1. Chinese University of Hong Kong Department of Information Engineering A Capacity Estimate Technique for JPEG-to-JPEG Image Watermarking Peter Hon Wah Wong Department of Information Engineering Chinese University of Hong Kong

2. Chinese University of Hong Kong Department of Information Engineering Outline n JPEG-to-JPEG (J2J) image watermarking n Background of capacity estimation for image watermarking n Proposed J2J capacity estimate technique n Necessary condition to achieve maximum capacity n Experimental results n Conclusions

3. Chinese University of Hong Kong Department of Information Engineering Background of capacity estimation for image watermarking n There are some existing methods to estimate the data hiding capacity of digital images n Ramkumar [1] et al. focused on comparing the capacity among different transforms n Moulin et al. [2] estimated the capacity under different kind and degree of attacks n Voloshynovskiy et al. [3] considered security issue of watermark to estimate the capacity

4. Chinese University of Hong Kong Department of Information Engineering Background of capacity estimation for image watermarking n Shannon [4] showed that for Gaussian channel n For watermarking, image is considered as noise

5. Chinese University of Hong Kong Department of Information Engineering Background of capacity estimation for image watermarking n Costa [5] showed that if the distribution of the image is only known at the watermark embedder

6. Chinese University of Hong Kong Department of Information Engineering n Most of the digital images are stored in JPEG format n Both the input and output images need to be JPEG compatible n It is called JPEG-to-JPEG (J2J) watermarking n All DCT coefficients need to be re-quantized after watermark insertion JPEG-to-JPEG (J2J) Image Watermarking

7. Chinese University of Hong Kong Department of Information Engineering JPEG-to-JPEG Watermarking (J2J)

8. Chinese University of Hong Kong Department of Information Engineering Proposed J2J Capacity Estimate Technique n Capacity of watermarking is defined as the maximum number of bits that can be embedded in the image and invisible n There are two assumptions –the watermarked images will be JPEG-compressed using after watermark insertion –the dimensions of the images are not changed in the watermark embedding n Human Visual System (HVS) model is used to estimate the Just Noticeable Difference (JND) of DCT coefficients n Does not assume any specific watermarking method and embedding domain

9. Chinese University of Hong Kong Department of Information Engineering J2J - Capacity Estimation n Denote the ij th quantized DCT coefficient of the k th block as D q (i,j,k) n The dequantized DCT coefficient D o (i,j,k) is given by n The quantized watermarked DCT coefficient D n (i,j,k) should satisfies n Guarantees the invisibility of the watermark

10. Chinese University of Hong Kong Department of Information Engineering J2J - Capacity Estimation n Only finite possible values of D n (i,j,k) is allowed n The no. of possible value is n J2J data hiding capacity of the image is given approximately by C w n K is the number of blocks in the image

11. Chinese University of Hong Kong Department of Information Engineering J2J - Capacity Estimation N w (i,j,k) = 5 Capacity = log 2 (5) bits

12. Chinese University of Hong Kong Department of Information Engineering J2J - Capacity Estimation n Agrees somewhat with the works of Costa n W is assumed to be uniformly distributed n power of the watermark is n assuming the quantization noise is uniformly distributed in n the power of quantization noise is

13. Chinese University of Hong Kong Department of Information Engineering J2J - Capacity Estimation

14. Chinese University of Hong Kong Department of Information Engineering Necessary Conditions to Achieve Capacity n Consider a DCT coefficient n The capacity of a communication channel with side information is given by where U is a finite alphabet auxiliary random variable, by setting U = D n where U is a finite alphabet auxiliary random variable, by setting U = D n

15. Chinese University of Hong Kong Department of Information Engineering Necessary Conditions to Achieve Capacity n The maximum of is achieved when is equally probable in when is known n the corresponding capacity is

16. Chinese University of Hong Kong Department of Information Engineering Experimental Results n Two common test images 512x512 gray-scale images are estimated and reported n Only the luminance component is used n Scaling factor (SF) is used to scale the default quantization table in JPEG to control the compression ratio

17. Chinese University of Hong Kong Department of Information Engineering Experimental Results LenaPepper

18. Chinese University of Hong Kong Department of Information Engineering Experimental Results LenaPepper

19. Chinese University of Hong Kong Department of Information Engineering Experimental Results – Block Capacity Lena, SFbefore=1, SFafter=0.5, Est. capacity=3507 bits Pepper, SFbefore=1, SFafter=0.5, Est. capacity=3663 bits

20. Chinese University of Hong Kong Department of Information Engineering Experimental Results - Histogram LenaPepper

21. Chinese University of Hong Kong Department of Information Engineering Conclusions n A method to estimate the watermarking capacity of digital images in the JPEG-to-JPEG watermarking framework is proposed n The estimation does not assume any specific watermarking method and embedding domain, it should apply to any watermarking method in the J2J framework More details can be founded from: P.H.W. Wong, Oscar C. Au, "A Capacity Estimation Technique for JPEG- To-JPEG Image Watermarking," IEEE Transactions on Circuits and Systems for Video Technology: Special Issue on Authentication, Copyright Protection and Information Hiding, pp. 746-752, Aug. 2003. A Capacity Estimation Technique for JPEG- To-JPEG Image WatermarkingA Capacity Estimation Technique for JPEG- To-JPEG Image Watermarking

22. Chinese University of Hong Kong Department of Information Engineering References 1. M. Ramkumar and A.N. Akansu, “Capacity Estimates for Data Hiding in Compressed Images,” IEEE Trans. Image Processing, vol. 10, no. 8, pp. 1252-1263, Aug. 2001. 2. P. Moulin and M.K. Mıhçak, “A Framework for Evaluating the Data- Hiding Capacity of Image Sources”, IEEE Trans. Image Processing, vol. 9, no. 8, pp. 1450-1455, Aug. 2000. 3. S. Voloshynovskiy and T. Pun, “Capacity-Security Analysis of Data Hiding Technologies,” in Proc. of IEEE Int. Conf. on Multimedia and Expo, vol. 2, pp. 477-480, Aug. 2002. 4. C.E. Shannon, “A Mathematical Theory of Communication,” Bell Systems Technical Journal, vol. 27, pp.373-423, 623-656, 1948. 5. M. Costa, “Writing on Dirty Paper,” IEEE Trans. Inform. Theory, vol. 29, no. 3, pp. 439-441, May 1983.