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QUT Digital Repository:
http://eprints.qut.edu.au/
Hanmandlu, M. and Kumar, Amioy and Madasu, Vamsi K. and Yarlagadda,
Prasad (2008) Fusion of Hand Based Biometrics using Particle Swarm
Optimization. In Latifi, Shahram, Eds. Proceedings Fifth International Conference
on Information Technology: New Generations, pages pp. 783-788, Las Vegas,
USA.


©
Copyright 2008 IEEE
Personal use of this material is permitted. However, permission to
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from the IEEE.
Fusion of Hand Based Biometrics using Particle Swar
m optimization


M. Hanmandlu
Dept.ofElec.Eng.
I.I.T.Delhi,India
mhmandlu@ee.iitd.ac.in


Amioy Kumar
Dept.ofElec.Eng.
I.I.T.Delhi,India
amioy.iitr@gmail.com


Vamsi K. Madasu
SchoolofEng.Systems
QUT,Australia

v.madasu@qut.edu.au


Prasad Yarlagadda
SchoolofEng.Systems
QUT,Australia
y.prasad@qut.edu.au



Abstract
Multi-modal biometrics has numerous advantages over
uni-
modal biometric systems. Decision level fusion is t
he most
popular fusion strategy in multimodal biometric sys
tems. Recent
research has shown promising performance of hand ba
sed
biometrics, i.e. palmprint and hand geometry over o
ther
biometric modalities. However, the improvement in
performance is constrained by the lack of optimal s
ensor points
and fusion strategy. In this paper, we have impleme
nted a
particle swarm based optimization technique for sel
ecting
optimal parameters through decision level fusion of
two
modalities: palmprint and hand geometry. The experi
mental
evaluation on a database of 100 users confirms the
utility of the
decision level fusion using particle swarm optimiza
tion.

Keywords:
 modalities, Biometrics, palmprint, hand
geometry,PSO,fusion,rules.

1. Introduction
Biometric systems suffer from several problems like

noisy sensor data, non&universality, lack of indivi
duality,
non&availability of invariant representations, etc,
 [1].
These problems are responsible for an increase in e
rror
rates and decrease in system reliability for high s
ecurity
needs. Multimodal biometric systems overcome some o
f
the problems associatedwith unimodal biometricsys
tems
by combining the decisions from different biometric
s
using an effective fusion rule, thus achieving high
er
accuracyandbetterperformance.
The fusioninmultimodalsystemscanbeperformeda
t
fourmajorlevels:sensor,feature,scoreanddeci
sion.The
firsttwolevelsoffusionarepreferabletoconduc
tpriorto
matching,whiletheothertwolevelscantakeplace
during
thefusionaftermatching.Fusionaftermatchingis
splitup
into four categories: dynamic classifier fusion, de
cision
level fusion, rank level fusion and score level fus
ion.
Dynamic classifier selection scheme works upon the
idea
of choosing certain input pattern that is likely to
 give the
most correct decisions [2]. The rank level fusion i
s
achieved by sorting the possible matches given by e
ach
biometricmatcherinadecreasingorderofconfiden
ce[5].
The score level fusion is performed by combining th
e
matching scores of different matchers. It involves
the
matching of scores generated by the features of the

biometrics by differentsensorsandfusionofthese
scores
by sum, product, and weighed sum rules. The feature
s of
individual matcher can be classified into one of th
e two
classes: Genuine (Accept) or imposter (Reject). The
se
classifiers are then used to make decisions. The sy
stem
error rates can be represented in terms of F
AR
 (False
acceptance rate) and F
RR
 (False rejection rate). The
decision level fusion comes into action when indivi
dual
matcher presents its decisions basedonitsinputp
atterns.
Each classifier under the binary hypothesis gives i
ts
decision based on its input pattern. The classifier

decisions are furtherfusedundersome rule like,m
ajority
votingrule[3]orChair&Varshney[4]fusionrule.

