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Presenter: Jin-Zuo Liu Research Advisor: Jian-Jiun Ding, Ph. D. Digital Image and Signal Processing Lab Graduate Institute of Communication Engineering National Taiwan University Image Compression 1

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Outlines Introduction to Image compression JPEG Standard JPEG2000 Standard Shape-Adaptive Image Compression Modified JPEG Image Compression Conclusions Reference 2

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Image Storage System 3

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Transform function: Y: the luminance represents the brightness Cb: the difference between the gray and blue Cr: the difference between the gray and red 4

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Downsampling formats of YCbCr 5

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Performance measures n 1 the data quantity of original image n 2 the data quantity of the generated bitstream. W the width H the height of the original image 6

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Outlines Introduction to Image compression JPEG Standard JPEG2000 Standard Shape-Adaptive Image Compression Modified JPEG Image Compression Conclusions Reference 7

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JPEG flowchart 8

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Why we apply DCT? Reduce the correlation between the neighboring pixels in the image coordinate rotation the f2 th pixel value Y X the f1 th pixel value f1-f2 = 3 pixels in horizontal 9

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Covariance Matrix Step1: Image partition Step2: Re-aligned the pixels of a 2-D block into a 1-D vector 10

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Karhunen-Loeve Transform (KLT) Coordinate rotation Normal orthogonal transformation V = [ v 1 v 2 v N ] v i the eigenvector of the corrosponding eigenvalue i of Cxx ( i 1 N ) 11

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DCT V.S KLT KLT is the Optimal Orthogonal Transform with minimal MSE but is difficult to implement DCT is the limit situation of KLT DCT advantages: 1. Eliminate the dependence on image data 2. Obtain the general transformation for every image 3. Reduce the correlation between pixels just like KLT 4. Smaller computation time 5. Real numbers 12

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Discrete Cosine Transform (DCT) Forward 2-D Discrete Cosine Transform Inverse 2-D Discrete Cosine Transform f(x,y) : the element in spatial domain F(u,v) : the DCT coefficient in the frequency domain 13

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Discrete Cosine Transform (DCT) 88 DCT 14

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JPEG Quantization Qantization: Qantization table 15

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DPCM for DC Components large correlation still exists between the DC components in the neighboring macroblocks 16

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Grouping method for DC component ValuesBits for the value group 00 -1,10,11 -3,-2,2,300,01,10,112 -7,-6,-5,-4,4,5,6,7000,001,010,011,100,101,110,1113 -15,...,-8,8,...,150000,...,0111,1000,...,11114 -31,...,-16,16,...3100000,...,01111,10000,...,111115 -63,...,-32,32,...63000000,...,011111,100000,...,1111116 -127,...,-64,64,...,1270000000,...,0111111,1000000,...,11111117 -255,..,-128,128,..,255...8 -511,..,-256,256,..,511...9 -1023,..,-512,512,..,1023...10 -2047,...,-1024,1024,...,2047...11 17

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Grouping method for DC component Example: diff=17 (17) 10 = (10001) 2 group 5 codeword: (110) 2 code: (11010001) 2 18

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Zigzag Scanning of the AC Coefficients 19

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Run Length Coding of the AC Coefficients The RLC step replaces the quantized values by Example: the zig-zag scaned 63 AC coefficients: Perform RLC : the number of zerosthe nonzero coefficients 20

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The Run/Size Huffman table for the luminance AC coefficients Run/Sizecode lengthcode word 0/0 (EOB)41010 15/0 (ZRL)1111111111001 0/1200... 0/671111000... 0/10161111111110000011 1/141100 1/2511011... 1/10161111111110001000 2/1511100... 4/5161111111110011000... 15/10161111111111111110 21

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Outlines Introduction to Image compression JPEG Standard JPEG2000 Standard Shape-Adaptive Image Compression Modified JPEG Image Compression Conclusions Reference 22

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The JPEG 2000 Standard JPEG2000 fundamental building blocks 23

