JPEG - JPEG2000

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