Density-Based Image Vector Quantization Using a Genetic Algorithm Authors: Chin-Chen Chang and Chih-Yang Lin

VQ Encoding Index table Original Image Codebook (120,155,…,80) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 (90,135,…,120) (100,125,…,150) … Index table Original Image (49,117,…,25) (50,42,…,98) (20,65,…,110) Codebook How to get a good codebook?

LBG Algorithm Step 1: Training Images Training vectors set x0 x1 . Dividing the images into vectors x59997 X59998 x59999 Training Images Training vectors set

LBG Algorithm Step2: Initial codebook Training vectors set x0 X1 . x73 x342 . Randomly choose 256 initial code-vectors 256 code- vectors x24312 x49810 x59997 x59998 x59999 Initial codebook Training vectors set

The set of training vectors = {x0, x1, … , x59999} LBG Algorithm Step3: Vector-groups x0 X1 . {x5, x5431, … } {x1, x306, … } {x67, x822, … } . . . 1 . 254 255 x59997 x59998 x59999 Codebook The set of training vectors = {x0, x1, … , x59999} Join the closest code-vector, and to form 256 vector-groups.

LBG Algorithm Step4: Vector-groups {x5, x5431, …} {x1, x306, … } 1 . 254 255 {x5, x5431, …} {x1, x306, … } {x67, x822, …} . . . Compute mean value of each group, replace the old code-vectors New Codebook Go to Step3 to repeat training until the total distortion has stabilized.

Motivation center center LBG-based Method Density-based Method

Motivation LBG-based Method Density-based Method

Choose Genes How to efficiently select good genes to form chromosomes from a large set of representative points? How to get good representative points?

Mating pool gene gene gene 255 254 253 255 254 253 255 254 253 . 2 10 Chromosome 1 Chromosome 2 Chromosome 100 Mating pool

Training Images Training vectors set x0 x1 . Dividing the images into vectors x59997 X59998 x59999 Training Images Training vectors set

Size of training vectors = 60000 Use K-NN (k=5) to get 10000 (= 60000 / (k + 1) = 60000 / (5 + 1)) good representative points How to choose k? x32 exclude x3213 x3 x41 … x997 x5762 x5132 x8137 x56 x0 x2 x23 x430 x1964 x3310 x411 x92 x9999

Curve of representative points Cut point Variation of k with the number of representative points

How to evaluate the perf. of chromosomes? Finally, we get 10000 representative points {x32, x67, x92, x132, x219, x473, x592, x612, x623, …, x1324, x1519} How to evaluate the perf. of chromosomes? 1 . 255 1 . 255 1 . 255 . . . Chro. 1 Chro. 2 Chro. 100 Arbitrarily choose x3 x41 x5762 x5132 x8137 … x56 x1964 x23 x430 x411 x3310 x92 x9999

(ADR: average distance rate) Fitness Function (CR: coverage rate ) (ADR: average distance rate) t : iteration m: chromosome size (fitness function)

Goal: maximize CR and minimize ADR Example: Covered points: 45 Size of representative points: 50 r=5 means gene Chromosome size: 7 CR=45/50=0.9 Uncovered points: 5 3 3 4 3 3 5 Goal: maximize CR and minimize ADR

Crossover Crossover: P0 P1 P2 P3 P4 P5 P6 Q0 Q1 Q2 Q3 Q4 Q5 Q6 P0 P1

Mutation Prob. = 1/100 P0 P1 P2 P3 P4 P5 P6 Mutate Candidate gene pool select

Comparison of image quality with the codebook sized 256 Experiments Comparison of image quality with the codebook sized 256 Images LBG TSVQ Hu and Chang’s method Ying et al.’s Proposed Lena 29.12 28.91 29.96 27.17 30.76 F16 30.54 30.51 30.73 28.03 30.58 Pepper 29.98 29.76 30.92 27.94 30.98 Sailboat 28.62 28.44 26.86 28.95 Baboon 24.37 24.31 24.41 23.14 24.46 Tiffany 28.33 27.61 28.70 24.06 28.94 Zelda 34.32 34.15 35.03 29.94 35.72

Experiments Proposed method LBG-based method

Experiments Coverage rate 8 10 12 14 16 0.73 0.74 0.742 0.745 0.75 Iteration 8 10 12 14 16 Proposed method 0.73 0.74 0.742 0.745 0.75 LBG 0.72

Conclusions A new codebook generation algorithm based on GA is presented. The proposed scheme generates codebook that outperforms some other previously proposed methods.