1. 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
Embedded Signal Processing Laboratory The University of Texas at Austin Austin, TX USA
{vishal, vats,

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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......

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

11. 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

12. 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

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

14. 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

15. 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

16. 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

17. Questions and Comments!

18. 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

19. 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

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

21. 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

22. 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

23. 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?

24. 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