Morphological Representation of DCT Coefficients for Image Compression

Outlines n n n n Introduction Morphological Representation DCT (MRDCT) Flowchart Reorganization Strategy of

Introduction n JPEG Compression flowchart -80 24 10 8 -2 12 0 4 -8

Morphological Representation DCT (MRDCT) Flowchart Block-based DCT Reorganization DCT Coefficients Quantization MRDCT Compression Result

Reorganization Strategy of DCT Coefficients DC AC 1 AC 5 AC 6 DC AC

Quantization n Dead-zone Uniform Scalar Quantization ：Stepsize Dead-zone：- ~ n Example 5 -4 1

Morphological Representation－Dilation Four elements of dilation operation 7

Morphological Representation of DCT Coefficients 1 -1 0 0 0 3 0 0 0

Arithmetic Coding Significant coefficients 2 3 0 0 0 -1 0 0 Range Table

Conclusions n n n Show the black-based DCT coefficients can have similar characteristics to

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Morphological Representation of DCT Coefficients for Image Compression Debin Zhao, Wen Gao, and Y. K. Chan, IEEE Transactions on Circuits and Systems for Video Technology, Vol. 12, No. 9, 2002, pp. 819 -823. Advisor：Prof. Chang Chin-Chen Student：Chen Yan-Ren Date： 2003/04/29 1

Outlines n n n n Introduction Morphological Representation DCT (MRDCT) Flowchart Reorganization Strategy of DCT Coefficients Quantization Morphological Representation of DCT Coefficients Arithmetic Coding Experimental Results Conclusions 2

Introduction n JPEG Compression flowchart -80 24 10 8 -2 12 0 4 -8 -4 0 8 -6 8 0 -2 6 6 0 6 12 -6 -4 0 -4 2 0 -4 10 0 0 -2 -2 0 4 4 -2 0 0 -2 0 4 -2 0 0 2 -2 0 0 -2 0 DCT Transfer -5 2 1 1 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 Quantization JPEG Compress Result Huffman Coding Zigzag Scan 3

Morphological Representation DCT (MRDCT) Flowchart Block-based DCT Reorganization DCT Coefficients Quantization MRDCT Compression Result Adaptive Arithmetic Coding Morphological Representation 4

Reorganization Strategy of DCT Coefficients DC AC 1 AC 5 AC 6 DC AC 2 AC 4 AC 7 12 AC 3 AC 8 11 13 AC 9 10 15 14 DC DC -80 24 3 1 10 5 2 4 -5 3 -1 2 -3 1 1 0 DC DC DC GO 0 DC G 01 AC 1 G 02 AC 2 G 03 AC 3 G 05 AC 8~AC 11 G 04 AC 4~AC 7 G 06 AC 12~AC 15 Reorganization -80 60 24 -8 5 3 1 2 -70 88 14 16 -4 12 8 3 10 9 -5 6 1 -3 -2 2 -15 12 10 8 -2 1 0 -1 3 -3 1 -1 4 2 1 0 0 -3 6 0 0 0 4 0 2 6 1 -2 0 5 1 -2 -4 0 0 0 0 Reorganization Result Block-based DCT 5

Quantization n Dead-zone Uniform Scalar Quantization ：Stepsize Dead-zone：- ~ n Example 5 -4 1 -2 3 12 -3 1 1 8 -2 0 2 3 2 -1 Quantization =4 1 -1 0 0 0 3 0 0 0 2 0 0 0 6

Morphological Representation－Dilation Four elements of dilation operation 7

Morphological Representation of DCT Coefficients 1 -1 0 0 0 3 0 0 0 2 0 0 0 Cluster detection in left-top-right bottom order GO 3 1 -1 0 0 0 3 0 0 0 2, 3, 0, 0, 0 0 0 1 -1 0 0 0 3 0 0 0 2 0 0 -1, 0 0 0 0 0 1 -1 0 0 0 3 0 0 0 2 0 0 0 0 0 8

Arithmetic Coding Significant coefficients 2 3 0 0 0 -1 0 0 Range Table Symbol Probability Range -1 0. 0≤r<0. 1 0 0. 6 0. 1≤r<0. 7 1 0. 7≤r<0. 8 2 0. 1 0. 8≤r<0. 9 3 0. 1 0. 9≤r<1. 0 Coding Steps Symbol Low Value High Value 0 1. 0 2 0. 8 0. 9 3 0. 89 0. 90 0 0. 891 0. 897 0 0. 8916 0. 8952 0 0. 89196 0. 89412 -1 0. 89196 0. 892176 0 0. 8919816 0. 8921112 1 0. 89207232 0. 89208528 0 0. 892073616 0. 892081392 0 0. 8920743936 0. 8920790592 9

Experimental Results 10

Conclusions n n n Show the black-based DCT coefficients can have similar characteristics to wavelet transform. Present an image coder utilizing these characteristics by morphological representation of DCT coefficients. The experimental results show that MRDCT is superior among the state-of-art DCT based image coders. 11