1. A Study of Digital Image Coding and Retrieving Techniques
數位影像編碼與擷取技術之研究
A Study of Digital Image Coding and Retrieving Techniques
指導教授: 張真誠 教授
研究生: 周永振
Dept. of Computer Science and Information Engineering, National Chung Cheng University

2. Outline Part 1: Compression domain data hiding
Part 2: Data hiding using Sudoku
Part 3: Reversible data hiding for color image
Part 4: High payload data embedding for color image
Part 5: SOC improvement
Yung-Chen Chou

3. Introduction Steganography SOC improvement Secret data delivery
Visual quality vs. embedding capacity
Categories:
Compression domain
Spatial domain
Frequency domain
Grayscale image/color image
SOC improvement
Indicator
Eliminate the indicator
Yung-Chen Chou

4. Introduction (Cont.) Information hiding (Data hiding) Hiding system
Stego image
Cover image
Secret message
Yung-Chen Chou

5. VQ domain data hiding
Vector quantization
Yung-Chen Chou

6. VQ domain data hiding (Cont.)
Codeword pairing
{d12, d13, d14, d15, d16, d23, d24, d25, d26
d34, d35, d36, d45, d46, d56}
cw6
d12
d13
d14
d15
d16
cw2
cw5
cw4
cw1
cw3 G0 G1
G-1
d36>TH
Yung-Chen Chou

7. VQ domain data hiding (Cont.)
Data embedding
NBVX = {x0, x1, x3, x4, X, X, X, x8, X, X, X, x12, X, X, X}
Indicator = ‘0’
Indicator = ‘1’
Image
If SMD(cwi,NBVX) < SMD(cwj, NBVX) then X is replaceable
Else X is non-replaceable
If secret bit = ‘0’ then encode X by cwi
else encode X by cwj
Encoded by cwi
cwi
cwj
Yung-Chen Chou G0 G1

8. VQ domain data hiding (Cont.)
Data extracting and restoring
If SMD(cwi) < SMD(cwj) and indicator = ‘0’  restore X by cwi
If SMD(cwi) < SMD(cwj) and indicator = ‘1’  restore X by cwj
If SMD(cwi)  SMD(cwj) and indicator = ‘0’  restore X by cwj
If SMD(cwi)  SMD(cwj) and indicator = ‘1’  restore X by cwi
Image
If X encoded by cwi then secret bit = ‘0’
If X encoded by cwj then secret bit = ‘1’
cwi
cwj
Yung-Chen Chou G0 G1

9. VQ domain data hiding (Cont.)
Experimental results
Yung-Chen Chou

10. VQ domain data hiding (Cont.)
Experimental results
Yung-Chen Chou

11. Data hiding using Sudoku
Spatial domain data embedding
Sudoku
A logic-based number placement puzzle
Yung-Chen Chou

12. Data hiding using Sudoku (Cont.)
Property
A Sudoku grid contains nine 3 × 3 matrices, each contains different digits from 1 to 9.
Each row and each column of a Sudoku grid also contain different digits from 1 to 9.
Possible solutions:
6,670,903,752,021,072,936,960
(i.e. ≈ 6.671×1021)
Yung-Chen Chou

