Detecting and restoring the tampered images based on iteration-free fractal compression

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. 131- 140, 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. A key point: • characteristic value restoration image Protected image Introduction network An intruder damage the picture Original image tampered 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 thevariance 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. Mean value: B=8 B D0 Iteration-free fractal image coding (Generate the domain pool) image F I range block Rr I=512 I/B=64 domain block Dd (B x B) I/B Domain pool: a set of all domain blocks. mean image M

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

7. Iteration-free fractal image coding (Encode the fractal code) Header information: 1 If thevariance 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: 0010101…1 • Data information: 0010111 0100010000 011 1000001 00110101… mean=46 mean=69 ι :(a) α =4 mean=130 53th block 00101110 01000101 10000010

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

11. Iteration-free fractal image coding (Generate the efficient domain pool) Ex:8-4+1=5 • 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)

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

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 thevariance 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: 0010010…11010100100101…1 • Make three copies of the characteristic values 0010010…11010100100101…1 0010010…11010100100101…1 0010010…11010100100101…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 0 (I/B)*(I/B)-1

17. Proposed method (cont.) 32 135 0 01001011101101…1 : characters values {7,5,47,…,37,…,3,…,19,…,11} 32 134 10000111 image F 10000110 00100000 Protected image F 00100000

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. {0010010…11010100100101…10000110…11010100100101…10010010…01010100100101…1 } • First, getting the header information • System checks the header bits whether correct by compares with the three copies. C1’:{0010010…1} C2’:{0000110…1} C3’:{0010010…0} =>0010110…1 • Getting other characteristic values.

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

21. The detected image 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.

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.