1. Lossless Compression Schemes of Vector Quantization Indices Using State Codebook
Chair Professor Chin-Chen Chang
Feng Chia University
National Chung Cheng University
National Tsing Hua University

2. Outline Introduction Proposed schemes Experimental results ConclusionsVQ
PCA
SOC
Proposed schemes
Scheme 1
Scheme 2
Experimental results
Conclusions

3. Alan Chang

4. Vector Quantization (VQ) Concept Encoding and Decoding

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

6. Introduction (VQ) (Cont.)

7. Introduction (VQ) (Cont.)
Training phase
Codebook
……………….
…...….
Codebook size
ex : 128, 256, 512 or 1024
divided into blocks with pixels
16-dimension

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

9. Introduction (VQ) (Cont.)
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

10. Ex:
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. Introduction (VQ) (Cont.)
Encoding
Codebook
Nc-1 Nc
Original image
encoding
index table

12. Introduction (VQ) (Cont.)
Decoding
look-up procedure
Codebook
Nc-1 Nc
decoding
index table

13. Introduction (PCA) Principal component analysis (PCA) Ex: 2-dimension. D2 . . . . . . . . . . . . X1 . . . . . . . . . . .

14. Introduction (SOC)
Search-order coding (SOC)
Ex:

15. Introduction (SOC) (Cont.)
Searched point
Non-searched point

16. Introduction (SOC) (Cont.)
The compressing steps
Indicator
P1 =
P2 =
P3 = 0 00
P6 = 0 01 31
207
211 8 7 35 … …
Compression codes = …

17. The proposed scheme start PCA SOC run SOC our scheme our scheme
yes
run SOC
end
our scheme no
yes
our scheme
end
original index value no
original index value
end

18. The proposed scheme (Cont.)
Indicator
SOC  “0”
Our scheme  “10”
Original index value  “11”

19. The proposed scheme (Cont.)
State codebook is generated in real-time
Three cases
CASE 1
One-bit indicator (0)+ SOC
CASE 2
Two-bits indicator (10)+ index value
CASE 3
Two-bits indicator (11)+ VQ index value

20. The proposed scheme (Cont.)
Example 1: 54 61
CASE 1
One-bit indicator (0)+ SOC
Compression result of (3,3) is
“0001”
SOC:
(101) 61
(001)
(010) 54
(100)
(000)

21. Scheme 1 CASE 2 Two-bits indicator (10)+ index value Example: 2 61
Compression result
of (3,3) is “101110”

22. Scheme 1 (Cont.) Example 3: 60 61 Two-bits indicator (11) + VQ index
CASE 3
No match found in
Cases 1 and 2
Two-bits indicator (11) + VQ index
“1110” 47

23. Scheme 2 Also called “The Optimized State Codebook Scheme”
The exclusion of repetition indices
Four state codebooks 61
Codebook 1

24. Scheme 2 (Cont.) Codebook 2?
Check if {53, 54, 56, 57} ∩{52, 53, 55, 56} = ø 61
Yes:
The similar neighboring index (2,2), which equals to “54”
The index of the state codebook
The indices of the closest codewords of “54” in the codebook
“0100”
“0101”
“0110”
“0111 52 53 55 56
NO:
The similar neighboring index (2,2), which equals to “54”
The index of the state codebook
The indices of the closest codewords of “54” in the codebook
“0100”
“0101”
“0110”
“0111 51 52 58 59 52 53 55 56 53 54 56 57

25. Scheme 2 (Cont.) Codebook 3?
Check if ({53, 54, 56, 57} ∪ {51, 52, 58, 59}) ∩ {50, 51, 53, 54} = ø
Yes: 61
The similar neighboring index (2,4), which equals to “52”
The index of the state codebook
The indices of the closest codewords of “52” in the codebook
“1000”
“1001”
“1010”
“1011” 50 51 53 54
NO: 51 52 . 58 59
The similar neighboring index (2,4), which equals to “52”
The index of the state codebook
The indices of the closest codewords of “52” in the codebook
“1000”
“1001”
“1010”
“1011” 49 50 60 61 50 51 53 54

26. Scheme 2 (Cont.) Codebook 3 CASE 2
The similar neighboring index (2,4), which equals to “52”
The index of the state codebook
The indices of the closest codewords of “52” in the codebook
“1000”
“1001”
“1010”
“1011” 49 50 60 61 61
CASE 2
Two-bits indicator (10)+ index value
Compression results of (3,3)= “ ”

27. Scheme 2 (Cont.) Codebook 4 ?
Check if ({53, 54, 56, 57} ∪ {51, 52, 58, 59} ∪ {49, 50, 61, 62}) ∩ {44, 45, 47, 48} = ø
Yes: 61
The similar neighboring index (3,1), which equals to “46”
The index of the state codebook
The indices of the closest codewords of “46” in the codebook
“1100”
“1101”
“1110”
“1111” 44 45 47 48

28. Experimental results (1/4)
The codebook is designed by using LBG algorithm

29. Experimental results (2/4)1

30. Experimental results (3/4)2

31. Experimental results (4/4)3

32. Conclusions Two new schemes for VQ index table
Scheme 2 excludes the repetitive indices
Scheme 2 presents better performance than SOC and Scheme 1
Both schemes achieve the goal of reducing bit rate