Optimal Histogram-pair and Prediction-error Based Image Reversible Data Hiding

1. Optimal Histogram-pair and Prediction-error Based Image Reversible Data Hiding Guorong Xuan1, Xuefeng Tong1, Jianzhong Teng1, Xiaojie Zhang1, Yun Q. Shi2 1Computer Science, Tongji University, Shanghai, China 2ECE, New Jersey Institute of Technology, Newark, New Jersey, USA Paper #44 IWDW2012 Shanghai, 11/3/2012

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 TF • Left-histogram shrinking threshold TL • Right-histogram shrinking threshold TR

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. (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. (I-1) Principle of “Histogram-pair scheme”

5. (I-2) Histogram modification (a) (b) (c) (a) Original gray level histogram (b) Histogram after modification with TL and TR (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. (I-3) Histogram-pair scheme considered as magnitude embedding

7. (II-1) Two factors for further improving the PSNR PE, 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. (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 domainwith sharp distribution ( PE = T, where T is embedding threshold). ○ The other is to embed data in local area with smaller gray-level neighbor fluctuation value F (F<TF , where TF is fluctuation threshold). The local area is with more sharp distribution in prediction-error domain. 8

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

10. (III-2) Parameters T, TF , TL and TR 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. (IV-1) Experimental works Experimental works on JPEG2000 test image

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

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

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

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