1. Planar-Oriented Ripple Based Greedy Search Algorithm for Vector Quantization Presenter: Tzu-Meng Huang Adviser:Dr. Yeou-Jiunn Chen Date:2011/11/16 2011/11/161

2. Outline Introduction Paper review Method Experiment Results and Discussion Conclusions Future Works References 2011/11/162

3. Introduction Vector quantization (VQ) has been widely used in data compression. Image compression Speech coding VQ Simply Definition A mapping function which maps a k-dimensional vector space into a finite subset Codebook Codeword k-dimensional 2011/11/163

4. Introduction Full search vector quantization (FSVQ) The larger the codebook size N, the greater the distortion computation overhead. 2011/11/164

5. Introduction VQ-based techniques Full-search equivalents Double test algorithm method Look-up tables Partial distance search method Partial-search methods Tree-based Projection-based structures Double Test of Principal Components Encoding Method (DTPC) 2011/11/165

6. Introduction Purpose A new partial-search method to speed up the complicated quantization process of the traditional VQ. Principal Component Analysis Voronoi-Diagram Construction Greedy Search 2011/11/166

7. Paper Review Fast Planar-Oriented Ripple Search Algorithm for Hyperspace VQ Codebook Chin-Chen Chang, Fellow, IEEE, and Wen-Chuan Wu IEEE Transaction on image processing, vol 16 June 2007 2011/11/167

8. Paper Review How many ripples is the best for an effective and efficient quantizer? 2011/11/168

9. Paper Review 2011/11/169

10. Method Principal Component Analysis (PCA) Finding a linear transformation that can project each k- dimensional vector into an s-dimensional space(s ≦ k). Step1 Calculate the co-variance matrix of these N vectors in the codebook. Step2 Discover all the eigen-values of this matrix and their corresponding eigen-vectors. is capable of preserving the most variation among the original vectors in the projected values. 2011/11/1610

11. Method Voronoi-Diagram Construction An implicit geometric interpretation of the nearest neighbors of objects in the space. Can be constructed in any k–dimensional space 2011/11/1611 source :http://mathworld.wolfram.co m/VoronoiDiagram.htmlhttp://mathworld.wolfram.co m/VoronoiDiagram.html

12. Method Voronoi-Diagram Construction Take as the generators of a Voronoi diagram For each point : 2011/11/1612

13. Method Preprocessing and Training Procedure Step 1.Using PCA technique to project codebook onto a space of m-dimensional. 2011/11/1613

14. Method Preprocessing and Training Procedure Step 2.Building a Voronoi diagram by the projected plan. 2011/11/1614

15. Method Preprocessing and Training Procedure Step 3.Generate the neighbor-ripple adjacency-list of each codeword. 2011/11/1615 PC1 … PC6 … PC10 PC4PC5PC6PC9PC8 PC1PC5PC3PC10PC9 PC2PC3PC6PC9

16. Method Preprocessing and Training Procedure Step 4.Projecting a training voctor onto this plane. Step 5.Determining the initial codeword and the best codeword for the training vector by binary search and FSVQ. 2011/11/1616

17. Method Preprocessing and Training Procedure Step 6.If the best codeword does not fall in the ripple domain of the initial codeword, add the best codeword into the neighbor-ripple adjacency-list of the initial codeword. Step 7.Repeat step 4 to step 6 until all training vectors are done. 2011/11/1617 PC1 … PC6 … PC10 PC4PC5PC6PC9PC8 PC1PC5PC3PC10PC9 PC2PC3PC6PC9 the best codeword PC4 initial codeword PC6 PC1PC5PC3PC10PC9PC4

18. Method Vector Searching Procedure with Cutoff Step 1.Using PCA to project the input vector p x onto the same space. Step 2.Using binary search to find the initial codeword C i of p x. Step 3.Let the best codeword C b is equal to C i. Step 4.Finding the closest codeword C c in adjacency-list of C i. Step 5.If C c is closer than C b, then let C b =C c and C i =C c else goto step 7. Step 6.Repeat step 4 and step 5 until the predefined number of ripples is reached. Step 7.Return the best codeword C b. 2011/11/1618

