1. Detecting and restoring the tampered images based on iteration-free fractal compression
Source: The Journal of Systems and Software,
Volume 67, Issue 2, pp ,
Aug. 2003
Authors: Ching-Te Wnag, Tung-Shou Chen,
Shao-Hau He
Speaker: Yu-Zheng Wang
Date: 2004/04/20

2. Outline Introduction Iteration-free fractal image coding
Proposed method
Experimental results
Conclusions

3. Introduction network A key point: characteristic value
An intruder damage the picture
Original image
tampered image
restoration image
A key point:
characteristic value
Protected image

4. Iteration-free fractal image coding
Generate the efficient domain pool
Output the header and the fractal code
image F
Partition into non-overlapping range block
If the variance of the range block > THv
Find a domain block which similar to the range block
Else
Code by the mean of the range block

5. Iteration-free fractal image coding (Generate the domain pool)
image F
Mean value:
B=8 B I
range block Rr
I=512
I/B=64 D0
domain block Dd (B x B)
I/B
Domain pool: a set of all
domain blocks.
mean image M

6. Iteration-free fractal image coding (Encode the fractal code)
B=8 B
Mean value:
Variance: I
range block Rr
I=512
image F
Header information: 0
If the variance of the range block <= THv
Save the mean of Rr as a fractal code

7. Iteration-free fractal image coding (Encode the fractal code)
Header information: 1
If the variance of the range block > THv
Find a domain block which similar to the range block
The new affine transformation (新相仿轉換)
D: all pixel values in a domain block
μR: the mean of the correlative range block
μD: the mean of D
α : the contrast scaling; α ={n/4, n=1,2,3,…,8}
μR- (α．μD): the luminance offset

8. Iteration-free fractal image coding (Encode the fractal code)
ι : isometric transformation
A fractal code contains:
the isometric transformation ; the contrast scaling ; mean of the range block ; the position of domain block

9. Iteration-free fractal image coding (Encode the fractal code)
The fractal code: (output)
Header information: …1
Data information: …
mean= mean= ι :(a) α =4 mean= th block

10. Iteration-free fractal image coding (Decode the fractal code)

11. Iteration-free fractal image coding (Generate the efficient domain pool)
We have (I/B-B+1)*(I/B-B+1)+1 domain blocks. (I:512; B:8)
(512/8-8+1)*(512/8-8+1)+1=(64-8+1)*(64-8+1)=3250
Some neighboring domain blocks are similar to each other.
There are two methods to obtain the efficient domain pool:
LBG algorithm
block-averaging method (better performance)
Ex:8-4+1=5

12. Iteration-free fractal image coding (Generate the efficient domain pool)
Block-averaging method
T’: the sampling period
ND: the number of domain blocks
Example: ND=225

13. Iteration-free fractal image coding (Generate the efficient domain pool)

14. Proposed method
Extraction and embedding stages

15. Proposed method (cont.)
Extract characteristic values from a specific image
If the variance of the range block > THv
characteristic value: isometric transformation(3 bits); the contrast scaling(3 bits);
mean(7 bits); position of domain block(BitsPD= log2ND )(ND=225:8 bits)
The header is recoded by 1 (1 bit)
Else
characteristic value: mean(7 bits); The header is recoded by 0 (1 bit);
And header information has to be added to characteristic values.

16. Proposed method (cont.)
Hiding characteristic values into the image
The sequence of characteristic values:
… …1
Make three copies of the characteristic values
… … … … … …1
Permute the characteristic values using the pseudorandom number generator with a seed (512*512=262144)
{7,18901,147,…,677,…,3,…,19,…,11111}
The characteristic values are embedded into the LSB.
Header information
data
(I/B)*(I/B)-1

17. Proposed method (cont.)32
135
…1 : characters values
{7,5,47,…,37,…,3,…,19,…,11} 32
134
image F
Protected image F

18. Proposed method (cont.)
Detecting and restoring the tampered image

19. Proposed method (cont.)
Extracting characteristic values
Using the seed to generate a random sequence {7,18901,147,…,677,…,3,…,19,…,11111}
We can extract characteristic values from LSB.
{ … … … … … …1 }
First, getting the header information
System checks the header bits whether correct by compares with the three copies.
C1’:{ …1}
C2’:{ …1}
C3’:{ …0}
=> …1
Getting other characteristic values.

20. Proposed method (cont.)
How to detect tampered blocks?
mean ?
The protected image F’
this = mean of
characteristic
values
The detected image

21. Proposed method (cont.)
Restoring the tampered image
It uses the decoding method.
It looks at the header information
If the value is 0
The tampered block is restored by the mean
If the value is 1
The tampered block is restored by its position in the domain pool, isometry, the mean of the range block, and the contrast scaling.
The detected image

22. Experimental results 512 x 512 LENA An efficient domain pool
mean image
Protected image
Tampered image
Restoration image
Detection image

23. Experimental results (cont.)
512 x 512 PEPPER
An efficient domain pool
Mean image
Protected image
Tampered image
Restoration image
Detection image

24. Conclusions
This paper has proposed a detection and restoration system for tampered image based on iteration-free fractal compression.
The restoration technique don’t need the source image.