13. Data hiding using Sudoku (Cont
Data hiding using Sudoku (Cont.) Review Zhang and Wang’s method (Embedding)
Extracting function: 8 7 9 4 79 54 55 11 20 21 12 24 10
Secret data: … p2
255 1 2 3 4 1 2 3 4 1 : : : : : : : : : : : : :
10002
1 35 … 11 2 3 4 1 2 3 4 1 2 3 2 … 10 1 2 3 4 1 2 3 4 1
Cover image … 9 3 4 1 2 3 4 1 2 3 4 3 … 8 1 2 3 4 1 2 3 4 1 2 1 … 7 4 1 2 3 4 1 2 3 4 4 … 6 2 3 4 1 2 3 4 1 2 3 2 … 5 1 2 3 4 1 2 3 4 1 7 10 4 … 4 3 4 1 2 3 4 1 2 3 4 3 … 3 1 2 3 4 1 2 3 4 1 2 1 … 2 4 1 2 3 4 1 2 3 4 4 … 1 2 3 4 1 2 3 4 1 2 3 2 … 1 2 3 4 1 2 3 4 1
Stego image 1 2 3 4 5 6 7 8 9 10 11 …
255 p1
Magic Matrix
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14. Data hiding using Sudoku (Cont
Data hiding using Sudoku (Cont.) Review Zhang and Wang’s method (Extracting) p2 7 10 4
255 1 2 3 4 1 2 3 4 1 : : : : : : : : : : : : : … 11 2 3 4 1 2 3 4 1 2 3 2 … 10 1 2 3 4 1 2 3 4 1 … 9 3 4 1 2 3 4 1 2 3 4 3 … 8 1 2 3 4 1 2 3 4 1 2 1
Stego image … 7 4 1 2 3 4 1 2 3 4 4 …
1 35 6 2 3 4 1 2 3 4 1 2 3 2 … 5 1 2 3 4 1 2 3 4 1 … 4 3 4 1 2 3 4 1 2 3 4 3 …
Extracted secret data: 10002 3 1 2 3 4 1 2 3 4 1 2 1 … 2 4 1 2 3 4 1 2 3 4 4 … 1 2 3 4 1 2 3 4 1 2 3 2 … 1 2 3 4 1 2 3 4 1 p1 1 2 3 4 5 6 7 8 9 10 11 …
255
Magic Matrix
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15. Data hiding using Sudoku (Cont.)
- 1
Reference Matrix M
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16. Data hiding using Sudoku (Embedding) (Cont.)8 7 11 12 79 54 55 20 21 24 10 9
Secret data: …
279
Cover Image 7 9
Stego Image
min.
d( , ) = ((8-8)2+(4-7)2)1/2=3
d( , ) = ((9-8)2+(7-7)2)1/2=1
d( , ) = ((6-8)2+(8-7)2)1/2=2.24
Yung-Chen Chou

17. Data hiding using Sudoku (Embedding) (Cont.)8 7 11 12 79 54 55 20 21 24 10 9
Secret data: …
279
Cover Image
d( , ) = ((11-11)2+(15-12)2)1/2=3
d( , ) = ((15-11)2+(12-12)2)1/2=4
d( , ) = ((9-11)2+(14-12)2)1/2=2.83 9 14 7
Stego Image
min.
Yung-Chen Chou

18. Data hiding using Sudoku (Extracting) (Cont.)9 7 14
Stego Image
Extracted data: 279 =
Yung-Chen Chou

19. Experimental results
Yung-Chen Chou

20. Experimental results (Cont.)
Yung-Chen Chou

21. Data hiding for color images
True color and color palette image
Color pixel (Red, Green, Blue)
Reversibility
Yung-Chen Chou

22. Data hiding for color images (Cont.)
Review Fridrich’s method
R+G+B mod 2 = ( ) mod 2 = 1
R+G+B mod 2 = ( ) mod 2 = 0
Image
Stego
Secret: 010…
Yung-Chen Chou

23. Data hiding for color images (Cont.)
Proposed method (Embedding)
( R, G, B)
pi = (112, 217, 110)
pi+1=(115, 216, 112)
(115, 216, 112)
(115, 112, 216)
(216, 115, 112)
(216, 112, 115)
(112, 115, 216)
(112, 216, 115)
d0 = 3.74
d1 =
d2 =
d3 =
d4 =
d5 = 5.1
If d0 is first one then embeddable
Else non-embeddable
Image
Sorting
d0 < d5 < d4 < d3 < d2 < d1
log2NG = log26 = 2
If d(pi+1, p’i+1) < TH=50 then embed secret
Else non-embeddable
require extra information
Stego
Secret: 011…
Yung-Chen Chou

24. Data hiding for color images (Cont.)
Proposed method (Extracting and restoring)
( R, G, B)
(112, 217, 110)
(112, 216, 115)
(112, 216, 115)
(112, 115, 216)
(216, 112, 115)
(216, 115, 112)
(115, 112, 216)
(115, 216, 112)
d0 = 5.1
d1 =
d2 =
d3 =
d4 =
d5 = 3.74
Stego
Sorting
d5 < d0 < d3 < d1 < d2 < d4
log2NG = log26 = 2
Extracted data: 01
Restored image
Yung-Chen Chou