Fusion strategies are an important aspect of an
y
multimodal biometric system. These strategies help
us to
choose some optimal rule for the fusion of multimod
al
biometrics. Some of the approaches that employ an
optimal fusion are: Deterministic methods, Probabil
istic
methods, and Evolutionary methods. The deterministi
c
methods involve an application of some traditional
heuristic approaches like, trajectory methods which

modify trajectories for optimization, penalty metho
ds
which imposes penalties for optimal decisions, etc.
 The
probabilisticmethodsrelyuponprobabilisticjudgm
entsto
yieldan optimaldecision[10].Incomparisontodi
fferent
adaptive stochastic search algorithms, Evolutionary

Computations (EC) techniques [11] generate a set of

relevant solutions, called
population
 and then find an
optimal solution through searching and updating the
 past
history ofthe particles(i.e.memories)ofthepo
pulation.
Some of the examples of such approaches are: Geneti
c
Algorithm(GA),SwarmIntelligence(SI)[8],AntCo
lony
Optimization(ACO),BacteriaForaging(BF),etc.

2. Background Work
There has been a lot of interest in multimodal
biometric systems. Frischholz et al. [7] proposed a

multimodal system called
BioID
 based on the fusion of
face,voiceandlipmovement.Theychosedifferent
fusion
strategies in order to vary the security levels. Ho
wever,
their algorithm is restricted to only a few fusion
rules,
typically the AND and OR rules. Their system has fi
xed
thresholdvaluesandhenceyieldsthefixederrorr
atesand
reduces one of the error rates successfully but not
 both.
Jainetal.[17]proposed theintegrationofmoret
hanone
matcher for the fingerprint verification system and

developed a decision level fusion for fingerprints
by
combiningfourdifferentmatchingalgorithms.
Fifth International Conference on Information Technology: New Generations
978-0-7695-3099-4/08 $25.00 © 2008 IEEE
DOI 10.1109/ITNG.2008.252
784
Fifth International Conference on Information Technology: New Generations
978-0-7695-3099-4/08 $25.00 © 2008 IEEE
DOI 10.1109/ITNG.2008.252
784
Fifth International Conference on Information Technology: New Generations
978-0-7695-3099-4/08 $25.00 © 2008 IEEE
DOI 10.1109/ITNG.2008.252
783
Fifth International Conference on Information Technology: New Generations
978-0-7695-3099-4/08 $25.00 © 2008 IEEE
DOI 10.1109/ITNG.2008.252
783
Fifth International Conference on Information Technology: New Generations
978-0-7695-3099-4/08 $25.00 © 2008 IEEE
DOI 10.1109/ITNG.2008.252
783
Despite proven efficiency of multimodal fusion, on
ly
fewworkshavebeenreportedtilldate.Moreoverat
tempts
on decision level fusion using optimization techniq
ues
basedonsocialbehaviorofindividualsarecompara
tively
new. Kalyan et al. [9] developed an adaptive multim
odal
biometric management algorithm for multisensory fus
ion
by combining biometric modalities. This algorithm c
an
adaptively selectthe optimalBayesianfusionrule
aswell
as the individual sensor operating points. The algo
rithm
not only reduces both error rates but also yields a
 broad
range of fusion rules to combine the biometric. How
ever
for the experimental evaluation, they used simulate
d data
and generated the Gaussian distribution using mean
and
standard deviation of the genuine and imposter scor
es.
Thepresentworkisinfluencedbythisapproach.

3. The proposed modalities
The biometric modalities considered in the paper ar
e
palmprint and hand geometry. One of the key objecti
ves
ofthisworkistoevaluatetheusageofpalmprint
andhand
geometry for the decision level multimodal fusion.
Despite the recent popularity of palmprint based sy
stems
[19], therehave been no attemptson PSObaseddeci
sion
levelfusion.Wethereforeinvestigatethepossible
usesof
palmprintandhandgeometryfortheadaptivemultim
odal
biometricmanagementalgorithm(AMBMA)describedin

[9]. Eachbiometricinvolvesfeatureextraction,ma
tching,
and decision making. The PSO algorithmfusesthesi
ngle
modalitydecisions.

3.1. Palmprint
The palmprint features employed in this work are
extracted using Discrete Cosine Transform (DCT). Th
e
palmprintimagedatabasefrom100users,with10sa
mples
per user, is used to show the performance of the fu
sion.
The discrete cosine transform based 144 features fr
om
eachofthepalmprints,using24
×
24pixelsblockwithan
overlapping of 6 pixels, are extracted. The feature

extraction from each of these 300
×
300pixelspalmprint
images is similar to that in [18]. These features a
re then
used to

calculate genuine and imposter scores using
similarity measure and by taking the first five ima
ges for
training and the rest five for testing for each use
r. The
errorratesaregeneratedusingdifferentthreshold
values.

