (3) 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 4

5 Image Compression - JPEG (4) 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 5

6 Image Compression - JPEG (5) 1) select color space 2) color-subsampling 3) DCT 4) quantization 5) coding 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 DCT 1) normalize values 2) enforce NxN blocks 3) apply 2-D DCT 6

7 Image Compression - JPEG (6) Quantization 1) select color space 2) color-subsampling 3) DCT 4) quantization 5) coding select table Q quantify DCTcoefficients 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 7

8 Image Compression - JPEG (7) Coding 1) select color space 2) color-subsampling 3) DCT 4) quantization 5) coding DC-coefficient AC-coefficients DC-coefficient coding table: 16 categories with increasing number of entries code difference to preceding DC-coefficient: 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:

Image Compression - JPEG (8) Coding 1) select color space 2) color-subsampling 3) DCT 4) quantization 5) coding DC-coefficient AC-coefficients AC-coefficients are traversed in zick-zack and coded

9 Image Compression - JPEG (8) Coding 1) select color space 2) color-subsampling 3) DCT 4) quantization 5) coding DC-coefficient AC-coefficients AC-coefficients are traversed in zick-zack and coded absolutely The (Z,C) table contains Huffman codes for ACsequences 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) ->

10 Image Compression - JPEG (9) Result 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 %] 10

11 Image Compression - JPEG (10) Interactive examples: JPEG Lines Applet JPEG Parrots - Applet 11

12 Image Compression - JPEG (11) Interactive examples: Do it yourself with ImageTrans (*) (*) This is a Java Webstart application; you'll probably need to install this software from 12

13 Image Compression - JPEG (12) JPEG PNG Size: 3,164 bytes Size: 810 bytes Size: 3,564 bytes Size: 19,047 bytes 13

14 Overview Wavelets in practice JPEG 2000 Preprocessing DWT Quantizer Tier 1 / Tier 2 coding Comparison of JPEG 2000 with JPEG 14

15 JPEG 2000 block diagram 15

16 Baboon original 16

17 Baboon rgb colorspace 17

18 Baboon YCrCb colorspace 18

19 Baboon luma subsampled 2x 19

20 Baboon luma subsampled 4x 20

21 Baboon luma subsampled 8x 21

22 Baboon original 22

23 Baboon chroma subsampled 2x 23

24 Baboon chroma subsampled 4x 24

25 Baboon chroma subsampled 8x 25

26 Baboon original 26

27 JPEG 2000 block diagram 27

28 Transformation in JPEG 2000 DWT provides frequency band decomposition of the image Multi-resolution image representation Full-frame transformation -> no blocking artifacts Uses daubechies (9,7) floating point or (5,3) integer filter Use of integer filters -> both lossless and lossy compression Two implementation approaches: filter based / lifting scheme 28

29 1-D two-band DWT 29

30 1-D two-band DWT 30

31 2-D wavelet decomposition 31

32 Lena original 32

33 Lena horizontal high-pass 33

34 Lena horizontal low-pass 34

35 Lena low + high-pass subsampled 35

36 1-level 2-D wavelet decomposition 36

37 2-level 2-D wavelet decomposition 37

38 3-level 2-D wavelet decomposition 38

39 JPEG 2000 block diagram 39

40 Quantization and Dequantization 40

41 Quantization in JPEG

42 Quantization by bit-plane coding 42

43 Bit-plane example Wavelet coefficient = 83; Quantizer step size = 3 Quantizer index = 83/3 = 27 = Dequantized value based on fully decoded index ( )*3 = 82, Dequantized value after decoding 6 BP s: Decoded index = = 6; Step size = 12 Dequantized value = (6 + 0,5)*12 = 78 Dequantized value after decoding 4 BP s: Decoded index = 0001 = 1; Step size = 48 Dequantized value = ( )*48 = 72 43

44 JPEG 2000 block diagram 44

45 Entropy coding in JPEG

46 JPEG 2000 Entropy coder blocks 46

47 Bit-plane 1 47

48 Bit-plane 1 enlarged by 8x 48

49 Bit-plane 2 49

50 Bit-plane 2 enlarged by 8x 50

51 Bit-plane 3 51

52 Bit-plane 4 52

53 Bit-plane 5 53

54 Bit-plane 6 54

55 Bit-plane 7 55

56 Bit-plane 8 56

57 Bit-plane 9 57

58 Bit-plane 10 58

59 Bit-plane 11 59

60 JPEG 2000 block diagram 60

61 Tier 2 role Tier 1 generates a collection of bitstreams One independent bitstream for each code-block Tier 2 multiplexes the bitstreams for inclusion in the codestream and signals the ordering of the resulting coded bitplane passes in an efficient manner Tier 2 enables SNR, resolution, spatial, ROI and arbitrary progression and scalability 61

62 Example of coded data 62

63 Example of coded data 63

64 Lowest resolution, highest quality 64

65 Medium resolution, highest quality 65

66 Highest resolution, highest quality 66

67 Highest resolution, target SNR quality 67

68 Highest resolution, target visual quality 68

69 SNR progressive example 69

70 SNR progressive example 70

71 SNR progressive example 71

72 Resolution progressive example 72

73 Resolution progressive example 73

74 Resolution progressive example 74

75 Resolution progressive example 75

76 JPEG vs. JPEG 2000 original JPEG 2000 (43:1) JPEG (43:1) 76

Video-Conferencing System

Video-Conferencing System Evan Broder and C. Christoher Post Introductory Digital Systems Laboratory November 2, 2007 Abstract The goal of this project is to create a video/audio conferencing system. Video