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A DSmT Based System for Writer-Independent Handwritten Signature Verification
ICIF 2016
&
Nassim ABBAS1
Youcef CHIBANI1
Bilal HADJADJI1
Zayen AZZOUZ OMAR1
, ,,
Florentin SMARANDACHE2
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.
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
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
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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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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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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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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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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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.
14
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
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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
18
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.
32
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