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JPEG - JPEG2000
Isabelle Marque
JPEG JPEG2000
JPEG
Joint Photographic Experts Group Committe created in 1986 by:
International Organization for Standardization (ISO)
and International Telecommunication Union (ITU)
A working group which creates the standard for still image compression
JPEG - JPEG2000
Two different standards Major differences :
JPEG JPEG2000Created for natural imagery
Discrete Cosine Transform algorithm
Created for computer generated imagery
Discrete Wavelet Transform algorithm
JPEG
Architecture of standard Forward transform Quantization Entropy coding
DC coefficient AC coefficients
Entropy encoding
Source image data
Forward transform Quantization
Compressed image data
JPEG
Forward transform
1. Level shifted
2. Divided into blocks of 8*8 pixels
3. Forward DCT:
N
ij
N
N
ij
NC ji
2
12cos
2
2
12cos
1
,
1,...,1,0,1,...,1,0
1,...,1,0,0
NjNi
Nji
12 p
Entropy encoding
Source image data
Forward transform
Quantization Compressed image data
JPEG
DCT basis functions
JPEG
Original image
156157158158155158159156
151150152152152152148150
139139139140142143142143
125127128130129128127127
124124125126125125124124
120120121121122123124126
118120120119119120121121
118117119122120122125124
JPEG
DCT coefficients
01.033.009.096.087.007.151.043.3
13.052.084.0051.055.039.252.597.3
00.046.126.099.177.045.013.098.5
76.030.165.262.077.075.174.037.3
17.013.022.041.181.032.124.267.5
23.010.021.250.125.077.131.177.37
48.005.163.035.012.126.256.443.102
13.179.008.137.022.124.256.688.39
JPEG
Quantization Quantization table
Zigzag scan
5.0
ij
ijij Ql
Entropy encoding
Source image data
Forward transform
Quantization Compressed image data
JPEG
Quantization table
9910310011298959272
10112012110387786449
921131048164553524
771031096856372218
6280875129221714
5669574024161314
5560582619141212
6151402416101116
JPEG
Labels after quantization
00000000
00000000
00000000
00000000
00000000
00000003
00000009
00000012
JPEG
Entropy encoding DC coefficient and AC coefficients are coded differently DC coefficient
Encode the difference Huffman code unmanageable
First bits to define the category and other bits to define the element in the category
Category Possible values
0 0
1 -1 1
2 -3 -2 2 3
3 -7 -6 -5 -4 4 5 6 7
Entropy encoding
Source image data
Forward transform
Quantization Compressed image data
JPEG
AC coefficients
Defined by a certain number of terms: Category C that a non zero label falls in Z: number of zero since the last non zero label
Z/C points to a specific code Follows by bits to define the element in the category +1 code
EOB stands for End Of Block:
A code after the last non zero value
JPEG
Sample table for obtaining the huffman code
Z/C Codeword Z/C Codeword
0/0 (EOB) 1010
0/1 00 1/1 1100
0/2 01 1/2 11011
0/3 100 1/3 1111001
0/4 1011 1/4 111110110
0/5 11010 1/5 11111110110
JPEG
Reconstructed image
155155156157157158159159
148149149150151151152152
137138138139140140141141
127128128128129129130130
120120121122122123124124
117117118119119120121121
118118118119120121121121
119119120120121122122123
JPEG
More accurate image Increase the bit rate Decrease quantization table elements
Less accurate image Decrease the bit rate Increase quantization table elements
Problem:
Low rate image: « blockiness »
JPEG2000
Can be both lossless and lossy Improves image quality Uses a layered file structure :
Progressive transmission Progressive rendering
File structure flexibility: Could use for a variety of applications
Many functionalities
JPEG2000
Architecture of standard Forward transform Quantization Entropy coding
Entropy encoding
Source image data
Forward transform Quantization
Compressed image data
JPEG2000
Forward transform
1. Level shifted
2. Divided into blocks
3. Forward Discrete Wavelet Transform
Entropy encoding
Source image data
Forward transform
Quantization Compressed image data
JPEG2000
Details
JPEG2000
JPEG2000
Discrete Wavelet Transform can be :
Irreversible: Daubechies 9-tap/7-tap filter Reversible: 5-tap/3-tap filter Any user could supply wavelet filter banks
JPEG2000
Quantization
Dynamic range: depends on the number of bits and the choice of the wavelet
Exponent
Mantissa
b
ijijl
Entropy encoding
Source image data
Forward transform
Quantization Compressed image data
212 bR
bbb
b
b
bR
JPEG2000
Entropy encoding Embedded Block Coding with Optimization Truncation of
the embedded bit stream (EBCOT) Each subband is divided into rectangular blocks which are coded
independently called code blocks Bitstream is organized in a succession of layers Each layer corresponds to a certain distortion level The quality of the reproduction is proportional to the numbers
layers received
Entropy encoding
Source image data
Forward transform
Quantization Compressed image data
JPEG2000
Layered structure
JPEG - JPEG2000 - Quality
At compression ratio: 43:1
JPEG JPEG2000
JPEG - JPEG2000 - Quality
Method of picture quality measurement:PSNR
Peak Signal To Noise Ratio in dB:
Pixel of the image
Pixel of the reconstructed image
Size of the image
Root Mean Squared Error
2
2
10
255log*20
N
FfRMSE
RMSEPSNR ijij
RMSE
NN
F
f
ij
ij
*
JPEG - JPEG2000 - Quality
Comparison of PSNR values (dB) compressed colour images
Bits per pixel 0.125 0.25 0.5 1.0 2.0
Lena JPEG 24.42 28.02 31.17 33.12 35.15
Lena
JPEG2000
28.12 30.61 32.95 35.05 37.35
CONCLUSION – Key points
JPEG: DCT algorithm JPEG2000: DWT algorithm
Layered structure Many functionalities
For a similar quality of PSNR, JPEG2000 compresses almost twice more than JPEG
REFERENCES
Introduction to Data Compression, K. Sayood, Morgan Kauffman, Second Edition, 2000. (Primary)
A.N. Skodra, C.A. Christopoulos, T. Ebrahimi, « JPEG2000, the upcoming still image compression standard », Proceeding of the 11th Portuguese Conference on Pattern recognition, Porto, Portugal, May 11th-12th, pp. 359-366, 2000
JPEG, Official site: http://www.jpeg.org Home page of a member: http
://www.etro.vub.ac.be/members/christopoulos.charilaos/welcome.html http://www.aware.com/products/compression/j2kmaindemo.html http://www.cs.sfu.ca/CC/820/li/material/presentations/paper21.ppt http://dmsun4.bath.ac.uk/research/sar/dwt.html http://www.us.design-reuse.com/articles/article6691.html PSNR:http://www.snellwilcox.com/knowledgecenter/whitepapers/papers/
picturequality_mpeg2.pdf Quality: http://jj2000.epfl.ch/jj_publications/papers/001.pdf