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
Slide 2
Outlines Introduction to Image compression JPEG Standard
JPEG2000 Standard Shape-Adaptive Image Compression Modified JPEG
Image Compression Conclusions Reference 2
Slide 3
Image Storage System 3
Slide 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 4
Slide 5
Downsampling formats of YCbCr 5
Slide 6
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
Slide 7
Outlines Introduction to Image compression JPEG Standard
JPEG2000 Standard Shape-Adaptive Image Compression Modified JPEG
Image Compression Conclusions Reference 7
Slide 8
JPEG flowchart 8
Slide 9
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
Slide 10
Covariance Matrix Step1: Image partition Step2: Re-aligned the
pixels of a 2-D block into a 1-D vector 10
Slide 11
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
Slide 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 12
Slide 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 13
DPCM for DC Components large correlation still exists between
the DC components in the neighboring macroblocks 16
Slide 17
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
Slide 18
Grouping method for DC component Example: diff=17 (17) 10 =
(10001) 2 group 5 codeword: (110) 2 code: (11010001) 2 18
Slide 19
Zigzag Scanning of the AC Coefficients 19
Slide 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 zerosthe nonzero
coefficients 20
Slide 21
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
Slide 22
Outlines Introduction to Image compression JPEG Standard
JPEG2000 Standard Shape-Adaptive Image Compression Modified JPEG
Image Compression Conclusions Reference 22
Slide 23
The JPEG 2000 Standard JPEG2000 fundamental building blocks
23
Slide 24
Discrete Wavelet Transform The analysis filter bank of the 2-D
DWT 24
Slide 25
Wavelet Transforms in Two Dimension Two-scale of 2-D
decomposition 25
Slide 26
Discrete Wavelet Transform One-scale of 2-D DWT 26
Slide 27
Outlines Introduction to Image compression JPEG Standard
JPEG2000 Standard Shape-Adaptive Image Compression Modified JPEG
Image Compression Conclusions Reference 27
Slide 28
Shape-Adaptive Image Compression Block-based transformation
disadvantages: 1. block effect 2. no take advantage of the local
characteristics in an image segment 28
Outlines Introduction to Image compression JPEG Standard
JPEG2000 Standard Shape-Adaptive Image Compression Modified JPEG
Image Compression Conclusions Reference 41
Slide 42
Modified JPEG Image Compression 2-D Orthogonal DCT Expansion in
Triangular and Trapezoid Regions 42
Slide 43
Trapezoid Definition Define the trapezoid : 43
Slide 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 44
Slide 45
Complete and Orthogonal DCT Basis in the Trapezoid Region
45
Slide 46
Complete and Orthogonal DCT Basis in the Trapezoid Region
46
Slide 47
Finding an approximate trapezoid region in an arbitrary shape
47
Slide 48
Modified JPEG Image Compression Divide Images into three
regions: 48
Slide 49
Simulation Results 49
Slide 50
Simulation Results 50
Slide 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, 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