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A DSmT Based System for Writer-Independent Handwritten Signature Verification ICIF 2016 & Nassim ABBAS 1 [email protected] Youcef CHIBANI 1 [email protected] Bilal HADJADJI 1 [email protected] Zayen AZZOUZ OMAR 1 [email protected] , , , Florentin SMARANDACHE 2 [email protected] 1 Communicating and Intelligent System Engineering Laboratory Faculty of Electronic and Computer Science University of Sciences and Technology Houari BoumedieneAlgiers, Algeria 2 Department of Mathematics University of New Mexico Gallup, NM 87301, U.S.A.

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Page 1: A DSmT Based System for Writer-Independent Handwritten ...fs.unm.edu/ScPr/ADSmTBasedSystem.pdf · A DSmT Based System for Writer-Independent Handwritten Signature Verification ICIF

A DSmT Based System for Writer-Independent Handwritten Signature Verification

ICIF 2016

&

Nassim ABBAS1

[email protected]

Youcef CHIBANI1

[email protected]

Bilal HADJADJI1

[email protected]

Zayen AZZOUZ OMAR1

[email protected]

, ,,

Florentin SMARANDACHE2

[email protected]

1Communicating and Intelligent System Engineering Laboratory

Faculty of Electronic and Computer Science

University of Sciences and Technology “Houari Boumediene”

Algiers, Algeria

2Department of Mathematics

University of New Mexico

Gallup, NM 87301, U.S.A.

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Outline

Introduction

One Class Support Vector Machines Classifier

Belief Function Theories

Proposed Combination Scheme for Handwritten Signature Verification

Conclusion and future works

2ICIF 2016 F. SMARANDACHE

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1. Introduction (1)

3

Figure 1. Structure of the recognition system

Data Acquisition Preprocessing Feature Generation Classification DecisionInputpattern

Statement of the problem

Solution

Parallel combination scheme

Figure 2. Parallel combination of classifiers

Feature Generation1

Classifier-1

Feature Generationp

Classifier-p

PreprocessingInput

pattern

Finaldecision

Parallel

Combination

Module

1n

Output-1

Output-p

ICIF 2016 F. SMARANDACHE

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1. Introduction (2)

4

Combination levels

Class level combination

Rank level combination

Measure level combination

Distance

Posterior probability

Confidence value

Match score

Belief function

Credibility

Possibility

Fuzzy measure

Uncertainty: is an unrealistic measure induced by the outputs of classifier, which leads

to interpret the response of the classifier as the result of a random phenomenon

Imprecision: is measure representing the uncertainty linked to incomplete knowledge

Belief functions take into considerations two notions:

ICIF 2016 F. SMARANDACHE

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5

1. Introduction (3)

Three theories dealing with uncertainty and imprecise information have beenintroduced

Figure 3. Belief Function Theories-Based Parallel Combination of Classifiers

Output(Classifier-c1)

Estimationof Masses

Estimationof Masses

Estimationof Masses

CombinationRule

DecisionMeasure

DecisionRule

Output(Classifier-c2)

Output(Classifier-cp)

1

2

n

Estimation Combination Decision

Probability theory (PT): uncertainty

Evidence theory (Dempster-Shafer Theory): uncertainty + imprecision

Plausible and paradoxical reasoning theory (Dezert-Smarandache Theory): uncertainty

+ imprecision

ICIF 2016 F. SMARANDACHE

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6

2. One Class Support Vector Machines Classifier

One Class Support Vector Machines (OC-SVM)

Support vector

OutliersTraining data

Original space Feature space

Projection

Support vector

Hyper sphere

),( ixxK

w

0)( xf

0)( xf0)( xf

Sv

jjj xxKxf

1

),()(

Decision function:j

Sv

: Number of Support Vectors: Lagrangian multipliers

: Distance of the hyperplane from the origin

Pattern x is accepted when 0)( xf Otherwise it is rejected

ICIF 2016 F. SMARANDACHE

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7

3. Belief Function Theories: Probability Theory (1)

Mathematical Formalism

nG ..,, 21

Discernment space: is defined as a finite set of exhaustive and mutually exclusive

hypotheses

ii m

Pm

1,0:

0,1

0

ii mm

m

i

n

i

ii

iii

PxP

PxPxP

1

.

.

