Image Authentication Under Geometric Attacks Via Structure Matching
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Transcript of Image Authentication Under Geometric Attacks Via Structure Matching
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Image Authentication Under Geometric Image Authentication Under Geometric Attacks Via Structure MatchingAttacks Via Structure Matching
Vishal Monga, Divyanshu Vats and Vishal Monga, Divyanshu Vats and Brian L. EvansBrian L. Evans
http://signal.ece.utexas.edu
Embedded Signal Processing LaboratoryThe University of Texas at AustinAustin, TX 78712-1084 USA{vishal, vats, bevans}@ece.utexas.edu
2005 IEEE Int. Conference on Multimedia and Expo
July 6th , 2005
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The Problem of Robust Image AuthenticationThe Problem of Robust Image AuthenticationIntroduction
• 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 AttacksGeometric Distortions or Attacks
• Motivation to study geometric attacks– Vulnerability of classical watermarking/signature schemes– Loss of synchronization in watermarking
Original Shearing Random bending
Global Local• Classification of geometric distortions
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Related WorkRelated 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]
SchemeLocal distortion
robustnessGlobal distortion
robustnessRemark
Periodic insertion no yes Leak informationTemplate insertion no yes easily removedInvariant domain
mark embedding no yesFragile under many signal processing
modificationsTessellations yes yes Too much pressure
on the feature detector
Related Work
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Proposed Authentication SchemeProposed Authentication Scheme
• System components
Visually significant feature extractorT: model of geometric distortionD(.,.) : robust distance measure
Proposed Framework
• Natural constraints– 0 < ε < δ
Received Image
Feature Extraction
T(.)
Compute d = D(M, T(N))
d = dmin?
dmin < ε ? dmin > δ ?
Reference Feature Points
Credible Tampered
Yes Yes
No No Human intervention
needed
Yes
No
Update T
M
N
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Hypercomplex or End-Stopped CellsHypercomplex 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
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Proposed Feature Detection MethodProposed 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
),,( max ),,( ''
),(
*
),(''
yxWyxW iNyx
iyx
TyxWi ),,( max *
Feature Extraction
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Distance Metric for Feature Set ComparisonDistance 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
)),(),,(max(),( MNNMNM hhH
||||minmax),( nmhnm
NM
NM
H.D. = small
Robust Distance Metric
• 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?Is Hausdorff Distance that Robust?
One outlier causes the distance to be large ||||minmax),( nmh
nm
NMNM
This is undesirable......
M N
h(N, M)
Distance Metric for feature comparison
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Solution: Define a Modified DistanceSolution: Define a Modified Distance
• One possibility
m ng nmhi ||||min1),( then ,1 if i NM
NMM
m n
nmh ||||minM1),(mod N
NM
i
inig nmh ||||min),(N
NM
• Generalize as follows
),(),(then ||||maxargfor ,1 if j NMNM hhnmm giij
Distance Metric for feature comparison
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Modeling the Geometric DistortionModeling the Geometric Distortion• Affine transformation defined as follows
x = (x1, x2) , y = (y1, y2), R – 2 x 2 matrix, t – 2 x 1 vector
tR xxTy )(
11.001
R
00
t
996.0087.0087.0996.0
R
00
t
Geometric Distortion Modeling
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Authentication ProcedureAuthentication 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
),(minarg* NTMTT
gH
Authentication
),( *min NTM gHd
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Results
Results: Feature ExtractionResults: Feature Extraction
00
8984.04287.04258.09141.0
t
R
10
9961.0009961.0
t
R
Original image
JPEG with Quality Factor of 10
Rotation by 25 degrees
Stirmark random bending
00
0000.1009224.0
t
R
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Quantitative ResultsQuantitative Results
Attack Lena Bridge PeppersJPEG, 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
Results
2.0),(
15.0),(*
*
NTM
NTM
g
g
H
H If N is a transformed version of M
otherwise
• Feature set comparison
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Randomized Feature ExtractionRandomized 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
Security Via Randomization
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• Future work– Extensions to watermarking– More secure feature extraction– Faster transformation matching for applications to
scalable image search problems
ConclusionConclusion
• 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
Questions and Comments!Questions and Comments!
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End-Stopped Wavelet BasisEnd-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
))(( )(22 ||
21||
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. xkxk oox
eee j
Mx – (x,y) 2-D spatial co-ordinates
ko – (k0, k1) wave-vector of the mother wavelet
Orientation control –0
11tankk
Back
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Computing Wavelet TransformComputing 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
))x;(()( x)( ME oFDoG
,, )),,((( Ziyx ki
E
)),,((* ),(),,( 111111 dydxyyxxyxIyxW iEi
Feature Extraction
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Search Strategy: ExampleSearch Strategy: Example
(-12,15) , (11,-10), (15,14)(15,12) , (-10,-11), (14,-14)
3:050500:3
1:050
502:3
3:250
502:3
1:050500:1
3:250500:1
050501
050
500
150
500
150501
01
10transformation
space
Example
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Solution: Data set normalizationSolution: 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
)()(
AAAAnorm
normalize
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Relation Based Scheme : DCT coefficientsRelation Based Scheme : DCT coefficientsDigital Signature Techniques
• 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
00 qpqp FFFF
pF
qF Back
1
0
1
0
2121 )12(
2cos)12(
2cos),(4),(
N
i
N
j
jNki
NkjiIkkB
8 x 8 block
p q N x N image
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Conclusion & Future WorkConclusion & Future WorkConclusion
• 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 BasisEnd-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
))(( )(22 ||
21||
21
. xkxk oox
eee j
Mx – (x,y) 2-D spatial co-ordinates
ko – (k0, k1) wave-vector of the mother wavelet
Orientation control –0
11tankk
Back