1. Chapter 3 向量量化編碼法

2. 3.1 Vector Quantization (VQ) Concept Encoding and Decoding

3. Vector Quantization (VQ)
Image compression technique w h
Image
Index table
Vector Quantization Encoder

4. Vector Quantization (VQ)
Image compression technique w h
Image
Index table
Vector Quantization Decoder

6. 3.2 標準向量量化編碼法

7. Vector Quantization (VQ) Codebook Training
Codebook generation 1 .
N-1 N
Training Images
Training set
Separating the image to vectors

8. Vector Quantization (VQ) Codebook Training
Codebook generation 1 . 1 .
254
255
N-1 N
Initial codebook
Training set
Codebook initiation

9. Vector Quantization (VQ) Codebook Training1 .
Index sets 1 .
254
255
(1, 2, 5, 9, 45, …)
(101, 179, 201, …)
(8, 27, 38, 19, 200, …)
N-1 N
(23, 0, 67, 198, 224, …)
Codebook Ci
Training set 1 .
Compute mean values
254
255
Replace the old vectors
New Codebook Ci+1
Training using iteration algorithm

10. Example
Codebook
To encode an input vector, for example, v = (150,145,121,130)
(1) Compute the distance between v with all vectors in codebook
d(v, cw1) = d(v, cw2) = d(v, cw3) = 112.3
d(v, cw4) = d(v, cw5) = d(v, cw6) = 235.1
d(v, cw7) = d(v, cw8) = 63.2
(2) So, we choose cw8 to replace the input vector v.

11. LBG Algorithm
一次訓練 256 個 codewords
做了100次
連續兩次 MSE 之差別已經夠小

12. 3.2.2 Full Search (FS) For example: Let the codebook size be 256
# of searched nodes
per image vector = 256
Time consuming
The closest codeword
Image vector
C = {c1, c2, …, cnc}

13. 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

14. Problem of FS
VQ encoding process (i.e., codebook search) is time-consuming.
How to speed up the VQ encoder (i.e., codebook search) is thus an important problem.

15. 3.3 細胞分裂法

16. 細胞分裂法
Motivation
The distribution of the codewords in the codebook has great influence on the codebook performance.
The codebook initialization is an important part of the VQ codebook design process.
Solve the codebook initialization problem using a tree-structured codebook design process.

17. 細胞分裂法

18. Example of tree growing function
Let the displacement thresholdδbe set to be four and the branch number equals two.
Given X = [126, 128, 126, 124].
Step 1:
Y = [126, 128, 126, 124] – [4, 4, 4, 4]
= [122, 124, 122, 120]
Z = [126, 128, 126, 124] + [4, 4, 4, 4]
= [130, 132, 130, 128]
Step 2: Return vector Y, Z to the caller.

19. Table 1: Performance of image quality (PSNR) with the codebook sized 256

20. Table 2: Performance of image quality (PSNR) with the codebook sized 128

21. Test image ‘Lena’
Original image 8bpp
0.5 bpp PSNR = dB

22. Test image ‘Pepper’
Original image 8bpp
0.5 bpp PSNR = dB

23. 3.3.2 結論 Progressively design the codebook using a tree structure.結論
Progressively design the codebook using a tree structure.
Develop a simple tree growing procedure to generate initial codewords in the training process.
Provide better codebook performance than that of the LBG algorithm.

24. 3.4 邊緣吻合向量量化法

25. 3.4.1 Side Match Vector Quantization (SMVQ)
Main Idea: Neighbor pixels within an image are similar unless there is an edge across
Figure 4-1:
Side match for the the block X

26. SMVQ(cont.)

27. SMVQ(cont.)
(40+38)/2
找出最接近
(36, x, x, x, 47, x, x, x, 92, x, x, x, 39, 47, 92, 33)
的codeword!!

28. SMVQ(cont.)
Implementation of SMVQ
Seed Block
Residual Block

29. SMVQ(cont.)
Derailment(出軌) Problem
Error
Error
Error

30. 的前 16 個codeword，組成 smaller codebook
SMVQ(cont.)
解決Derailment(出軌) Problem
找出最接近
(x1,x2,x3,x4,x5,x,x,x,x9,x,x,x,x13,x,x,x)
的前 16 個codeword，組成 smaller codebook

31. SMVQ(cont.) 解決Derailment(出軌) Problem
Error =< TH
0010
Error > TH
計算原始圖的black vector與smaller codebook 的誤差 Error
If Error =< Threshold，選擇 smaller codebook 的index
If Error > Threshold，選擇 原始 codebook 的index

32. 3.4.2 Variable-rate SMVQ with a Block Classifer (CSMVQ)
CSMVQ use two thresholds THc and THs.
THc is used to choose size of a state codebook.
THs is used to control the derailment problem.

33. CSMVQ(cont.) h
4hs
2hs hs
Original codebook
State codebooks

34. Edge Block Detection -1 1 -1 1 -1 1 -1 1 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9
(b) vertical edge mask (VM)
(a) horizontal edge mask (HM) -1 1 -1 1
(c) +45。 edge mask (DM+)
(c) -45。 edge mask (DM-)

35. Edge Block Detection (cont.)
Define a threshold THe. For a block Z.
If one of the RHM, RVM, RDM+ and RDM- is larger than THe, Z is considered to be an edge block.
Otherwise, Z is a non-edge block.