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Discrete Wavelet Transform The analysis filter bank of the 2-D DWT 24

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Wavelet Transforms in Two Dimension Two-scale of 2-D decomposition 25

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Discrete Wavelet Transform One-scale of 2-D DWT 26

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Outlines Introduction to Image compression JPEG Standard JPEG2000 Standard Shape-Adaptive Image Compression Modified JPEG Image Compression Conclusions Reference 27

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Shape-Adaptive Image Compression Block-based transformation disadvantages: 1. block effect 2. no take advantage of the local characteristics in an image segment 28

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Shape-Adaptive Image Compression Algorithm structure 29

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Shape-Adaptive Transformation(1) Padding Algorithm Padding zeros into the pixel positions out of the image segment 30

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Shape-Adaptive Transformation(2) Arbitrarily-Shaped DCT Bases For and, where W: the width of the image segment H: the height of the image segment 31

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Shape-Adaptive Transformation(2) Arbitrarily-Shaped DCT Bases The shape matrix The 8x8 DCT bases with the shape 32

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Gram-Schmidt algorithm The 37 arbitrarily-shape orthogonal DCT bases 33

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Shape-Adaptive Transformation(3) Shape-Adaptive DCT Algorithm ( SADCT ) 34

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Shape-Adaptive DCT Algorithm ( SADCT ) The variable length (N-point) 1-D DCT transform matrix DCT-N : the pth DCT basis vector Transform function: 35

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Morphological Erosion 36

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Morphological Erosion Contour sub-region Interior sub-region The overall object 37

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Morphological Erosion Algorithm structure 38

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Shape-Adaptive Image Compression 1010101011011111 Image segments 100111101 010 101010111111111001 111000111000101011111 Quantizing & encoding EOB DCT coefficients boundary encoding bit stream of boundaries 1001111010101010101111111110 111000111000101011111 EOB 01 M1M1 M2M2 M3M3 S.A. DCT Bit-stream of image segments combine 39

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Simulation Results 40

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Outlines Introduction to Image compression JPEG Standard JPEG2000 Standard Shape-Adaptive Image Compression Modified JPEG Image Compression Conclusions Reference 41

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Modified JPEG Image Compression 2-D Orthogonal DCT Expansion in Triangular and Trapezoid Regions 42

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Trapezoid Definition Define the trapezoid : 43

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Trapezoid Definition Shearing a region that satisfies into the trapezoid region whose first pixels in each row are aligned at the same column. A triangular region can be viewed as a special case of the trapezoid region where 44

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Complete and Orthogonal DCT Basis in the Trapezoid Region 45

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Complete and Orthogonal DCT Basis in the Trapezoid Region 46

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Finding an approximate trapezoid region in an arbitrary shape 47

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Modified JPEG Image Compression Divide Images into three regions: 48

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Simulation Results 49

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Simulation Results 50

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Reference [1] R. C. Gonzalea and R. E. Woods, "Digital Image Processing", 2nd Ed., Prentice Hall, 2004. [2] Liu Chien-Chih, Hang Hsueh-Ming, "Acceleration and Implementation of JPEG 2000 Encoder on TI DSP platform" Image Processing, 2007. ICIP 2007. IEEE International Conference on, Vo1. 3, pp. III-329-339, 2005. [3] ISO/IEC 15444-1:2000(E), "Information technology-JPEG 2000 image coding system-Part 1: Core coding system", 2000. [4] Jian-Jiun Ding and Jiun-De Huang, "Image Compression by Segmentation and Boundary Description", Masters Thesis, National Taiwan University, Taipei, 2007. [5] Jian-Jiun Ding and Tzu-Heng Lee, "Shape-Adaptive Image Compression", Masters Thesis, National Taiwan University, Taipei, 2008. [6] G. K. Wallace, "The JPEG Still Picture Compression Standard", Communications of the ACM, Vol. 34, Issue 4, pp.30-44, 1991. [7] JPEG 2000 ( ) IC 2003.8 . [8] 2004. 51

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Thank you for listening ~ 52