Bayesian rule:

Basic probability assignment (bpa):

ICIF 2016 F. SMARANDACHE

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8

3. Belief Function Theories: Probability Theory (2)

Basic Sum combination rule

otherwise.0

,if1

1j

p

iji

sumc

AmpAmAm

: Simple class belonging todiscernment space

A

p : Number of information sources

.im : bpa issued from the i-th source

Advantage: Simple

Limitation: No managing conflict between two sources

ICIF 2016 F. SMARANDACHE

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3. Belief Function Theories: Dempster-Shafer Theory (1)

Evidence Theory

Dempster-Shafer theory (DST) allows to model both ignorance andimprecision, and to consider compound hypotheses such as theunion of classes.

It is generally recognized as a convenient and flexible alternative tothe bayesian theory.

Mathematical Formalism

n ..,, 21Discernment space:

,,,,,,,,,2 121312121 nnG Power-set:

ii AmA

m

1,02:

0,1

0

2

i

Ai AmAm

m

i

Basic belief assignment (bba):

ICIF 2016 F. SMARANDACHE

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3. Belief Function Theories: Dempster-Shafer Theory (2)

Estimation of belief mass functions

It's not directly explicit in term of modelling of the problem underconsideration.

It's specific to each application area according the nature of the data.

Handwriting recognition.B

aye

sian

Mo

de

l

Tran

sfe

r M

od

el

1

2

n

1xP

2xP

nxP

1Axm

2Axm

xm

ICIF 2016 F. SMARANDACHE

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11

3. Belief Function Theories: Dempster-Shafer Theory (3)

Dissonant model of Appriou

,

.1

..

ij

iji

ijxPR

xPRm

,.1 ij

iij

xPRm

,1 ijm

ini

j xPR supmax,0,1

ixP

jR

i

: Conditional probability of an object given the class . xi

: Normalization factor

: Coarsening factor.

Axiom (1): Consistency with the Bayesian approach

Axiom (2): Separability of the evaluation of the hypotheses

Axiom (3): Consistency with the probabilistic association of sources

ICIF 2016 F. SMARANDACHE

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3. Belief Function Theories: Dempster-Shafer Theory (4)

Dempster’s orthogonal sum rule

2,

21

212,,, 1

ABmAm

ABBBBBB

p

kkk

p

p

2,1

AK

AmAmAm

c

DSc

p

p

BBBBBB

p

kkkc BmmK

21

212,,, 1

: Focal element of the power-set . 2A

: Combined mass of Dempster’s

conjunctive rule.

Am

cK : Conflict measure between the different

masses issued from information

sources , respectively.

.km

kS

Advantage: Taking into account the imprecise and uncertain information

Limitation: No managing high conflict between two sources of information

ICIF 2016 F. SMARANDACHE

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3. Belief Function Theories: Dempster-Shafer Theory (5)

Decision rules

Selecting the more realistic hypothesis.

Combined mass function : uncertainty

[Belief function, Plausibility function] : imprecision

ICIF 2016 F. SMARANDACHE

Rules used for decision-making:

Maximum of belief function.

Maximum of plausibility function.

Maximum of Pignistic Probability.

Minimization of mass function with an acceptance threshold.

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3. Belief Function Theories: Dempster-Shafer Theory (6)

Limitations of DST

Foundation of the DST Does not take into account the

paradoxical information

Significant conflict

measure

DST based combination is not

possible

Solution: Dezert-Smarandache Theory (DSmT)

ICIF 2016 F. SMARANDACHE

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3. Belief Function Theories: Dezert-Smarandache Theory (1)

It has been originally developed since 2003 by Jean Dezert andFlorentin Smarandache.

Plausible and Paradoxical Reasoning Theory

It has the advantage of being able to represent explicitly theuncertainty from imprecise knowledge.

It was elaborated for dealing with paradoxical sources of information(i.e. classes, descriptors, classifiers, sensors,…etc).

It is based on a particular framework where the finite discrete frameof discernment is exhaustive but not necessarily exclusive.

ICIF 2016 F. SMARANDACHE

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3. Belief Function Theories: Dezert-Smarandache Theory (2)

Mathematical Formalism

Discernment space:

Hyperpower-set:

Generalized belief assignment (gbba):

n ..,, 21

DG

1. .

