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Image Compression Jin-Zuo Liu Jian-Jiun Ding , Ph. D. Presenter:
Research Advisor: Jian-Jiun Ding , Ph. D. Digital Image and Signal Processing Lab Graduate Institute of Communication Engineering National Taiwan University
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Outlines Introduction to Image compression JPEG Standard
Shape-Adaptive Image Compression Modified JPEG Image Compression Conclusions Reference
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Image Storage System
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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
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Downsampling formats of YCbCr
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Performance measures n1: the data quantity of original image
n2:the data quantity of the generated bitstream. W: the width H : the height of the original image
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Outlines Introduction to Image compression JPEG Standard
Shape-Adaptive Image Compression Modified JPEG Image Compression Conclusions Reference
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JPEG flowchart
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Why we apply DCT? Reduce the correlation between the neighboring pixels in the image coordinate rotation the f2th pixel value Y X the f1th pixel value ︱ f1-f2 ︱= 3 pixels in horizontal
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Covariance Matrix Step1: Image partition
Step2: Re-aligned the pixels of a 2-D block into a 1-D vector
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Karhunen-Loeve Transform (KLT)
Coordinate rotation Normal orthogonal transformation V = [ v1 v2 . .vN ] vi :the eigenvector of the corrosponding eigenvalue λi of Cxx ( i =1 ~N )
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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
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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
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Discrete Cosine Transform (DCT)
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JPEG Quantization Qantization: Qantization table
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DPCM for DC Components large correlation still exists between the DC components in the neighboring macroblocks
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Grouping method for DC component
Values Bits for the value group -1,1 0,1 1 -3,-2,2,3 00,01,10,11 2 -7,-6,-5,-4,4,5,6,7 000,001,010,011,100,101,110,111 3 -15,...,-8,8,...,15 0000,...,0111,1000,...,1111 4 -31,...,-16,16,...31 00000,...,01111,10000,...,11111 5 -63,...,-32,32,...63 000000,...,011111,100000,...,111111 6 -127,...,-64,64,...,127 ,..., , ,..., 7 -255,..,-128,128,..,255 ... 8 -511,..,-256,256,..,511 9 -1023,..,-512,512,..,1023 10 -2047,...,-1024,1024,...,2047 11
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Grouping method for DC component
Example: diff=17 (17)10 = (10001)2 group 5 codeword: (110)2 → code: ( )2
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Zigzag Scanning of the AC Coefficients
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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 zeros the nonzero coefficients
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The Run/Size Huffman table for the luminance AC coefficients
code length code word 0/0 (EOB) 4 1010 15/0 (ZRL) 11 0/1 2 00 ... 0/6 7 0/10 16 1/1 1100 1/2 5 11011 1/10 2/1 11100 4/5 15/10
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Outlines Introduction to Image compression JPEG Standard
Shape-Adaptive Image Compression Modified JPEG Image Compression Conclusions Reference
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The JPEG 2000 Standard JPEG2000 fundamental building blocks
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Discrete Wavelet Transform
The analysis filter bank of the 2-D DWT
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Wavelet Transforms in Two Dimension
Two-scale of 2-D decomposition
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Discrete Wavelet Transform
One-scale of 2-D DWT
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Outlines Introduction to Image compression JPEG Standard
Shape-Adaptive Image Compression Modified JPEG Image Compression Conclusions Reference
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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
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Shape-Adaptive Image Compression
Algorithm structure
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Shape-Adaptive Transformation(1)
Padding Algorithm Padding zeros into the pixel positions out of the image segment
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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
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Shape-Adaptive Transformation(2)
Arbitrarily-Shaped DCT Bases The shape matrix The 8x8 DCT bases with the shape
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Gram-Schmidt algorithm
The 37 arbitrarily-shape orthogonal DCT bases
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Shape-Adaptive Transformation(3)
Shape-Adaptive DCT Algorithm ( SADCT )
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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:
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Morphological Erosion
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Morphological Erosion
Contour sub-region Interior sub-region The overall object
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Morphological Erosion
Algorithm structure
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Shape-Adaptive Image Compression
Image segments Quantizing & encoding EOB DCT coefficients boundary encoding bit stream of boundaries 01 M1 M2 M3 S.A. DCT Bit-stream of image segments combine
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Simulation Results
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Outlines Introduction to Image compression JPEG Standard
Shape-Adaptive Image Compression Modified JPEG Image Compression Conclusions Reference
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Modified JPEG Image Compression
2-D Orthogonal DCT Expansion in Triangular and Trapezoid Regions
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Trapezoid Definition Define the trapezoid :
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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
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Complete and Orthogonal DCT Basis in the Trapezoid Region
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Complete and Orthogonal DCT Basis in the Trapezoid Region
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Finding an approximate trapezoid region in an arbitrary shape
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Modified JPEG Image Compression
Divide Images into three regions:
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Simulation Results
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Simulation Results
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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, ICIP IEEE International Conference on, Vo1. 3, pp. III , 2005. [3] ISO/IEC :2000(E), "Information technology-JPEG image coding system-Part 1: Core coding system", 2000. [4] Jian-Jiun Ding and Jiun-De Huang, "Image Compression by Segmentation and Boundary Description", Master’s Thesis, National Taiwan University, Taipei, 2007. [5] Jian-Jiun Ding and Tzu-Heng Lee, "Shape-Adaptive Image Compression", Master’s Thesis, National Taiwan University, Taipei, [6] G. K. Wallace, "The JPEG Still Picture Compression Standard", Communications of the ACM, Vol. 34, Issue 4, pp.30-44, 1991. [7] 張得浩,“新一代JPEG 2000之核心編碼 — 演算法及其架 構(上) ”,IC設計月刊 2003.8月號. [8] 酒井善則、吉田俊之 共著,白執善 編譯,“影像壓縮 技術”,全華,2004.
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