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New Feature Presentation of Transition Probability Matrix for Image Tampering Detection

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. Outline.

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New Feature Presentation of Transition Probability Matrix for Image Tampering Detection

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  1. New Feature Presentation of Transition Probability Matrix for Image Tampering Detection Luyi Chen1 Shilin Wang2 Shenghong Li1 Jianhua Li1 1Department of Electrical Engineering, Shanghai Jiaotong University 2School of Information Security, Shanghai Jiaotong University

  2. 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. 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. 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. 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. Feature Extraction of Transition Probability Matrix

  6. Example: Transition Probability Matrix

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

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

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

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

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

  12. Feature Dimension Linearly Proportional to Threshold

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

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

  15. Single Feature Performance

  16. Combined Features Performance

  17. Computation Complexity Comparison On Core 2 Duo 1.6G, 3G Ram

  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

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