Image Authentication Under Geometric Attacks Via Structure Matching
This paper presents a robust image authentication framework that addresses the challenge of verifying image authenticity in the presence of geometric attacks. It highlights the limitations of conventional watermarking and digital signature methods when faced with distortions. The proposed approach employs an effective feature extraction process focused on visually significant points, utilizing end-stopped wavelets and a modified Hausdorff distance metric for accurate comparison. The framework shows resilience to incidental modifications while remaining sensitive to genuine content changes, paving the way for enhanced image verification techniques.
Image Authentication Under Geometric Attacks Via Structure Matching
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http://signal.ece.utexas.edu 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 Embedded Signal Processing LaboratoryThe University of Texas at AustinAustin, TX 78712-1084 USA {vishal, vats, bevans}@ece.utexas.edu
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 authenticationsystem: 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
Global Local Original Shearing Random bending 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
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[Baset. al, 2002] Related Work Related Work
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 > δ ? dmin< ε? No No Human intervention needed Yes Yes Credible Tampered
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
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
H.D. = small 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
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......
Distance Metric for feature comparison Solution: Define a Modified Distance • One possibility • Generalize as follows
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 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
Results Results: Feature Extraction Original image JPEG with Quality Factor of 10 Rotation by 25 degrees Stirmark random bending
Results Quantitative Results • Feature set comparison If N isa transformed version of M otherwise Generalized Hausdorff distance between features of original and attacked (distorted) images Attacked images generated by Stirmark benchmark software
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 • Future work • Extensions to watermarking • More secure feature extraction • Faster transformation matching for applications to scalable image search problems • Highlights • 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
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
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
Example 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
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 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
