A Fast LBG Codebook Training Algorithm for Vector Quantization Presented by 蔡進義

2 Motivation A fast codebook-training algorithm based on LBG algorithm. A fast codebook-training algorithm based on LBG algorithm. To reduce the computational cost in the codebook training processes. To reduce the computational cost in the codebook training processes.

3 Outline Introduction Introduction Previous Works Previous Works Proposed Method Proposed Method Some Experiments Some Experiments Discussions and Conclusions Discussions and Conclusions

4 Image Compression techniques Block truncation coding Block truncation coding Transform coding Transform coding Hybrid coding Hybrid coding Vector quantization Vector quantization Simple structure and low bit rate Simple structure and low bit rate

5 VQ scheme The VQ scheme can be divided into three parts: The VQ scheme can be divided into three parts: Codebook generation Codebook generation Encoding procedure Encoding procedure Decoding procedure Decoding procedure encoding decoding CodebookCodebook

6 Codebook Generation The most important task for VQ scheme is to design a good codebook. The most important task for VQ scheme is to design a good codebook. LBG (Linde-Buzo-Gray) algorithm / Lloyd clustering algorithm LBG (Linde-Buzo-Gray) algorithm / Lloyd clustering algorithm The LBG algorithm is an iterative procedure. The LBG algorithm is an iterative procedure. cb 0 cb 1 cb n …

7 Euclidean Distance The dimensionality of vector = k (= w*h) The dimensionality of vector = k (= w*h) An input vector x = (x 1, x 2, …, x k ) An input vector x = (x 1, x 2, …, x k ) A codeword y i = (y i1, y i2, …, y ik ) A codeword y i = (y i1, y i2, …, y ik ) The Euclidean distance between x and y i The Euclidean distance between x and y i

8 Codebook Generation

9 Codebook generation Codebook generation Training Images Training set N-1 N VQ Codebook Training

10 Codebook generation Codebook generation Training set Codebook initiation Initial codebook N-1 N VQ Codebook Training

11 Image Index table Vector Quantization Encoder w h Image compression technique VQ Encoding Procedure

12 Image Index table Vector Quantization Decoder w h Image compression technique VQ Decoding Procedure

13 Codebook search To reduce the computational cost for the segmentation procedure in the LBG algorithm, many fast algorithms for codebook search have been developed. To reduce the computational cost for the segmentation procedure in the LBG algorithm, many fast algorithms for codebook search have been developed. Partial Distortion Search (PDS) Partial Distortion Search (PDS) Mean-distance-ordered Partial Codebook Search (MPS) Mean-distance-ordered Partial Codebook Search (MPS) Integral Projection Mean-sorted Partial Search (IPMPS) Integral Projection Mean-sorted Partial Search (IPMPS)

14 Another fast codebook design The tree-structured VQ (TSVQ) The tree-structured VQ (TSVQ) The k-d tree VQ The k-d tree VQ

15 Outline Introduction Introduction Previous Works Previous Works Proposed Method Proposed Method Some Experiments Some Experiments Discussions and Conclusions Discussions and Conclusions

16 Goal To reduce the computation cost in finding the closest codeword in the codebook. To reduce the computation cost in finding the closest codeword in the codebook. PDS PDS MPS MPS IPMPS IPMPS

17 Partial distortion search (PDS) Closest codeword search Closest codeword search If the minimal distance of each input vector could not be found early, the PDS method can just reduce little computation time. If the minimal distance of each input vector could not be found early, the PDS method can just reduce little computation time. (a0, a1, a2, …, a15) input vector (b0, b1, b3, …, b15) codeword

18 Mean-distance-ordered Partial Codebook Search Algorithm (MPS) The Squared Euclidean Distance (SED) The Squared Euclidean Distance (SED) The Squared Mean Distance (SMD) The Squared Mean Distance (SMD) The minimal SED codeword is usually in the neighborhood of the minimal SMD codeword. The minimal SED codeword is usually in the neighborhood of the minimal SMD codeword.

19 Mean-distance-ordered Partial Codebook Search Algorithm (MPS) SMD SED reject

20 Integral Projection Mean-sorted Partial Search Algorithm (IPMPS) Based on multiple distortion measures with different levels of computational complexity. Based on multiple distortion measures with different levels of computational complexity. Three kinds of integral projections: Three kinds of integral projections:

21 Integral Projection Mean-sorted Partial Search Algorithm (IPMPS) Three distortion measures: Three distortion measures: For each codeword Y i Test conditions

22 Outline Introduction Introduction Previous Works Previous Works Proposed Method Proposed Method Some Experiments Some Experiments Discussions and Conclusions Discussions and Conclusions

23 Generalized Integral Projection Model (GIP) To reduce the computational cost To reduce the computational cost MPS and IPMPS MPS and IPMPS IPMPS employs the concept of integral projection to reject further codeword in search. IPMPS employs the concept of integral projection to reject further codeword in search.

24 Generalized Integral Projection Model (GIP) 1. Initially, choose one possible projection map of the pair (p, q).  p segments with q pixels in each segment 2. For each input vector, compute the projection P X (k) of these p segments. 3. The distortion measure corresponding to this projection map is defined as:

25 Generalized Integral Projection Model (GIP) 4. For each codeword, the following inequality can be easily proven true 5. The test condition for this projection map can be constructed. pair(p, q) test conditionpossible projection map

26 Segment maps

27 Fast LBG Algorithm 1. Initially, select a set of test conditions by repeatedly applying the GIP model with different projection maps of the desired pair (p, q). 2. Sort the current codebook by the mean values of the codewords. 3. For each vector, find the corresponding closest codeword.

28 Fast LBG Algorithm 4. Record the index of the closest codeword for each training vector. 5. Update each codeword 6. Overall averaged distortion

29 Outline Introduction Introduction Previous Works Previous Works Proposed Method Proposed Method Some Experiments Some Experiments Discussions and Conclusions Discussions and Conclusions

30 Experiment Methods 512*512 image LBG PDS MPS

31 Experiment Results the property of the training set FLBG-1a FLBG-1b

32 Outline Introduction Introduction Previous Works Previous Works Proposed Method Proposed Method Some Experiments Some Experiments Discussions and Conclusions Discussions and Conclusions

33 Conclusions A generalized integral projection model is developed to produce the test conditions for the speedup of the search process for the VQ codebook design. A generalized integral projection model is developed to produce the test conditions for the speedup of the search process for the VQ codebook design. To use these test conditions to eliminate the need of calculating the squared Euclidean distance. To use these test conditions to eliminate the need of calculating the squared Euclidean distance. The property of image The property of image By choosing proper sets of test conditions for different training sets, a great deal of computation cost can be reduced. By choosing proper sets of test conditions for different training sets, a great deal of computation cost can be reduced.