A Fast LBG Codebook Training Algorithm for Vector Quantization

1. 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. • To reduce the computational cost in the codebook training processes.

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

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

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

6. cb0 cb1 … cbn Codebook Generation • The most important task for VQ scheme is to design a good codebook. • LBG (Linde-Buzo-Gray) algorithm / Lloyd clustering algorithm • The LBG algorithm is an iterative procedure.

7. Euclidean Distance • The dimensionality of vector = k (= w*h) • An input vector x = (x1, x2, …, xk) • A codeword yi = (yi1, yi2, …, yik) • The Euclidean distance between x and yi

8. Codebook Generation

9. VQ Codebook Training • Codebook generation 0 1 . . . N-1 N Training Images Training set

10. VQ Codebook Training • Codebook generation 0 1 . . . 0 1 . . . 254 255 N-1 N Initial codebook Training set Codebook initiation

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

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

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. • Partial Distortion Search (PDS) • Mean-distance-ordered Partial Codebook Search (MPS) • Integral Projection Mean-sorted Partial Search (IPMPS)

14. Outline • Introduction • Previous Works • Proposed Method • Some Experiments • Discussions and Conclusions

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

16. Partial distortion search (PDS) • 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. (a0, a1, a2, …, a15) input vector (b0, b1, b3, …, b15) codeword

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

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

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

20. Integral Projection Mean-sorted Partial Search Algorithm (IPMPS) • Three distortion measures: Test conditions For each codeword Yi

21. Outline • Introduction • Previous Works • Proposed Method • Some Experiments • Discussions and Conclusions

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

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

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

25. Segment maps

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

27. Fast LBG Algorithm • Record the index of the closest codeword for each training vector. • Update each codeword • Overall averaged distortion

28. Outline • Introduction • Previous Works • Proposed Method • Some Experiments • Discussions and Conclusions

29. Experiment Methods 512*512 image LBG PDS MPS

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

31. Outline • Introduction • Previous Works • Proposed Method • Some Experiments • Discussions and Conclusions

32. 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. • To use these test conditions to eliminate the need of calculating the squared Euclidean distance. • The property of image • By choosing proper sets of test conditions for different training sets, a great deal of computation cost can be reduced.