Vector Error Diffusion

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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_at_ece.utexas.
edu
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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

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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

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Related Work
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 no yes easily removed
Invariant domain mark embedding no yes Fragile under many signal processing modifications
Tessellations yes yes Too much pressure on the feature detector
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Proposed Authentication Scheme
Proposed Framework
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 lt e lt d

dmin gt d ?
dmin lt e ?
No
No
Human intervention needed
Yes
Yes
Credible
Tampered
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Hypercomplex or End-Stopped Cells
Feature Extraction

• 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
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Feature Extraction
Proposed Feature Detection Method

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

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Distance Metric for Feature Set Comparison
Robust Distance Metric

• 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

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

• One possibility

• Generalize as follows

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Modeling the Geometric Distortion
Geometric Distortion Modeling

• Affine transformation defined as follows
• x (x1, x2) , y (y1, y2), R 2 x 2 matrix, t
  2 x 1 vector

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Authentication Procedure
Authentication

• Determine T such that
• Let
• dmin lt e ? credible
• dmin gt d ? tampered
• Else human intervention needed
• Search strategy based on structure matching
  Rucklidge 1995
• Based on a divide and conquer rule

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

• 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

• Future work
• Extensions to watermarking
• More secure feature extraction
• Faster transformation matching for applications
  to scalable image search problems

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Questions and Comments!
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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
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Feature Extraction
Computing Wavelet Transform

• Generalize end-stopped wavelet
• Employ wavelet family
• Scale parameter 2, i scale of the wavelet
  
• Discretize orientation range 0, p into M
  intervals i.e.
• ?k (k p/M ), k 0, 1, M - 1
• End-stopped wavelet transform

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

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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