1. Authors: Jun Tian Speaker: J.H. Liu
Reversible Data Embedding Using Difference Expansion IEEE Transactions on Circuits and Systems for Video Technology, Vol. 13, No. 8, Aug. 2003, page(s):
Authors: Jun Tian
Speaker: J.H. Liu

2. Outline Data Embedding Conclusions Reversible Data Hiding
Difference Expansion
Expandable
Changeable
Difference Expansion Decoding
Expandable decoding
Changeable decoding
Conclusions

3. Data Embedding
Reversible data hiding 1

4. Difference Expansion One of data embedding methods Basic case:
h = x – y
l = (x + y) / 2
x=l + h /2 + LSB(h)
y=l - h /2
Hint : There divide(/) is integer divide.
For example, x/y meaning floor(x/y). +3 -2
x=206
y=201
average
l= 203 2

5. Difference Expansion One of data embedding methods Basic case:
h = x – y
l = (x + y) / 2
x=l + h /2 + LSB(h)
y=l - h /2
Hint : There divide(/) is integer divide.
For example, x/y meaning floor(x/y). +3 -2
x=206
y=201
average
l= 203
If h is odd, bit will lost with h /2.
We must return it into x . 2

6. Difference Expansion - method
location map L
Case1. expandable : h’ = 2×h + b 1
h = x - y Case2. changeable : bitstream C 0
Case3. non-changeable 0
bitstream C = collection of LSBs(h)
Expandable : |h’| = |2xh+b| ≦ min(2(255-l),2xl-1)
Changeable : |h’| = |2x(h/2)+b| ≦ min(2(255-l),2xl-1) 3

7. Expandable 1st step: h’ = hx2 + secret bit (b)
2nd step: x’ = l + h’/2 + LSB(h’)
y’ = l - h’/2
location map L = 1
l = 203 +6 -5
y’=198
x’=209
206 +3 -2
201 4

8. Expandable 1st step: h’ = hx2 + secret bit (b)
2nd step: x’ = l + h’/2 + LSB(h’)
y’ = l - h’/2
location map L = 1
l = 203
b = 1
l=203 +6 -5
y’=198
x’=209
206 +3 -2
201 4

9. Expandable 1st step: h’ = hx2 + secret bit (b)
2nd step: x’ = l + h’/2 + LSB(h’)
y’ = l - h’/2
location map L = 1
l = 203
b = 1
l=203
h’=5*2+1=11 +6 -5
y’=198
x’=209
206 +3 -2
201 4

10. Expandable 1st step: h’ = hx2 + secret bit (b)
2nd step: x’ = l + h’/2 + LSB(h’)
y’ = l - h’/2
location map L = 1
l = 203
b = 1
l=203
h’=5*2+1=11
x’=203+11/2+11%2=209
y’=203-11/2=198 +6 -5
y’=198
x’=209
206 +3 -2
201 4

11. Changeable It is non-expandable
x’, y’ will overflow or underflow with expandable method
l = 223
+46
-46
y’=177
x’=292
246
+23
-23
200 5

12. Changeable It is non-expandable 1st step: h’ = (h/2)x2 + b
2nd step: lost bit(c) = LSB(h)
3rd step: x’ = l + h’/2 + LSB(h’)
y’ = l - h’/2
location map L = 0
+23
-23
x=246
y=200
l = 223 5

13. Changeable It is non-expandable 1st step: h’ = (h/2)x2 + b
2nd step: lost bit(c) = LSB(h)
3rd step: x’ = l + h’/2 + LSB(h’)
y’ = l - h’/2
location map L = 0
+23
-23
x=246
y=200
l = 223
There we will lost the LSB of h. 5

14. Changeable It is non-expandable 1st step: h’ = (h/2)x2 + b
2nd step: lost bit(c) = LSB(h)
3rd step: x’ = l + h’/2 + LSB(h’)
y’ = l - h’/2
location map L = 0
+23
-23
x=246
y=200
l = 223
There we will lost the LSB of h.
We record the LSBs of h at bitstream C. 5

15. Changeable It is non-expandable 1st step: h’ = (h/2)x2 + b
2nd step: lost bit(c) = LSB(h)
3rd step: x’ = l + h’/2 + LSB(h’)
y’ = l - h’/2
location map L = 0
+23
-23
x=246
y=200
l = 223
There we will lost the LSB of h.
We record the LSBs of h at bitstream C.
+24
-23
x’=247
y’=200 5

16. Expandable decoding 1st step: get h’ = x’-y’ 2nd step: get b = LSB(h’)
3rd step: get h = h’/2
4th step: get x = l + h/2 + LSB(h)
y = l - h/2 +6 -5
x‘= 209
y‘= 198
l = 203 6

