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

2. 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?

3. LBG Algorithm Step 1: Training Images Training vectors setx0 x1 .
Dividing the images into vectors
x59997
X59998
x59999
Training Images
Training vectors set

4. LBG Algorithm Step2: Initial codebook Training vectors setx0 X1 .
x73
x342 .
Randomly choose 256 initial code-vectors
256 code-
vectors
x24312
x49810
x59997
x59998
x59999
Initial codebook
Training vectors set

5. 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.

6. 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.

7. Motivation
center
center
LBG-based Method
Density-based Method

8. Motivation
LBG-based Method
Density-based Method

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

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

11. Training Images Training vectors setx0 x1 .
Dividing the images into vectors
x59997
X59998
x59999
Training Images
Training vectors set

12. Size of training vectors = 60000
Use K-NN (k=5) to get (= / (k + 1) = / (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

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

14. How to evaluate the perf. of chromosomes?
Finally, we get 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

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

16. 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

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

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

19. 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

20. Experiments
Proposed
method
LBG-based
method

21. 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

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