2. If , then and .

3. No other elements belong to , except thoseobtained by using rules 1 or 2.

Dn ,,Ø, 1

DBA, DBA DBA

D

Estimation techniques of masses in DST framework Valid in DSmTframework

ii AmA

Dm

1,0:

0,1

0

i

DAi AmAm

m

i

ICIF 2016 F. SMARANDACHE

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Classical DSm combination rule (DSmC)

DSm Hybrid combination rule (DSmH)

Proportional Conflict Redistribution rules (PCR1, …, PCR5, PCR6)

Combination rules

3. Belief Function Theories: Dezert-Smarandache Theory (3)

Decision rules

Minimum of mass function with an acceptance threshold

ICIF 2016 F. SMARANDACHE

otherwiseRejected

,minifAcceptedDecision

21 opttesttest tmm

Note:

: Denotes the optimal value of the acceptance decision thresholdoptt

: Defines the combined mass of the simple class i .testm

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Parallel Combination of Classifiers for Handwritten Signature Verification

Application

Handwritten Signature Verification

(HSV)

Writer-Independent HSV

ICIF 2016 F. SMARANDACHE

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4. Proposed Combination Scheme for Handwritten Signature Verification (1)

Motivation

Fingerprint Face

Iris

Biological

DNA

SmellHand geometry

Writing Keyboarding

SignatureGait

BehavioralPhysiological

ICIF 2016 F. SMARANDACHE

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Motivation

Sign a document to identify himself is a natural gesture.

Handwritten signature is the biometric modality the most acceptedby many peoples.

It is used in many countries as legal or administrative element.

Design of a signature verification system is cheaper and more simplecomparatively to other biometric systems (for instance iris or face).

4. Proposed Combination Scheme for Handwritten Signature Verification (2)

ICIF 2016 F. SMARANDACHE

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Acquisition of the handwritten signature

Difficulties of the offline handwritten signature verification:

High variability intra-writer

Easy to imitate

Quality of the signature (Paper, Pen, Scanner)

Electronic tablet

Dynamic features (Velocity, Pressure, ….)

Scanner

Static features (Image)

Motivation

4. Proposed Combination Scheme for Handwritten Signature Verification (3)

ICIF 2016 F. SMARANDACHE

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Why use a writer-independent HSV approach ?

4. Proposed Combination Scheme for Handwritten Signature Verification: Writer-Independent Handwritten Signature Verification

Off-line HSV problem

Writer-dependent approach

Writer-independent approach

Off-line HSV writer-dependent approach:

Advantage: Providing a high performance verification

Limitation: Need of learning the model each time when a new writer should be

included in the system

Solution: (1) Off-line HSV writer-independent approach, (2) Using only genuine

signatures, (3) through combination scheme of two individual verification systems

ICIF 2016 F. SMARANDACHE

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Verification scheme using an OC-SVM classifier

Learning data

Vectors of (dis) similarity measures

Learning algorithm

Testing data

Vectors of (dis) similarity measures

Decision

OC-SVM classifier

Learning phase Verification phase

Generation of the model

Selection of the optimal threshold

4. Proposed Combination Scheme for Handwritten Signature Verification: Writer-Independent Handwritten Signature Verification

ICIF 2016 F. SMARANDACHE

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Classification based on DSmT

Source 1 Source 2

Combined sources

]1,0[)( ji AmMass function:

Space of discernment:

Such that:

2,1i (Source 1 or 2)

)()()( 21 YmXmAmc GGGYXA

,,

Combined masses:

Combination space:

PT:

DST:

DSmT:

)(

1

1)(

GCard

j

jc Am

2211 , descriptordescriptor

21,G

2121 ,,ø,2 G

212121 ,,,ø, DG

Combination(Conflict management)

4. Proposed Combination Scheme for Handwritten Signature Verification: Writer-Independent Handwritten Signature Verification

)1SVMOC( )2SVMOC(

ICIF 2016 F. SMARANDACHE

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Decision making in both DST and DSmT frameworks

Combinaison of masses (learning and validation)

Compute the optimal decisionthreshold

Decision making

Combinaison of masses (validation phase)

Select outputs of both classifiers (validation phase)

21 ,min

1

ccmass mmt

21 min,minmin

2

learnlearnmass mmt

221

massmass

mass

ttt

opt

otherwiseRejected

,minifAcceptedDecision

21opt

masstesttest tmm

4. Proposed Combination Scheme for Handwritten Signature Verification: Writer-Independent Handwritten Signature Verification