36. 3.4.3 Pattern-based SMVQ (PSMVQ)
What is a pattern?
A pattern is a group of w×w blocks.
Why is it called a pattern?
The encoding order of blocks within a pattern is defined.
PSMVQ
The Generation of Edge Codebook and Non-edge Codebook
The Encoder of PSMVQ
The Decoder of PSMVQ

37. PSMVQ (cont.)
The Generation of Edge Codebook and Non-edge Codebook

38. PSMVQ (cont.) PSMVQ The map of the block type
The definition of the order of seed block generation
The adjustment of the order of the seed blocks
The encoding order of the residual blocks

39. PSMVQ (cont.)

40. PSMVQ (cont.) The map of the block type (cont.)
Table 4-1: The numbers of edge blocks and non-edge blocks, the size of the map of block type with THe=70, and the compression ratio of the map of block type

41. PSMVQ (cont.) The definition of the order of seed block generation
Two principles:
(1) Uniform
(2) The priority of blocks in the right end column and the bottom row will be higher than the other blocks.

42. PSMVQ (cont.)
The definition of the order of seed block generation (cont.) 1 49 17 61 4 52 20 64 33 9 45 25 36 12 51 28 13 57 5 53 16 60 8 56 41 21 37 29 42 22 38 30 3 50 19 63 2 18 62 35 10 46 26 34 11 47 27 15 59 7 54 14 58 6 55 43 23 39 31 44 24 40 32 1 4 3 2
(a) 1 13 4 16 9 5 12 7 2 15 3 14 11 6 10 8
(b)
(c)
Different pattern sizes which are 2×2, 4×4, and 8×8, respectively

43. Non-edge block Edge block
PSMVQ (cont.)
The adjustment of the order of the seed blocks
A non-edge block is predicted easily.
An edge block is predicted hardly.
Non-edge block Edge block

44. Figure4-6: An example of reorder a pattern
PSMVQ (cont.)
The adjustment of the order of the seed blocks (cont.)
Add the priority of the block and the number of the blocks to change the encoding order. 1 13 4 16 9 5 12 7 2 15 3 14 11 6 10 8
+16 1 13 4 16 9 5 12 23 2 31 19 30 11 22 26 24
(a) The original order (b) the type of blocks (c) the result of reorder
Figure4-6: An example of reorder a pattern

45. PSMVQ (cont.) The encoding order of the residual blocks 1 3 2 1 2 1 2

46. PSMVQ (cont.)
Encoder of PSMVQ 3 1 2

47. PSMVQ (cont.)
Encoder of PSMVQ (cont.) 3 2 1

48. PSMVQ (cont.)
Decoder of PSMVQ

49. Experimental results of PSMVQ
Experimental Environment
Linux operation system
Pentium 233
Training set: “Airplane”, “Lena”, “Barb”, “Boat”, and “Toys”
Testing images: “Airplane”, “Lena”, “Toys”, “Girl” and “Pepper”
Images size: 512×512 pixels
Image color: 256 gray levels
Block size: 4×4 pixels

50. Experimental results of PSMVQ (cont.)
The image quality, the bit rate, and the encoding time of VQ(h=256), SMVQ(h=256, hs=64), CSMVQ(h=256, hs=16 THc=50, and THs=500), and PSMVQ(THe=70, THp=6000, and 2×2 blocks in a pattern)

51. Experimental results of PSMVQ (cont.)
Figure 4-7: Average results of test images when the pattern size is 2×2 blocks (T:time, B:bit rate)

52. Experimental results of PSMVQ (cont.)
Figure 4-8: Average results of test images when the pattern size is 4×4 blocks (T:time, B:bit rate)

53. Experimental results of PSMVQ (cont.)
Figure 4-9: Average results of test images when the pattern size is 8×8 blocks (T:time, B:bit rate)

54. Experimental results of PSMVQ (cont.)
Figure 4-10: Average results of test images for the different pattern sizes

55. Experimental results of PSMVQ (cont.)
Figure 4-12: The reconstructed image of SMVQ(h=256, hs=16; PSNR=28.574dB, and bit rate=0.3125bpp)
Figure 4-13: The reconstructed image of CSMVQ(h=256, hs=16, THc=50, and THs=500; PSNR=30.657dB, and bit rate=0.355bpp)

56. Experimental results of PSMVQ (cont.)
Figure 4-14(a): The reconstructed image of PSMVQ(THp=1000; PSNR=31.536dB, and bit rate=0.39bpp)
Figure 4-14(b): The reconstructed image of PSMVQ(THp=3000; PSNR=31.225dB, and bit rate=0.315bpp)

57. Experimental results of PSMVQ (cont.)
Figure 4-14(c): The reconstructed image of PSMVQ(THp=6000; PSNR=30.712dB, and bit rate=0.274bpp)
Figure 4-14(d): The reconstructed image of PSMVQ(THp=10000; PSNR=30.1dB, and bit rate=0.247bpp)