17. Expandable decoding 1st step: get h’ = x’-y’ 2nd step: get b = LSB(h’)
3rd step: get h = h’/2
4th step: get x = l + h/2 + LSB(h)
y = l - h/2 +6 -5
x’= 209
y‘= 198
l=( )/2=203
h’= =11
l = 203 6

18. Expandable decoding 1st step: get h’ = x’-y’ 2nd step: get b = LSB(h’)
3rd step: get h = h’/2
4th step: get x = l + h/2 + LSB(h)
y = l - h/2 +6 -5
x‘= 209
y‘= 198
l=( )/2=203
h’= =11
b=11%2=1
l = 203 6

19. Expandable decoding 1st step: get h’ = x’-y’ 2nd step: get b = LSB(h’)
3rd step: get h = h’/2
4th step: get x = l + h/2 + LSB(h)
y = l - h/2 +6 -5
x‘= 209
y‘= 198
l=( )/2=203
h’= =11
b=11%2=1
h=11/2=5
l = 203 6

20. Expandable decoding 1st step: get h’ = x’-y’ 2nd step: get b = LSB(h’)
3rd step: get h = h’/2
4th step: get x = l + h/2 + LSB(h)
y = l - h/2 +6 -5
x’= 209
y‘= 198
l=( )/2=203
h’= =11
b=11%2=1
h=11/2=5
x=203+5/2+5%2
= =206
y=203-5/2=201
l = 203 6

21. Expandable decoding 1st step: get h’ = x’-y’ 2nd step: get b = LSB(h’)
3rd step: get h = h’/2
4th step: get x = l + h/2 + LSB(h)
y = l - h/2 +6 -5
x‘= 209
y‘= 198
l=( )/2=203
h’= =11
b=11%2=1
h=11/2=5
x=203+5/2+5%2
= =206
y=203-5/2=201
l = 203 +3 -2
x = 206
y = 201
l = 203 6

22. Expandable decoding 1st step: get h’ = x’-y’ 2nd step: get b = LSB(h’)
3rd step: get h = h’/2
4th step: get x = l + h/2 + LSB(h)
y = l - h/2 +6 -5
x‘= 209
y‘= 198
l=( )/2=203
h’= =11
b=11%2=1
h=11/2=5
x=203+5/2+5%2
= =206
y=203-5/2=201
l = 203
Note: average l is never changed. +3 -2
x = 206
y = 201
l = 203 6

23. Changeable decoding 1st step: get h’ = x’ - y’
2nd step: get b = LSB(h’)
3rd step: get h = h’- b + bitstream(c)
4th step: get x = l + h/2 + LSB(h)
y = l - h/2
+24
-23
x’ = 247
y’ = 200
l = 223 7

24. Changeable decoding 1st step: get h’ = x’ - y’
2nd step: get b = LSB(h’)
3rd step: get h = h’- b + bitstream(c)
4th step: get x = l + h/2 + LSB(h)
y = l - h/2
+24
-23
x’ = 247
y’ = 200
l = 223
l=( )/2=223
h’= =47 7

25. Changeable decoding 1st step: get h’ = x’ - y’
2nd step: get b = LSB(h’)
3rd step: get h = h’- b + bitstream(c)
4th step: get x = l + h/2 + LSB(h)
y = l - h/2
+24
-23
x’ = 247
y’ = 200
l = 223
l=( )/2=223
h’= =47
b=47%2=1 7

26. Changeable decoding 1st step: get h’ = x’ - y’
2nd step: get b = LSB(h’)
3rd step: get h = h’- b + bitstream(c)
4th step: get x = l + h/2 + LSB(h)
y = l - h/2
+24
-23
x’ = 247
y’ = 200
l = 223
l=( )/2=223
h’= =47
b=47%2=1
h=47-1+0=46 7

27. Changeable decoding 1st step: get h’ = x’ - y’
2nd step: get b = LSB(h’)
3rd step: get h = h’- b + bitstream(c)
4th step: get x = l + h/2 + LSB(h)
y = l - h/2
+24
-23
x’ = 247
y’ = 200
l = 223
l=( )/2=223
h’= =47
b=47%2=1
h=47-1+0=46
x=223+(46/2)+46%2
= =246
y=223-46/2=200 7

28. Changeable decoding 1st step: get h’ = x’ - y’
2nd step: get b = LSB(h’)
3rd step: get h = h’- b + bitstream(c)
4th step: get x = l + h/2 + LSB(h)
y = l - h/2
+24
-23
x’ = 247
y’ = 200
l = 223
l=( )/2=223
h’= =47
b=47%2=1
h=47-1+0=46
x=223+(46/2)+46%2
= =246
y=223-46/2=200
+23
-23
x=246
y=200
l = 223 7

29. Conclusions Simple and efficient reversible embedding method.
The method of location map L is not good enough. We may improve the method of location map anywise.
The case of changeable is a kind of useless. 8