1. 1/18 New Feature Presentation of Transition Probability Matrix for Image Tampering Detection Luyi Chen 1 Shilin Wang 2 Shenghong Li 1 Jianhua Li 1 1 Department of Electrical Engineering, Shanghai Jiaotong University 2 School of Information Security, Shanghai Jiaotong University

2. 2/18 Outline Markov Transition Probability  Second order statistics and Feature Extraction  Dimension and correlation between variables New Form of the feature  Two elements and three elements Experiment Result Conclusion

3. 3/18 Context Inspired by applying Markov Transition Probability Matrix to solve Image Tampering Detection as a two-class classification (proposed by Shi et al 07) Current feature extraction method  Every element from 2D matrix (huge dimension)  Boosting selection or PCA for dimension reduction, and the low dimensional features do not have corresponding physical meaning Goal: dimension reduction by decomposing adjacent elements to be statistically uncorrelated

4. 4/18 Second Order Statistical Modeling of Image Image transformed with 8x8 BDCT Horizontal difference array Modeled with horizontal transition probability Can be applied to four directions

5. 5/18 Feature Extraction of Transition Probability Matrix Thresholding is applied to difference array (with threshold of T) The transition probability matrix is used as the feature Dimension of the feature is (2T+1) 2 If we consider four directional transition, the dimension needs to be multiplied by 4.

6. 6/18 Example: Transition Probability Matrix

7. 7/18 Problem of Current Presentation of the Feature Dimension of the feature is square proportional to the threshold

8. 8/18 Correlation Between Adjacent Elements in Difference Array Assume adjacent BDCT coefficients are uncorrelated, i.e.,

9. 9/18 Correlation Calculated on Dataset Figure. Correlation between adjacent elements on difference array of block DCT coefficients: (1) k=1; (2) k=2

10. 10/18 PCA Transform of Two-component Random Parameters Correlation Matrix Eigenvectors Uncorrelated new random variables Eigenvalues

11. 11/18 Decomposition of Second Order Statistics into Marginal Ones Marginal histograms are output of two linear filters

12. 12/18 Feature Dimension Linearly Proportional to Threshold

13. 13/18 The Approach Can be Generalized to Three Elements Correlation Matrix Eigenvectors Eigenvalues Decomposed variables

14. 14/18 Dataset and Classifier Columbia Splicing Detection Evaluation Dataset 921 authentic, 910 spliced 2/3 Training, 1/3 Test LibSVM, Gaussian RBF kernel

15. 15/18 Single Feature Performance Type of Joint Statistics FeatureDimensionAccuracy 2 elements 1 st order Markov Transition Probability 8187.09 (1.39) Our new form (Sec. 3.1)4687.97 (1.45) 3 elements 2 nd order Markov Transition Probability 72985.84 (0.92) Our new form (Sec. 3.2)7785.54 (1.34)

16. 16/18 Combined Features Performance FeatureTDimensionAccuracy Moment+Transition Probability Matrix 326689.86 (1.02) Moment+New Form 322089.62 (0.91) 423689.78 (1.03) 525289.78 (1.09)

17. 17/18 Computation Complexity Comparison Feature TypeComputing Time (seconds) Transition Probability Matrix0.0516 (0.0054) Marginal Distribution of two new variables 0.0502 (0.0005) On Core 2 Duo 1.6G, 3G Ram

18. 18/18 Conclusion Our new form has lower feature dimension, faster computation, and almost as good performance Dimension Reduction is more obvious in higher order, but further research is needed to improve discrimination performance