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Smooth Side-Match Classified Vector Quantizer with Variable Block Size IEEE Transaction on image processing, VOL. 10, NO. 5, MAY 2001 Department of Applied Mathematics National Chung Hsing University Shiueng 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 m vd ( w) ( wi1 lin ) 2 i 1 n hd ( w) ( w1 j umj ) 2 j 1 smd ( w) hd ( w) vd ( w) Basic algorithm SMVQ with CVQ (encoder) Basic algorithm SMVQ 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 Blocks of size of 4x4 with high variance are high-detail blocks Use three master codebooks 4x4 8x8 16x16 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 Upper _ vd ( y ) | i 1 n Upper _ hd ( y) | i 1 (dif (d 2,i , d1,i ) dif ( ym,i , ym 1,i )) 2 (dif (l j ,n1 , l j ,n ) dif ( y j ,1 , y j , 2 )) 2 D( y ) Upper _ vd ( y ) Upper _ hd ( y ) dif (d1,i , ym ,i ) | dif (l j ,n , y j ,1 ) | Smooth side-match distortion (3) Lower triangular region n Lower _ vd ( y ) | i 1 n Lower _ hd ( y) | i 1 (dif (um 1,i ,um,i ) dif ( y1,i , y2,i )) 2 (dif (rj , 2 , rj ,1 ) dif ( y j ,n , y j ,n1 )) 2 D( y ) Lower _ vd ( y ) Lower _ hd ( y ) dif (um,i , y1,i ) | dif (rj ,1 , y j ,n ) | Genetic Clustering Algorithm (1) First Stage Use nearest neighbor (NN) algorithm to reduce the computation time and space in the second stage. (1) d NN (Oi ) min O j Oi j i (2) d av 1 n d NN (Oi ) n i 1 1, if Oi O j d A(i, j ) 0, otherwise d d av * u u is empirical chosen to be 1.5 (4) Let the connected components be denoted by (3) B1, B2 ,..., Bm 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] B1, B2 ,...Bm T , Bj C j S ' j T T1, T2 ,..., Ts if Vi S j Vi Sk S j * C j Vi * Bi C j Bi Genetic Clustering Algorithm Data Representation Gene Individual Chromosome N strings is randomly generated. a1, b1, c1...... a2 , b2 , c2 ...... an , bn , cn ...... N individuals Population Size=N Genetic Clustering Algorithm Evolution Processes 1. 2. 3. Self Reproduction Crossover Mutation Genetic Clustering Algorithm Fitness Function fitness( R) Dinter (Ci ) * w Dintra(Ci ) Dintra(Ci ) Dinter (Ci ) V Bk Ci k Si * Bk min V S * B k i k i j Bk Ci evaluation(1) f a1 , b1 , c1...... evaluation( 2) f a2 , b2 , c2 ...... evaluation( n ) f an , bn , cn ...... Genetic Clustering Algorithm Self Reproduction P1 f ( xi ) Pi f ( xi ) i 1 i qi Pk k 1 if qi 1 rk qi k= ai , bi , ci ...... P2 P3 Genetic Clustering Algorithm Crossover Set Probability of crossover Pc Position q Randomly generate Pc1 Pcn If Pck Pc Pcl Pc ......ak , bk , cl , d l ...... ......al , bl , ck , d k ...... Position=q Genetic Clustering Algorithm Mutation Set Probability of mutation Pm Randomly generate Pm Pm If Pmq Pm 1 a , b , c q q new ...... n 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 Fitness( R) Dinter (Ci ) * w Dint ra (Ci ) 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 sidematch distortion could increase quality