ICIF 2016 F. SMARANDACHE

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Case study: Combining two Off-Line HSV Systems (1)

55 Writers 30 Writers

5 Signatures for learning

1 Writer

25 Writers

24 impostorsignatures

1 Writer

24 genuinesignatures

5 Referencesignatures

14 Signatures for validation

5 Referencesignatures

43 Signatures for testing

24 genuinesignatures

4. Proposed Combination Scheme for Handwritten Signature Verification: Writer-Independent Handwritten Signature Verification

Partitioning of the CEDAR database:

ICIF 2016 F. SMARANDACHE

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Feature generation: Simple features are generated from each off-line signature image, which are:

Discrete cosine transform (DCT) based featuresCurvelet transform (CT) based features

Performance criteria: Three popular errors are consideredFalse Rejection Rate (FRR)False Acceptance Rate (FAR)Average Error Rate (AER)

Sources of information: Two sources are consideredSource 1: DCT based descriptorSource 2: CT based descriptor

4. Proposed Combination Scheme for Handwritten Signature Verification: Writer-Independent Handwritten Signature Verification

Advantage of both transforms :DCT: Two important properties: Decorrelation and energy compactionCT: Analyzing local line or curve singularities

Case study: Combining two Off-Line HSV Systems (2)

ICIF 2016 F. SMARANDACHE

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Table 3. Experimental results of proposed individual systems and classical combination algorithms

Algorithm Optimal

Threshold

Verification Error Rates (%)

FRR FAR AER

OC-SVM classifier 1 (DCT) -0.060712 28.7719 44.0278 37.2868

OC-SVM classifier 2 (CT) -0.419880 9.6491 0.0000 4.2636

Max combination rule -0.060710 17.5439 44.0278 32.3256

Sum combination rule -0.480590 6.8421 44.0278 27.5969

Min combination rule -0.419880 9.6491 0.0000 4.2636

4. Proposed Combination Scheme for Handwritten Signature Verification: Writer-Independent Handwritten Signature Verification

Comparative analysis:

Case study: Combining two Off-Line HSV Systems (3)

ICIF 2016 F. SMARANDACHE

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Conflict managing in DSmT framework:

Signature index

Conflict measure

Kc

Figure 1. Conflict between both OC-SVM classifiers using DCT and CT-based descriptors for testing signatures

4. Proposed Combination Scheme for Handwritten Signature Verification: Writer-Independent Handwritten Signature Verification

Case study: Combining two Off-Line HSV Systems (4)

ICIF 2016 F. SMARANDACHE

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Algorithm Optimal

Threshold

Verification Error Rates (%)

FRR FAR AER

OC-SVM classifier 1 (DCT) -0.060712 28.7719 44.0278 37.2868

OC-SVM classifier 2 (CT) -0.419880 9.6491 0.0000 4.2636

Max combination rule -0.060710 17.5439 44.0278 32.3256

Sum combination rule -0.480590 6.8421 44.0278 27.5969

Min combination rule -0.419880 9.6491 0.0000 4.2636

DS combination rule 0.334200 0.0000 6.3158 2.7907

PCR6 combination rule 0.267100 0.0000 6.1404 2.7132

Table 4. Experimental results of proposed algorithms

4. Proposed Combination Scheme for Handwritten Signature Verification: Writer-Independent Handwritten Signature Verification

Comparative analysis:

Case study: Combining two Off-Line HSV Systems (5)

ICIF 2016 F. SMARANDACHE

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6. Conclusion and futur work

Conclusion

Proposed combination scheme with PCR6 rule yields the best verification accuracy

compared to the statistical match score combination algorithms and DS theory-based

combination algorithm even when the individual writer-independent off-line HSV

systems provide conflicting outputs.

ICIF 2016 F. SMARANDACHE

Futur works

Adapt the use of the evidence supporting measure of similarity (ESMS) criteria to

select complementary sources of information using the same proposed combination

scheme in order to attempt to improve the FRR.

Replace the OC-SVM classifier by the “Histogram Symbolic Representation” (SHR) –

based one class classifier.

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Many thanks for your attention

Questions…

2Department of Mathematics

University of New Mexico

Gallup, NM 87301, U.S.A.

Florentin [email protected]

ICIF 2016 F. SMARANDACHE