19. Method Vector Searching Procedure without Cutoff Step 1.Using PCA to project the input vector p x onto the same space. Step 2.Using binary search to find the initial codeword C i of p x. Step 3.Let the best codeword C b is equal to C i. Step 4.Finding the closest codeword C c in adjacency-list of C i. Step 5.If C c is closer than C b, then let C b =C c Step 6.Let C i =C c. Step 7.Repeat step 4 and step 6 until the predefined number of ripples is reached. Step 8.Return the best codeword C b. 2011/11/1619

20. Experiment Results and Discussion Data TCC300 Codebook 2048×39 Training data 3026×39 Testing data 6654×39 Software MATLAB 2011/11/1620

21. Experiment Results and Discussion The Analysis of Dimension of Voronoi-Diagram 2011/11/1621

22. Experiment Results and Discussion GS_PVDS with cutoff GS_PVDS without cutoff 2011/11/1622 Level of Greedy Search Procedure The line of square mark, triangle mark, and circle mark represent GS_PVDS(2), GS_PVDS(3), and GS_PVDS(4), respectively.

23. Experiment Results and Discussion GS_PVDS with cutoff GS_PVDS without cutoff 2011/11/1623 Level of Greedy Search Procedure The line of square mark, triangle mark, and circle mark represent GS_PVDS(2), GS_PVDS(3), and GS_PVDS(4), respectively.

24. Experiment Results and Discussion GS_PVDS with cutoff GS_PVDS without cutoff 2011/11/1624 Level of Greedy Search Procedure The line of square mark, triangle mark, and circle mark represent GS_PVDS(2), GS_PVDS(3), and GS_PVDS(4), respectively.

25. Experiment Results and Discussion GS_PVDS without cutoff and PVDS 2011/11/1625 The line of triangle mark and square mark represent GS_PVDS and GS_PVDS without cutoff

26. Conclusions The greedy search algorithm is successful to improve the performance of PVDS in high dimension of Voronoi diagram. The distortions of GS_PVDS and PVDS are 4.665 and 6.676. The numbers of compared codewords are 185.3 and 341.1 for GS_PVDS and PVDS. 2011/11/1626

27. Future Works More experiment results with different data Dynamic increasing codewords into the codebook 2011/11/1627

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29. References J. Makhoul, S. Roucos, and H. Gish, “Vector quantization in speech coding,” Proc. IEEE, vol. 73, pp. 1551–1588, Nov. 1985. C. C. Chang, F. J. Shiue, and T. S. Chen, “Tree structured vector quantization with dynamic path search,” in Proc. Int. Workshop on Multimedia Network Systems, Aizu, Japan, Sep. 1999, pp. 536–541. C. C. Chang, D. C. Lin, and T. S. Chen, “An improved VQ codebook search algorithm using principal component analysis,” J. Vis. Commun. Image Represent., vol. 8, no. 1, pp. 27–37, Mar. 1997. C. C. Chang, W. C. Wu, "Fast Planar-Oriented Ripple Search Algorithm for Hyperspace VQ Codebook", IEEE Transaction on image processing, vol 16, no.6, pp.: 1538-1547, June 2007. A. Okabe, B. Boots, and K. Sugihara, Spatial Tessellations: Concepts and Applications of Voronoi Diagrams. New York: Wiley, 1992. Y. J. Sher, Y. J. Chen, Y. H. Chiu, K. C. Chung, and C. H. Wu, “MAP based perceptual speech modeling for noisy speech recognition,” J. Inf. Sci. Eng., vol. 22, no. 5, pp. 999–1013, 2006. 2011/11/1629

30. 2011/11/1630 Thank You for Your Attention !