3.2. Hand Geometry
Handgeometryisthegeometryofthehandimagewit
h
palm and fingers. The features of the hand geometry
 are
represented by the length of fingers, distances bet
ween
knuckle points, height and thickness of the hand an
d the
fingers etc.This isanimportantbiometricinmul
timodal
fusionasitisextremelyuserfriendlyandrequir
esavery
low cost acquisition system.Thehandgeometrydata
base
consists of 100 users, with 10 images each having 2
3
extracted features. The genuine and imposter scores
 are
calculated using distance similarity. The error rat
es are
generatedbysettingdifferentthresholdsvalues.


4. Decision Making
A classifier can make its decision in binary mode
according to the hypothesis testing approach. Let t
he
stored biometric template be represented by T and t
he
inputtemplateforauthenticationberepresentedby
I.The
nullandthealternatehypothesisare:
H
0
:T≠Ithepersonisanimposter.
(1)
H
1
:T=Ithepersonisgenuine.

Thetwoassociateddecisionsdenotedby:
 s
i
=0,thepersonisanimposter.


 s
i
=1,thepersonisgenuine.
(2)
The most likely decisions are genuine acceptance an
d
imposter rejection.  These are difficult to realize
 in
practice. Hence the accuracy in decisions is specif
ied in
thetermsoferrorrates:Falserejectionrate(F
RR
)andfalse
acceptancerate(F
AR
).Thesetermsaredefinedintermsof
conditionalprobabilitiesas:
F
AR
i
=P(s
i
=1/H
0
).(3)
F
RR
i
=P(s
i
=0/H
1
).(4)
Thedecisionconcerningaperson’sgenuinenessism
ade
throughthefollowinglikelihoodratiotest:

i 1
i 0
P(s/H )
P(s/H )

1
0
i
i
s
s
=
=
λ
i
.(5)

where,
i
λ
 is an appropriate threshold that should be set
dependinguponsensor’sperformancecriteria.

4.1. Binary Fusion
The decisions made by the biometric sensors are bin
ary
basedontheirpresenceorabsenceandhencetheyn
eedto
befusedbysomebinaryfusionrule.Let
N
bethenumber
of sensors and their binary decisions be dented by
s
i
,

i=
1,2,3,….,
N
.Thebinarydecisionsaregivenby:
s
i

=0ifi
th
sensordecidesfor
H
0
.
 =1ifi
th

sensordecidesfor
H
1
.
(6)
All the decisions made by sensors are treated as bi
nary
stringsoflength:
L
=log
2
(
p
).(7)
where,
p
=
N
2
2
is the number of possible rules for
N

sensors.
The fusion rule R
i
 is an integer of length L

varyingfrom
0 1
i
R p
≤ ≤ −
For
N
inputsensorstheoutput
is a fusion ruleas shownin Fig. 1.Thefinaldec
isionR
i

can be made in p possible ways and is subject to th
e
desired performance. The most frequently used fusio
n
rulesareAND ruleandORrule[6].IntheANDrule
the
output decision is 1 if and only if all the input d
ecisions
areone.
785
785
784
784
784
R
2
=1


×
i
=1.  (8)
 =0otherwise.

In the OR rule the output decision is 1 if any one
of the
inputsensor’sdecisionis1:
R
8
=1

×


i
=1.
=0otherwise.
(9)
The 16 fusion rules for 2 sensors are shown in Tabl
e 1.
The rule
2
R
MpltplwlbiwMislMk?uMp.alMAshalMislMp.alM
8
R
M
pltplwlbiwMislMTSMp.al-McslMp.alM
1
R
MhwMwlal ilvMAslbMgaaM
islMvl hwhmbwMgplM”lpmnMh-l-MgaaMymvgahihlwMplXl il
vMgbvMislM
p.alM
16
R
MhwMwlal ilvMAslbMgaaMymvgahihlwMg ltilv-McslM
p.alM
3
R
MehIlwMislMg ltigb lMmoMislMohpwiMwlbwmpMAshalMisl
M
p.alM
7
R
Mg ltiwMislMwl mbvMwlbwmp-MM


