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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