Smooth Side-Match Classified Vector Quantizer with Variable Block Size

IEEE Transaction on image processing, VOL. 10, NO. 5, MAY 2001Department of Applied MathematicsNational Chung Hsing UniversityShiueng Bien Yang and Lin Yu Tseng

Outline

Introduction Basic Algorithm Smooth Side-Match Method with

Variable Block Size Genetic Clustering algorithm Experimental Results Conclusion

Introduction

The evolution of SMVQ SMVQ SMVQ with CVQ SSM-CVQ

Feature of SSM-CVQ Variable block size Smooth side-match method Genetic clustering algorithm is applied

on codebooks generation

Basic algorithm SMVQ

n

jmjj uwwhd

1

21 )()(

m

iini lwwvd

1

21 )()(

)()()( wvdwhdwsmd

Basic algorithmSMVQ with CVQ (encoder)

Basic algorithmSMVQ with CVQ (decoder)

Smooth Side-Match Method with Variable Block Size

Variable Block Size Image Compression with Variable Block

Size Segmentation Quadtree is used to address blocks of

different sizes Smooth side-match method

Diagonal basic blocks Smooth side-match distortion

Image Compression with Variable Block Size Segmentation

Quadtree is used to address blocks of different sizes

Block size and codebooks

Blocks of sizes of 16x16 and 8x8 and 4x4 with low variance are low-detail blocks Use three master codebooks

4x4 8x8 16x16

Blocks of size of 4x4 with high variance are high-detail blocks Use CLUSTERING algorithm, we have q classes

and q master codebooks for each class Total : 3 + q master codebooks

Diagonal basic blocks

Diagonal blocks are encoded first. In the experiments, the number of the basic blocks

required is approximately 25% to 28% of that of the conventional SMVQ.

Smooth side-match distortion (1)

The encoded is divided into two parts Upper triangular region Lower triangular region

Problem of SMVQ

Different, dif(e, f) is defined as dif(e, f) = (gray level of e) – (gray level of f)

Smooth side-match distortion (2) Upper triangular region

n

iimi

imimii yddifyydifdddif

yvdUpper1

,,1,1,,1,,2 |),(

2

)),()((|)(_

n

ijnj

jjnjnj yldifyydiflldif

yhdUpper1

1,,2,1,,1, |),(

2

)),(),((|)(_

)(_)(_)( yhdUpperyvdUpperyD

Smooth side-match distortion (3) Lower triangular region

n

iiim

iiimim yudifyydifuudif

yvdLower1

,1,,2,1,,,1 |),(

2

)),()((|)(_

n

injj

njnjjj yrdifyydifrrdif

yhdLower1

,1,1,,1,2, |),(

2

)),(),((|)(_

)(_)(_)( yhdLoweryvdLoweryD

Genetic Clustering Algorithm (1)

First Stage Use nearest neighbor (NN) algorithm to reduce the

computation time and space in the second stage. (1)

(2)

(3)

(4) Let the connected components be denoted by

ijij

iNN OOOd

min)(

n

iiNNav Od

nd

1

)(1

1.5 be tochosen empirical is u *

otherwise ,0

if ,1),(

udd

dOOjiA

av

ji

mBBB ,...,, 21

Genetic Clustering Algorithm (2)

Second Stage Use genetic algorithm to find an appropriate number of

clusters.

Initialization Step chromosome (string): numbers of 1’s in the strings almost uniformly distributes within [1,m]

sm TTTTTBBB ,...,, ,,..., 2121

kijijj SVSVCB if

ij

iijj

jBC

BVCSS

**'

Genetic Clustering Algorithm Data Representation

Chromosome

Gene

Individual

......,,

......,,

......,,

222

111

nnn cba

cba

cba

N individuals

Population Size=N

N strings is randomly generated.

Genetic Clustering Algorithm Evolution Processes

1. Self Reproduction2. Crossover3. Mutation

Genetic Clustering Algorithm Fitness Function

......,,)(

......,,)2(

......,,)1(

222

111

nnn cbafnevaluation

cbafevaluation

cbafevaluation

kCB

ikji

iinter

kCB

ikiintra

BSVCD

BSVCD

ik

ik

*min)(

*)(

)(*)()( iintraiinter CDwCDRfitness

i

kki

ii

ii

Pq

xf

xfP

1

1

)(

)(

1P2P

3P

Genetic Clustering Algorithm Self Reproduction

if

iki qrq 1

k= ......,, iii cba

Genetic Clustering Algorithm Crossover

Set Probability of crossover Position q

Randomly generateIf

cP

ncc PP 1

cccc PPPPlk

......,,,......

......,,,......

kkll

llkk

dcba

dcba

Position=q

Genetic Clustering Algorithm Mutation

Set Probability of mutation Randomly generateIf

mP

nmm PP 1

mm PPq

......,, newqq cba

Experimental results

High-detailed Blocks ：why 28 edge-classifiers

Outside image: Lena & F-16 The PSNRs of the coding for Lena SSM-CVQ outperforms the others in

both the PSNR & the bit rate

High-detailed Blocks ：why 28 edge-classifiers

)(*)()( intint iraier CDwCDRFitness

Outside image: Lena & F-16

JPEG Lena 32.01 0.2681

SMVQ with CVQ

30.44 0.2704

The PSNRs of the coding for Lena

CLUSTERING is best !

SSM-CVQ outperforms the others in both the PSNR & the bit rate

Conclusion

The CLUSTERING clusters the appropriate number of clusters.

Low-detail blocks could reduce bit rates

High-detail blocks and smooth side-match distortion could increase quality