Table1
.Fusionrulesfortwosensors
1
s
M
2
s
M
1
R
M
2
R
M
3
R
M
4
R
M
5
R
M
6
R
M
7
R
M
OM OM OM OM OM OM OM OM OM
OM NM OM OM OM OM NM NM NM
NM OM OM OM NM NM OM OM NM
NM NM OM NM OM NM OM NM OM
8
R
M
9
R
M
10
R
M
11
R
M
12
R
M
13
R
M
14
R
M
15
R
M
16
R
M
d
M
OM NM NM NM NM NM NM NM NM
0
d
M
NM OM OM OM OM NM NM NM NM
1
d
M
NM OM OM NM NM OM OM NM NM
2
d
M
NM OM NM OM NM OM NM OM NM
3
d
M
M
4.2. Multi-Modal Fusion
IfN=3,p=256requiresmanyrules.Tocircumventth
is
problem, two&modal fusion is extended to the case o
f
multi&modal fusion. Let
1
i
R
xlMislMo.whmbMp.alMwlal ilvMompM
islMiAmMwlbwmpwM
1
s
gbv
2
s
-M—mbwhvlpMbmAMislMgIghagxhahifMmoM
gM ishpvM wlbwmp
3
s
-M ChisM
1
i
R
gbvM
3
s
AlM gbM elblpgilM islM
wl mbv0MalIlaMNDMo.whmbMp.alwMvlbmilvMxf
2
i
R
-MT.iMmoMishwM
mblM o.whmbM p.alM hwM wlal ilvM xfM mtihyh”gihmbM il sbhz
.l-M
cg1hbeMislMwlal ilvMo.whmbMp.alMgbvMislMom.pisMwlbw
mpM
4
s
AlM
ompyMislMblWiMalIlaMNDM myxhbgihmbwMgbvMislbMwlal i
MmblM
opmyMisly-M>lb lnMishwMtpm lv.plMAsh sMygfMxlM mhbl
vM
Lshlpgp sh gaMM hwM mbihb.lvM ompM gbfM b.yxlpM moM wlbwm
pw-MM
cslMx.pvlbMmoM myt.igihmbMhwM mbwhvlpgxafMplv. lvMl
g sM
ihylMvlgahbeMAhisMmbafMNDMp.alw-MChisMishwnMAlMplz.
hplMmbafM
5<Mp.alwMimMxlM sl 1lvMompM5Mymvgahihlw-M>mAlIlpMis
hwM
gttpmg sMhwMw.xmtihyganMx.iMompMmtihygahifMAlMbllvM
imMipfM
islM myxhbgihmbMmoMhbt.iMlppmpMpgilw-M
M
4.3. Optimal Fusion Rule
One of the tasks of decision level fusion is to sel
ect an
optimal fusion rule that minimizes the total errors
 of the
system. There are 16 possible fusion rules correspo
nding
totwosensorsbutmostofthemhavenosignificant
roleto
playintheimprovementofperformance.Onlymonoto
nic
rulesneedtobeselectedastheyareshowntoyiel
dbetter
performanceexperimentally[9].Themostfrequently
used
rules are AND (
2
R
EMp.alMgbvMTSM)
8
R
EMp.al-McslMAmpwiM
tlpompyhbeMp.alMhwM?k?uMp.alM)
9
R
EMAsh sMhwMpgplafMmoM
hbilplwi-McslMhbvhIhv.gaMlppmpMpgilwMo.wlvMxfMk?uMp
.alwMgplM
gwMomaamAwVMMP
AR
=F
AR
1
*F
AR
2
and
F
RR
=F
RR
1
+F
RR
2
&F
RR
1
*F
RR
2

(10)

This rule can improve F
AR
 but degrades F
RR
 and hence
GAR. The OR rules can be opted for the reverse effe
ct.
FusionbyORruleleadsto:
 F
AR
=F
AR
1
+F
AR
2
&F
AR
1
*F
AR
2

F
RR
=F
RR
1
*F
RR
2
(11)
InTable1,s
1
isthedecisionofthefirstsensorwhiles
2
is
thedecisionofthesecondsensor.Theglobaldecis
ions
i
d
MM
gphwlM opmyM islM o.whmbM p.alwM hbM cgxalM N-M M cslwlM eamx
gaM
vl hwhmbwMplw.aiMhbMislMeamxgaMlppmpMpgilwMehIlbMxf
VM
MMMMMMMMMMMMMMM(P
AR
=
1
0
1
j
N
L
i AR
i
j
d
φ

