ApplicationApplicationof Generalized Representationsof Generalized Representationsfor Image Compressionfor Image Compressionusing Vector Quantization

Technion - Israel Institute of TechnologyDepartment of Electrical EngineeringThe Image and Computer Vision Laboratory

Sheingart Michael & Tseitlin Yuri

Supervisor: Wajcer Daniel

Project GoalsProject Goals

Checking an efficiency of the multifrequency representation used for image compressing and coding .

Implementing and simulation of the Wavelet Image Coder .

Comparation with another families of Image Coders .

The general structureThe general structure

The Wavelet Transform .The Vector Quantization .The Entropy Coder is

implemented by Adaptive Arithmetic Coding .

The Wavelet Coder SchemeThe Wavelet Coder Scheme

D esired R a te

T ra n sm ittedp ic tu re

T ra in in g p ic tu re

T ra in in g o f th e Q u an tiz e r

P ru n in g o f th e co d eb o o k tre e b y R O P A

R eco m p u te th e n ew p a rtitio n v ec to rb y q u an tiz a tio n o f th e tran sm itted p ic tu re

A d ap tiv e A rith m e tic C o d in g o fn ew p a rtitio n v ec to r

D eco d in g o f p a rtitio n v ec to r

T h e reco n stru cted p ic tu re

R eco n s tru c tin g o f th e tran sm ittedp ic tu re u s in g th e v ec to r q u an tiz e r co d eb o o k

T ran sm ittin g

The reasons for using Wavelet The reasons for using Wavelet TransformTransform Majority of information

is stored in low pass filter and high pass filters are very sparse .

The lack of redundancy between the transform coefficients .

The transform is mathematically stable .

The Vector QuantizationThe Vector Quantization

Computing the binary tree by Splitting Algorithm and training the codebooks by Max-Lloyd Algorithm .

Pruning the tree by ROPA Algorithm .

The Bit Allocation Algorithm to obtain the desired Rate .

The Adaptive Arithmetic CoderThe Adaptive Arithmetic Coder

The coder is free from the statistical issues associated with the design of Huffman Code .

The coder adapts to varied statistic features of a source .

There is free error coding .

Comparative performance of Comparative performance of the Vector Quantizerthe Vector Quantizer

The comparation between Entropy -Constrained Scalar Quantizer ( right ) and our Vector Quantizer ( left ) .

Comparative performance of Comparative performance of the Wavelet Image Coderthe Wavelet Image Coder

The comparation between Embedded Zerotree Wavelet Coder ( right ) and our Wavelet Image Coder ( left ) .

Performance of Wavelet Image Performance of Wavelet Image CoderCoder

1. Original picture2. Quantized picture with __Rate = 1 bpp3. Coded picture with __training codebook

2

1

3

ConclusionConclusion

The wavelet representation is powerful tool for image coding and compression .

The vector quantization using Splitting Algorithm yields a minimum distortion quantizer for fixed code word length vectors .

Any intermediate rate can be obtained . The quantizer is sub-optimal but easy

for training and using since it is tree-structured quantizer .