1. 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

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

3. Image Storage System

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

5. Downsampling formats of YCbCr

6. 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

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

8. JPEG flowchart

9. 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

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

11. 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 )

12. 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

13. 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

14. Discrete Cosine Transform (DCT)

15. JPEG Quantization
Qantization:
Qantization table

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

17. 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

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

19. Zigzag Scanning of the AC Coefficients

20. 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

21. 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

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

23. The JPEG 2000 Standard
JPEG2000 fundamental building blocks

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

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

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

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

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

29. Shape-Adaptive Image Compression
Algorithm structure

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

31. 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

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

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

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

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

36. Morphological Erosion

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

38. Morphological Erosion
Algorithm structure

39. 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

40. Simulation Results

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

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

43. Trapezoid Definition
Define the trapezoid :

44. 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

45. Complete and Orthogonal DCT Basis in the Trapezoid Region

46. Complete and Orthogonal DCT Basis in the Trapezoid Region

47. Finding an approximate trapezoid region in an arbitrary shape

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

49. Simulation Results

50. Simulation Results

51. 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.

52. Thank you for listening ~