1. Optimal Histogram-pair and Prediction-error Based Image Reversible Data Hiding 1 Computer Science, Tongji University, Shanghai, China 2 ECE, New Jersey Institute of Technology, Newark, New Jersey, USA Guorong Xuan 1, Xuefeng Tong 1, Jianzhong Teng 1, Xiaojie Zhang 1, Yun Q. Shi 2 Paper #44 IWDW2012 Shanghai, 11/3/2012

2. 2 Abstract This proposed algorithm reversibly embeds data to image by using “histogram-pair scheme” and “ prediction-error” with the following four thresholds for optimal performance: Embedding threshold T Fluctuation threshold T F Left-histogram shrinking threshold T L Right-histogram shrinking threshold T R

3. 3 Outline (I) Principle of “Histogram-pair scheme”: “histogram- pair scheme” is considered as magnitude based embedding. (II) Embedding data in sharp distribution region : ○ One is to embed data in prediction-error domain ○ The other is to embed data in smaller neighbor fluctuation value region (III) Four threshold: for both underflow/overflow avoidance and optimality. (IV) Experimental works: including JPEG2000 test image and other popularly images. (V) Conclusion

4. (I-1) Principle of “Histogram-pair scheme” (1) Proposed “magnitude based embedding” : data to be embedded by magnitude of image by using “x+b” (x is image and b is data).The histogram modification (histogram shrinking or bookkeeping) are needed for reversible hiding. (2) “Location based embedding” of Tian’s method (DE): data to be embedded by location and using “2x+b ”. The location map is used for reversible hiding.

5. 5 (I-2) Histogram modification (a) (b) (c) (a) Original gray level histogram (b) Histogram after modification with T L and T R (c) Histogram after data embedding Fig. 2 Histogram modification in reversible data hiding The image gray level histogram modification shrinking towards the center from sides is conducted for avoiding underflow and/or overflow.

6. 6 (I-3) Histogram-pair scheme considered as magnitude embedding

7. 7 (II-1) Two factors for further improving the PSNR P E, prediction error, is defined from the central pixel and its eight-neighbors (weighted). F, fluctuation value, is the variance (weighted) defined from eight-neighbors of the central pixel.

8. 8 (II-2) Two factors for further improving the PSNR Embedding data in sharp distribution region in an image for improving PSNR. There are Two factors for further improving the PSNR ○ One is to embed data in prediction-error domain with sharp distribution ( P E = T, where T is embedding threshold). ○ The other is to embed data in local area with smaller gray-level neighbor fluctuation value F (F<T F, where T F is fluctuation threshold). The local area is with more sharp distribution in prediction-error domain.

9. (III-1) Parameters T, T F, T L and T R for optimality. There are four thresholds : T, T F, T L and T R, which are used for underflow and/or overflow avoidance and optimality.

10. (III-2) Parameters T, T F, T L and T R for optimality. “Fail” means the length of embedding data is not enough, “UNF” means underflow, “OVF” means overflow, “UOF ” means both underflow and overflow.

11. 11 (IV-1) Experimental works Experimental works on JPEG2000 test image

12. 12 (IV-2) Experimental works Fig. 8 Data embedding for woman

13. 13 (IV-3) Experimental works Fig. 9 embedding for Lena

14. 14 (IV-4) Experimental works Fig. 10 embedding for Barbara

15. 15 1.An optimal histogram-pair and prediction-error based reversible data hiding is proposed. 2.“Histogram-pair scheme” is adopted and to be considered as a magnitude based embedding. 3.The better performance is achieved by embedding at the sharper distribution region of prediction-error domain. 4.Four thresholds have been utilized for optimality. 5.The performance has been further enhanced, in particular for Woman image with peaks on both ends of histogram. V. Conclusion