1. Hiding Information in VQ Index Tables with Reversibility
Chair Professor Chin-Chen Chang
Feng Chia University
National Chung Cheng University
National Tsing Hua University

2. Outline Introduction Related works The proposed scheme
Experimental results
Conclusions

3. Introduction VQ compression Index table Original Image Codebook
(16, 200, …, 90) 1
(35, 22, …, 100) 2
(40, 255, …, 59) .
254
(90, 102, …, 98)
255
(145, 16, …, 99) 1 60 61
175 …
100 95
203 .
. . .
Index table
Original Image
Codebook

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

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

7. 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
Replace the old vectors
254
255
New Codebook Ci+1
Training using iteration algorithm

8. 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.

9. 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. 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}

11. 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

12. 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.

13. The Proposed Scheme Embedding Processes
Selecting the two preserved codewords:
(89, 33, …, 187)  index 0
(55, 25, …, 124)  index 255
(89, 33, …, 187) 1
(35, 22, …, 100) 2
(40, 255, …, 59) .
254
(90, 102, …, 98)
255
(55, 25, …, 124) 1 60 61
175 …
100 95
203 .
. . .
Two least frequently used codewords
Index table

14. The Proposed Scheme Embedding Processes
2. Compress original images with the modified codebook
(89, 33, …, 187) 1
(35, 22, …, 100) 2
(40, 255, …, 59) .
254
(90, 102, …, 98)
255
(55, 25, …, 124) 1 60 61 …
100 95
203 .
. . .
Index table
Original Image
Modified Codebook

15. The Proposed Scheme Embedding Processes
3. Bound each two indices as an index pair (i1, i2) 1 60 61 …
100 95
203 .
. . .
Index table

16. The Proposed Scheme 4. Analyzing all index pairs i1 > i2
n1: the number of index pairs (i1, i2) in which
i1 > i2
n2: the number of index pairs (i1, i2) in which
i1 < i2
Case A: n1 ≧ n2
Case B: n1 < n2

17. The Proposed Scheme 5.1 Embedding rules (Case A)
To Embed secret bit s into index pair (i1, i2)

18. The Proposed Scheme 5.2 Embedding rules (Case B)
To Embed secret bit s into index pair (i1, i2)

19. The Proposed Scheme Example (Case A)；
Codebook size = 256, F = 0, L = 255,
and s = 1101
(90, 30)
(50, 60)
(70, 70)
(254, 1)
Original VQ index table

20. Watermarked index pair:
The Proposed Scheme s: 1
Index pair:
(90, 30)
(50, 60)
(70, 70)
(254, 1)
(j1, j2) = (i1, i1 – i2)
=(90, 90-30)
(j1, j2) = (F, i1)
=(0, 70)
(j1, j2) = (i1, i1 – i2)
=(254, 254-1)
(j1, j2) = (L, i1, i2)
Watermarked index pair:
(90, 60)
(255, 50, 60)
(0, 70)
(254, 253)

21. The Proposed Scheme Extracting procedure
1.1 The extracting rules (Case A)
index by index

22. The Proposed Scheme Extracting procedure
1.2 The extracting rules (Case B)
index by index

23. Watermarked index pair:
The Proposed Scheme
Extracting procedure
Example (Case A):
Watermarked index pair:
(90, 60)
(255, 50, 60)
(0, 70)
(254, 253)
(i1, i2) = (j1, j1 – j2)
=(90, 90-60)
(i1, i2) = (j2, j3)
=(50, 60)
(i1, i2) = (j2, j2)
=(70, 70)
(i1, i2) = (j1, j1 – j2)
=(254, )
Recovered index pair:
(90, 30)
(50, 60)
(70, 70)
(254, 1)
j1 ≠L; j1 ≠F; j1 > j2
j1 =L; j2 < j3
j1 ≠L; j1 ≠F; j1 > j2
j1 =F 1 1
Secret bits: 1

24. Experimental results Original VQ-coded Images
Recovered VQ-coded Images

25. Experimental results The proposed scheme Scheme [11] Lena Jet Pepper
Method
Images
Scheme [11]
The proposed scheme
Lena
Capacity
4524
8192
Bit rate (bpp)
0.7239
0.5918
Jet
3379
0.7938
0.5742
Pepper
4749
0.7101
0.5790
Toys
5102
0.6886
0.5515
[11] C. C. Chang, Y. H. Chen, Z. H. Wang and M. C. Li, "A reversible data embedding scheme based on Chinese remainder theorem for VQ index tables," Proceedings of 2009 Second ISECS International Colloquium on Computing, Communication, Control, and Management(CCCM 2009), Sanya, China, Aug. 8-9, 2009, Vol. I, pp

26. Conclusions
Simple
Efficient
Reversible

27. Thanks for your listening~