25. Data hiding for color images (Cont.)
Experimental results
Yung-Chen Chou

26. Data hiding for color images (Cont.)
Experimental results
Yung-Chen Chou

27. High payload data hiding for color images
Review Tzeng’s method
v = 0.3  r  g  b
v1 = 0.3   15 = 16.45
v2 = 8.17
v3 = 10.22
v4 = 15.21
vc = 18.17
Image
c1 >c2, if (v1>v2) or
(v1=v2 and r1>r2) or
(v1 = v2 and r1=r2 and g1>g2)
c1 = c2, if (r1=r2 and g1=g2 and g1=g2)
c1 < c2, otherwise c1 c2 c3 c4 1 c
Secret: 101…
Yung-Chen Chou

28. High payload data hiding for color images (Cont.)
The proposed (Embedding) 6 15 8 14 16 … 6 15 8 10 20 15
 log2(8-6)=1
14+1=15 6 15 8 14 16 …
Image 10 20 16
10+6 =16
 log2(20-10)=3
Stego
Secret: …
Yung-Chen Chou

29. High payload data hiding for color images (Cont.)
The proposed (Extracting) 6 15 8
Stego 10 20 16
 log2(20-10)=3
16-10 = 6 = 1102
 log2(8-6)=1 6 15 8 14 16 …
14-15=1=12 1
110
Extracted secret:
Yung-Chen Chou

30. High payload data hiding for color images (Cont.)
Experimental results
Yung-Chen Chou

31. High payload data hiding for color images (Cont.)
Yung-Chen Chou

32. SOC improvement Scan-order coding (SOC) Compression code: …1 011…
Indicator 52
State codebook
Compression code: …1 011… 53 1 49 2 50 57 55 48 47 3 4 5 6 7
Index table
Indicator
Index table 52
State codebook
Compression code: … … 53 1 49 2 50 57 55 48 47 3 4 5 6 7
Yung-Chen Chou

33. SOC improvement (Cont.)
Review Lin and Chang’s method
NBVB = {b0, b1, b3, b4, X, X, X, b8, X, X, X, b12, X, X, X}
If SMD(α, NBVB) <SMD(α, NBVB)
If SMD(α, NBVB)  SMD(α, NBVB)
Secret = 0
Secret = 1 α
111 || α
000 ||α
Yung-Chen Chou

34. SOC improvement (Cont.)
The proposed method (Encoding)
Index table
Sorted SCB
Can be compressed by
SOC (i.e. indicator = 1)
Index table
Sorted SCB
If SMD(cw50, NBVBi) < SMD(cw55, NBVBi)
Compression code: …101
Else Compression code: …
For indicator = 0
For indicator = 1
Yung-Chen Chou

35. SOC improvement (Cont.)
Index table
Can be compressed by
SOC (i.e. indicator = 1)
For indicator = 0
For indicator = 1
Index table
Sorted SCB
For indicator = 0
For indicator = 1
If SMD(cw130, NBVBi) < SMD(cw3, NBVBi)
Compression code: …
Else Compression code: …
Yung-Chen Chou

36. SOC improvement (Cont.)
The proposed method (Decoding)
Compression code: …101…
The indicator for next block is ‘1’
Using cw50 to decode Bi
SMD(cw55, NBVBi)  SMD(cw50, NBVBi)
Index table
Sorted SCB
For indicator = 0
For indicator = 1
Yung-Chen Chou

37. SOC improvement (Cont.)
Compression code: … …
The indicator for next block is ‘1’
Using cw50 to decode Bi
Index table
Sorted SCB
For indicator = 0
For indicator = 1
Yung-Chen Chou

38. SOC improvement (Cont.)
Yung-Chen Chou

39. SOC improvement (Cont.)
Experimental results

40. Conclusions Steganography
Achieve high payload data embedding
Reversibility
Achieve high payload data embedding for color images
Success eliminate the indicator of SOC
Yung-Chen Chou