Transportation-theoretic image counterforensics to First Significant Digit histogram forensics

Transcription

1 Transportation-theoretic image counterforensics to First Significant Digit histogram forensics Cecilia Pasquini Giulia Boato University of Trento, DISI, Multimedia Signal Processing and Understanding Lab Pedro Comesaña-Alfaro Fernando Pérez-González University of Vigo, Signal Processing in Communications Group

2 Motivation Multimedia forensic scenario Manipulation Forensic analysis Tampered Adversarial environment Manipulation Counterforensics action Forensic analysis Authentic

3 Adversarial signal processing Study of general theoretic solutions to problems involving an attacker and a defender [Barni and Pérez-González, 2013] For the case of multimedia forensics, tradeoff between the fidelity of the statistics recovered and the distortion introduced in the object [Kirchner and Boehme, 2013] Analysis of the optimal strategy for one or both players under specific hypothesis [Barni and Tondi, 2013] [Barni et al., 2012] [Comesaña-Alfaro and Pérez-González, 2013]

4 First Significant Digits in JPEG image forensics... Number of compressions n Detectors discriminating single, double or multiple compressed images using FSD probabilities as features [Li et al., 2008] [Milani et al., 2012] Attacks modifying the distribution of FSDs in order to mislead the forensic analysis [Milani et al., 2013] [Pasquini and Boato, 2013] GENERAL PROBLEM: n compressions FSD histogram m compressions FSD histogram Is there an optimal strategy for a generic detector?

5 Outline Transportation-theoretic formulation of the problem as a two-step optimization process Design of a novel technique providing an approximated solution of the optimization problem for a class of distortion measures (including the MSE) Analysis of the distortion introduced on a dataset of images and comparison with state-of-the-art method

6 Basic definitions Pixel DCT FSD FSD histogram Bijective orthonormal transformation EX: distance between the DCT vectors and Fixed, we define and distance between the FSD vectors and PROBLEM: given a starting DCT vector and a target histogram, modify such that its FSD histogram is equal to minimizing the distortion:

7 Transportation-theoretic formulation The problem can be formulated as a two-step optimization process: Computationally unfeasible! DCT VECTORS FSD VECTORS FSD HISTOGRAMS

8 Approximated optimization technique I Assumption: where is a symmetric convex function depending on the difference between its input arguments (it holds for any metrics induced by a norm, like the MSE). Given the subset to which we can move the initial values, we define so that each is minimized. EX: integer numbers, NOVEL PROCEDURE: a new DCT vector is determined starting from a given input vector and a target histogram for every component of in descending order of magnitude, a new FSD is chosen by means of the map

9 Approximated optimization technique II set of digits with histogram is sorted in descending order ITERATIVE PROCEDURE For EX: Minimization of end Definition of Extraction from the set of the digit obtained After a reordering operation, is obtained as approximated solution instead of the exact one

10 Experimental setting Three different binary hypothesis testing problems: H 0 : 0 compressions H 1 : 1 compression H 0 : 0 compressions H 1 : 2 compressions H 0 : 1 compression H 1 : 2 compressions where different quality factors have been considered. UCID dataset: 600 images for creating the reference target histograms (by means of an averaging operation), 738 images for the testing phase; Comparison with a state-of-the-art method based on waterfilling techniques in terms of mean MSE (converted to PSNR) over the testing set [Milani et al., 2013]

11 Experimental results QF TT WF QF TT WF QFt QF TT WF TT WF TT WF TT WF TT WF

12 Visual comparison PSNR=48.04 db PSNR=40.29 db Starting FSD histograms: 2 compressions (75, 90). Target FSD histograms: 1 compression (70).

13 Final discussions and future work Extension to other distortion measures based on visual perception, like WPSNR or SSIM Joint analysis with the problem of DCT histogram modification Experiments on a wider datasets composed by images of different source and size Dealing with multiple compression steps

14 Thank you!

15 References [Pasquini and Boato, 2014] [Barni and Pérez-Gonzalez, 2013] [Kirchner and Boehme, 2013] [Barni and Tondi, 2013] [Barni et al., 2012] [Comesaña and Pérez-González, 2013] [Li et al., 2008] [Milani et al., 2012] [Milani et al., 2013] [Pasquini and Boato, 2013] C. Pasquini, P. Comesaña-Alfaro, F. Pérez-González, Transportation-theoretic image counterforensics to first significant digit histogram forensics, accepted to IEEE ICASSP, M. Barni, F. Pérez-González, Coping with the enemy: advances in adversary-aware signal processing, in Proceedings of IEEE ICASSP, M. Kirchner, R. Boehme, Counter-forensics: attacking image forensics, in H.T. Sencar and N.D. Memon (eds.): Digital Image Forensics, M. Barni, B. Tondi, The source identification game: an information-theoretic perspective, IEEE Transactions on Information Forensics and Security, vol. 8, no. 3, M. Barni, M. Fontani, B. Tondi, A universal technique to hide traces of histogrambased image manipulations, in Proceedings of ACM MM&Sec, P. Comesaña-Alfaro, F. Pérez-González, Optimal counterforensics to histogram-based forensics, in Proceedings of IEEE ICASSP, Li, Y.Q. Shi, J. Huang, Detecting doubly compressed JPEG images by using mode based first digit features, in Proceedings of IEEE MMSP, S. Milani, M. Tagliasacchi, S. Tubaro, Discriminating multiple JPEG compression using first digit features, in Proceedings of IEEE ICASSP, S. Milani, M. Tagliasacchi, S. Tubaro, Antiforensics attacks to Benford's law for the detection of double compressed images, in Proceedings of IEEE ICASSP, C. Pasquini, G. Boato, JPEG compression anti-forensics based on first significant digits distribution, in Proceedings of IEEE MMSP, 2013.