planar-oriented ripple based greedy search algorithm for vector quantization presenter: tzu-meng...
TRANSCRIPT
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.
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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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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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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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0
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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.
• C. C. Chang and T. S. Chen, “New tree-structured vector quantization with closest-coupled multipath searching method,” Opt. Eng., vol. 36, no. 6, pp. 1713–1720, Jun. 1997.
• 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 !