Vishal Monga, Divyanshu Vats and Brian L. Evans 2005 IEEE Int. Conference on Multimedia and Expo Image Authentication Under Geometric Attacks Via Structure Matching Vishal Monga, Divyanshu Vats and Brian L. Evans July 6th , 2005 http://signal.ece.utexas.edu Embedded Signal Processing Laboratory The University of Texas at Austin Austin, TX 78712-1084 USA {vishal, vats, bevans}@ece.utexas.edu

The Problem of Robust Image Authentication Introduction The Problem of Robust Image Authentication Given an image Make a binary decision on the authenticity of content Content : defined (rather loosely) as the information conveyed by the image, e.g. one-bit change or small degradation in quality is NOT a content change Robust authentication system: required to tolerate incidental modifications yet be sensitive to content changes Two classes of media verification methods Watermarking: Look for pre-embedded information to determine authenticity of content Digital Signatures: feature extraction; a significant change in the signature (image features) indicates a content change

Geometric Distortions or Attacks Introduction Geometric Distortions or Attacks Motivation to study geometric attacks Vulnerability of classical watermarking/signature schemes Loss of synchronization in watermarking Classification of geometric distortions Original Shearing Random bending Global Local

Related Work Geometric distortion resistant watermarking Periodic insertion of the mark [Kalker et. al, 1999 ] [Kutter et. al, 1998 ] Template matching [Pun et. al, 1999 ] Geometrically invariant domains [Lin et. al, 2001], [Pun et. al, 2001] Feature point based tessellations [Bas et. al, 2002] Scheme Local distortion robustness Global distortion robustness Remark Periodic insertion no yes Leak information Template insertion easily removed Invariant domain mark embedding Fragile under many signal processing modifications Tessellations Too much pressure on the feature detector

Proposed Authentication Scheme Proposed Framework Proposed Authentication Scheme Received Image System components Visually significant feature extractor T: model of geometric distortion D(.,.) : robust distance measure Feature Extraction N Update T T(.) Reference Feature Points M Compute d = D(M, T(N)) d = dmin? No Yes Natural constraints 0 < ε < δ dmin < ε ? dmin > δ ? No No Human intervention needed Yes Yes Credible Tampered

Hypercomplex or End-Stopped Cells Feature Extraction Hypercomplex or End-Stopped Cells Cells in visual cortex that help in object recognition Respond strongly to line end-points, corners and points of high curvature [Hubel et al.,1965; Dobbins, 1989] End-stopped wavelet basis [Vandergheynst et al., 2000] Apply First Derivative of Gaussian (FDoG) operator to detect end-points of structures identified by Morlet wavelet Synthetic L-shaped image Morlet wavelet response End-stopped wavelet response

Proposed Feature Detection Method Feature Extraction Proposed Feature Detection Method Compute wavelet transform of image I at suitably chosen scale i for several different orientations Significant feature selection: Locations (x,y) in the image identified as candidate feature points satisfy Avoid trivial (and fragile) features: Qualify location as final feature point if

Distance Metric for Feature Set Comparison Robust Distance Metric Distance Metric for Feature Set Comparison Hausdorff distance between point sets M and N M = {m1,…, mp} and N = {n1,…, nq} where h(M, N) is the directed Hausdorff distance Why Hausdorff ? Robust to small perturbations in feature points Accounts for feature detector failure or occlusion H.D. = small

Is Hausdorff Distance that Robust? Distance Metric for feature comparison Is Hausdorff Distance that Robust? h(N, M) M N One outlier causes the distance to be large This is undesirable......

Solution: Define a Modified Distance Distance Metric for feature comparison Solution: Define a Modified Distance One possibility Generalize as follows

Modeling the Geometric Distortion Geometric Distortion Modeling Modeling the Geometric Distortion Affine transformation defined as follows x = (x1, x2) , y = (y1, y2), R – 2 x 2 matrix, t – 2 x 1 vector

Authentication Procedure Determine T* such that Let dmin < ε  credible dmin > δ  tampered Else human intervention needed Search strategy based on structure matching [Rucklidge 1995] Based on a “divide and conquer” rule Search Strategy

Results: Feature Extraction Original image JPEG with Quality Factor of 10 Rotation by 25 degrees Stirmark random bending

Quantitative Results Feature set comparison If N is a transformed version of M otherwise Attack Lena Bridge Peppers JPEG, QF = 10 0.0857 0.1112 0.105 Scaling by 50% 0.0000 0.0020 0.1110 Rotation by 250 0.0030 0.1277 0.0078 Random Bending 0.0345 0.0244 0.0866 Print and Scan 0.0905 0.1244 0.1901 Cropping by 10% 0.0833 0.0025 0.1117 Cropping by 25% 0.2414 0.2207 0.2766 Generalized Hausdorff distance between features of original and attacked (distorted) images Attacked images generated by Stirmark benchmark software

This yields a pseudo-random signal representation Security Via Randomization Randomized Feature Extraction Randomization Partition the image into N random (overlapping) regions Random tiling varies significantly based on the secret key K, which is used as a seed to a (pseudo)-random number generator This yields a pseudo-random signal representation

Conclusion Highlights Future work Robust feature detector based on visually significant end-stopped wavelets Hausdorff distance: accounts for feature detector failure or occlusion; generalized the distance to enhance robustness Randomized feature extraction for security against intentional attacks Future work Extensions to watermarking More secure feature extraction Faster transformation matching for applications to scalable image search problems

Questions and Comments!

End-Stopped Wavelet Basis Morlet wavelets [Antoine et al., 1996] To detect linear (or curvilinear) structures having a specific orientation End-stopped wavelet [Vandergheynst et al., 2000] Apply First Derivative of Gaussian (FDoG) operator to detect end-points of structures identified by Morlet wavelet x – (x,y) 2-D spatial co-ordinates ko – (k0, k1) wave-vector of the mother wavelet Orientation control – Back

Computing Wavelet Transform Feature Extraction Computing Wavelet Transform Generalize end-stopped wavelet Employ wavelet family Scale parameter = 2, i – scale of the wavelet Discretize orientation range [0, π] into M intervals i.e. θk = (k π/M ), k = 0, 1, … M - 1 End-stopped wavelet transform

Search Strategy: Example (-12,15) , (11,-10), (15,14) (15,12) , (-10,-11), (14,-14) transformation space

Solution: Data set normalization Normalize data points in the following way Why do normalization? Preserves geometry of the points Brings feature points to a common reference normalize

Relation Based Scheme : DCT coefficients Digital Signature Techniques Relation Based Scheme : DCT coefficients Discrete Cosine Transform (DCT) Typically employed on 8 x 8 blocks Digital Signature by Lin Fp, Fq, DCT coefficients at the same positions in two different 8 x 8 blocks , DCT coefficients in the compressed image 8 x 8 block p q N x N image Back

Conclusion & Future Work Decouple image hashing into Feature extraction and data clustering Feature point based hashing framework Iterative feature detector that preserves significant image geometry, features invariant under several attacks Trade-offs facilitated between hash algorithm goals Clustering of image features [Monga, Banerjee & Evans, 2004] Randomized clustering for secure image hashing Future Work Hashing under severe geometric attacks Provably secure image hashing?

End-Stopped Wavelet Basis Morlet wavelets [Antoine et al., 1996] To detect linear (or curvilinear) structures having a specific orientation End-stopped wavelet [Vandergheynst et al., 2000] Apply First Derivative of Gaussian (FDoG) operator to detect end-points of structures identified by Morlet wavelet x – (x,y) 2-D spatial co-ordinates ko – (k0, k1) wave-vector of the mother wavelet Orientation control – Back