Planar-Oriented Ripple BasedGreedy Search Algorithm for

Vector Quantization

Presenter: Tzu-Meng Huang

Adviser:Dr. Yeou-Jiunn Chen

Date:2011/11/16

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Outline

• Introduction

• Paper review

• Method

• Experiment Results and Discussion

• Conclusions

• Future Works

• References

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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

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kS 1 2, , , NC C C

1 2, , ,i kC x x x

Introduction

• Full search vector quantization (FSVQ)

• The larger the codebook size N, the greater the distortion computation overhead.

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1

( , ) ( , ) , whereminbm ii N

d X C d X C

2

2

1

, || ||k

i i j ijj

d X C X C x c

O k N

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)

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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

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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

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Paper Review

• How many ripples is the best for an effective and efficient quantizer?

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Paper Review

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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.

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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

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source :http://mathworld.wolfram.com/VoronoiDiagram.html

Method

• Voronoi-Diagram Construction

Take as the generators of a Voronoi diagram

For each point :

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2( ) | , ,Ci x x ci x cji jVNC P p R d p p d p p

Method

• Preprocessing and Training Procedure

• Step 1. Using PCA technique to project codebook onto a space of m-dimensional.

2011/11/16 13-6 -5 -4 -3 -2 -1 0 1 2 3 4

-5

-4

-3

-2

-1

0

1

2

3

PC1

PC2

PC3

PC4 PC5

PC6

PC7

PC8PC9

PC10

Method

• Preprocessing and Training Procedure

• Step 2. Building a Voronoi diagram by the projected plan.

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-5

-4

-3

-2

-1

0

1

2

3

PC1

PC2

PC3

PC4 PC5

PC6

PC7

PC8PC9

PC10

Method

• Preprocessing and Training Procedure

• Step 3. Generate the neighbor-ripple adjacency-list of each codeword.

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-6 -5 -4 -3 -2 -1 0 1 2 3 4-5

-4

-3

-2

-1

0

1

2

3

PC1

PC2

PC3

PC4 PC5

PC6

PC7

PC8PC9

PC10 PC1

…PC6

…

PC10

PC4 PC5 PC6 PC9 PC8

PC1 PC5 PC3 PC10 PC9

PC2 PC3 PC6 PC9

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.

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-4

-3

-2

-1

0

1

2

3

PC1

PC2

PC3

PC4 PC5

PC6

PC7

PC8PC9

PC10

training data

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.

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PC1

…

PC6

…

PC10

PC4 PC5 PC6 PC9 PC8

PC1 PC5 PC3 PC10 PC9

PC2 PC3 PC6 PC9

the best codeword

PC4

initial codeword

PC6

PC1 PC5 PC3 PC10 PC9 PC4

Method

• Vector Searching Procedure with Cutoff• Step 1. Using PCA to project the input vector px onto the same

space.

• Step 2. Using binary search to find the initial codeword Ci of px.

• Step 3. Let the best codeword Cb is equal to Ci.

• Step 4. Finding the closest codeword Cc in adjacency-list of Ci.

• Step 5. If Cc is closer than Cb, then let Cb=Cc and Ci=Cc 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 Cb.

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Method

• Vector Searching Procedure without Cutoff• Step 1. Using PCA to project the input vector px onto the same

space.

• Step 2. Using binary search to find the initial codeword Ci of px.

• Step 3. Let the best codeword Cb is equal to Ci.

• Step 4. Finding the closest codeword Cc in adjacency-list of Ci.

• Step 5. If Cc is closer than Cb, then let Cb=Cc

• Step 6. Let Ci=Cc.

• Step 7. Repeat step 4 and step 6 until the predefined number of ripples is reached.

• Step 8. Return the best codeword Cb.2011/11/16 19

Experiment Results and Discussion

• Data

• TCC300

• Codebook 2048×39

• Training data 3026×39

• Testing data 6654×39

• Software

• MATLAB

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Experiment Results and Discussion

• The Analysis of Dimension of Voronoi-Diagram

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Experiment Results and Discussion

GS_PVDS with cutoff GS_PVDS without cutoff

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• 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.

Experiment Results and Discussion

GS_PVDS with cutoff GS_PVDS without cutoff

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• 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.

Experiment Results and Discussion

GS_PVDS with cutoff GS_PVDS without cutoff

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• 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.

Experiment Results and Discussion

• GS_PVDS without cutoff and PVDS

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The line of triangle mark and square mark represent GS_PVDS and GS_PVDS without cutoff

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.

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Future Works

• More experiment results with different data

• Dynamic increasing codewords into the codebook

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References• C. Lin, Y. Zhao, and C. Zhu, “Two-Stage Diversity-Based Multiple Description Image

Coding,” IEEE Signal Processing Letters, vol. 15, pp. 837-840, 2008.

• C. C. Chang and I. C. Lin, “Fast search algorithm for vector quantisation without extra look-up table using declustered subcodebooks,” IEEE Proc. Vis., Image, Signal Process., vol. 152, no. 5, pp. 513–519, Oct. 2005.

• L. Torres and J. Huguet, “An improvement on codebook search for vector quantisation,” IEEE Trans. Commun., vol. 42, no. 2, pp. 208–210, Feb. 1994.

• H. Park and V. K. Prasana, “Modular VLSI architectures for real-time full-search-based vector quantization,” IEEE Trans. Circuits Syst. Video Technol., vol. 3, no. 4, pp. 309–317, Aug. 1993.

• C. D. Bei and R. M. Gray, “An improvement of the minimum distortion encoding algorithm for vector quantization,” IEEE Trans. Commun., vol. 33, no. 10, pp. 1132–1133, Oct. 1985.

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• W. C. Chu, "Embedded quantization of line spectral frequencies using a multistage tree-structured vector quantizer," IEEE Trans. Audio, Speech, Language Process., vol. 14, no. 4, pp 1205-1217, Jul. 2006.

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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.

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Thank You for Your Attention !