Image Compression Presenter JinZuo Liu Research Advisor JianJiun

Image Compression 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 1

Outlines �Introduction to Image compression �JPEG Standard �JPEG 2000 Standard �Shape-Adaptive Image Compression �Modified JPEG Image Compression �Conclusions �Reference 2

Image Storage System 3

�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

�Downsampling formats of YCb. Cr 5

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

Outlines �Introduction to Image compression �JPEG Standard �JPEG 2000 Standard �Shape-Adaptive Image Compression �Modified JPEG Image Compression �Conclusions �Reference 7

JPEG flowchart 8

Why we apply DCT? �Reduce the correlation between the neighboring pixels in the image �coordinate rotation the f 2 th pixel value Y X the f 1 th pixel value � f 1 -f 2 � = 3 pixels in horizontal 9

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

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

DCT V. S 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

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

Discrete Cosine Transform (DCT) 8× 8 DCT 14

JPEG Quantization �Qantization: �Qantization table 15

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

Grouping method for DC component Values Bits for the value 0 17 group 0 -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, . . . 31 00000, . . . , 01111, 10000, . . . , 11111 5 -63, . . . , -32, . . . 63 000000, . . . , 011111, 100000, . . . , 111111 6 -127, . . . , -64, . . . , 127 0000000, . . . , 0111111, 1000000, . . . , 1111111 7 -255, . . , -128, . . , 255 . . . 8 -511, . . , -256, . . , 511 . . . 9 -1023, . . , -512, . . , 1023 . . . 10 -2047, . . . , -1024, . . . , 2047 . . . 11

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

Zigzag Scanning of the AC Coefficients 19

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

The Run/Size Huffman table for the luminance AC coefficients Run/Size code length code word 0/0 (EOB) 4 1010 15/0 (ZRL) 11 1111001 0/1 2 00 7 1111000 0/10 16 111110000011 1/1 4 1100 1/2 5 11011 1/10 16 11111000 2/1 5 11100 16 111110011000 16 111111110 . . . 0/6. . 4/5. . . 15/10 21

Outlines �Introduction to Image compression �JPEG Standard �JPEG 2000 Standard �Shape-Adaptive Image Compression �Modified JPEG Image Compression �Conclusions �Reference 22

The JPEG 2000 Standard �JPEG 2000 fundamental building blocks 23

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

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

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

Outlines �Introduction to Image compression �JPEG Standard �JPEG 2000 Standard �Shape-Adaptive Image Compression �Modified JPEG Image Compression �Conclusions �Reference 27

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

Shape-Adaptive Image Compression �Algorithm structure 29

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

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

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

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

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

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

Morphological Erosion 36

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

Morphological Erosion �Algorithm structure 38

Shape-Adaptive Image Compression DCT coefficients Image segments Quantizing & encoding 100111101 010 M 1 EOB 10101011111001 S. A. DCT boundary encoding EOB M 2 111000101011111 EOB M 3 bit stream of boundaries combine 100111101010 Bit-stream of image segments EOB 101010111110 101011011111 01 39 EOB 111000101011111 EOB

Simulation Results 40

Outlines �Introduction to Image compression �JPEG Standard �JPEG 2000 Standard �Shape-Adaptive Image Compression �Modified JPEG Image Compression �Conclusions �Reference 41

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

Trapezoid Definition �Define the trapezoid : 43

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

Complete and Orthogonal DCT Basis in the Trapezoid Region 45

Complete and Orthogonal DCT Basis in the Trapezoid Region 46

Finding an approximate trapezoid region in an arbitrary shape 47

Modified JPEG Image Compression �Divide Images into three regions: 48

Simulation Results 49

Simulation Results 50

Reference � [1] R. C. Gonzalea and R. E. Woods, "Digital Image � � � 51 � Processing", 2 nd 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, Vo 1. 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", 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, 2008. [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.

Thank you for listening ~ 52