=
=
 
×
 
 


(12)

where,
j
AR
ϕ
=1&F
AR
j

(s
j
=0).&
j
AR
ϕ
=F
AR
j
(s
j
=1).
 GF
RR
=
( )
1
1
1
j
N
L
i RR
i o
j
d
ϕ

=
=
 
 
− ×
 
 
 


(13)
where,
j
RR
ϕ
=F
RR
j
(s
j
=0)&
j
RR
ϕ
=1&F
RR
j

(s
j
=1)
These global error rates can be evaluated by any fu
sion
rule like majority voting rule or Chair&Varshney fu
sion
ruletoarriveatanoptimaldecision.


5. Need for Optimization
The goal of a fusion system is to minimize the erro
rs,
F
AR
 and F
RR
 by using their weighted sum. The design of
thesystemissuchthatitshoulditselfchoosethe
optimum
decision fusion rule (Table 1) using the Bayesian
framework. The fusion rules are used to calculate g
lobal
error rates GF
AR
 and GF
RR
, which in turn are used to
calculate the weighted sum in Eqn. (14), where the
weights are the associated costs with these errors.
 The
optimizationtechniquemustdeterminetheoptimals
ensor
points adaptively. The objective function E require
d to
optimizeisdefinedasfollows:

MinimizeE=C
FA
*GF
AR
+C
FR
*GF
RR
(14)


C
FR
=2&C
FA

C
FA
isthecostoffalselyacceptinganimposterindivi
dual.
C
FR
isthecostoffalselyrejectingthegenuineindivi
dual.
The error rates (F
AR
andF
RR
)forbothsensorsbecome
input to the optimization technique. The objective
function E should be minimized at each stepbysele
cting
one set of error rates. The optimal values correspo
nd to
theminimumE.Inthiswork,particleswarmoptimiz
ation
786
786
785
785
785
technique is used to arrive at the optimal fusion r
ule and
sensorpoints(errorrates).


5.1. Particle Swarm Optimization
Particle swarm optimization (PSO) was proposed by
Eberhart and Kennedy in [13] for the solution of
optimizationproblemsusingsocialandcognitivebe
havior
of swarm. In PSO each particle has some velocity
according to which it moves in the multi&dimensiona
l
solution space; and memory to keep information of i
ts
previousvisitedspace.Hence,itsmovementisinfl
uenced
bytwofactors:thelocalbestsolutionduetoitse
lfandthe
globalbestsolutionduetoallparticlesparticipa
tinginthe
solution space. The algorithm is guided by two fact
ors:
themovementofparticlesintheglobalneighborhoo
dand
the movement in the local neighborhood. In the glob
al
neighborhood each particle searches for the best po
sition
(solution) and towards the best particle in the who
le
swarm while in the local neighborhood, each particl
e
moves towards the best position (solution) towards
the
best particle in the restricted neighborhood (swarm
).
During an iteration of the algorithm, the local bes
t
position and theglobalbestpositionareupdated i
f better
solution is found  and the process is repeated till
 the
desired results are achieved or specified number of

iterationsareexhausted.
Let us consider an N&dimensional solution space. Th
e
i
th
 particle of the swarm can be represented as an N&
dimensional vector,
1 2
(,,..,)
i i i iN
X x x x
=
 such
that
id id
X x
=
,wherethefirstsubscriptdenotestheparticle
number and the second subscript denotes the dimensi
on.
The velocity of this particle is denoted by a N&
dimensional vector,
1 2
(,,..,)
i i i iN
V v v v
=
such that
id id
V v
=
.
Thememoryofthepreviousbestpositionofthepar
ticleis
represented by an N&dimensional vector
1 2
(,,...,)
i i i iN
Pos p p p
=
such that
id id
Pos p
=
and the global
best position by
1 2
(,,...,)
g g g gN
Pos p p p
=
 such
that
gd gd
Pos p
=
. The particle’s motion is affected by its
ownbestpositionandglobalbestposition.

Thevelocityofaparticleat
k
thiterationisupdatedby:

(
)
(
)
1
1 2
k k k k
id id id id gd id
V V r Pos X r Pos X
ω α β
+
= + − + −
(15)

Thecorrespondingpositionoftheparticleisupdat
edby:

1 1
k k k
id id id
X X V
+ +
= +
(16)
where,i=1,2,3…..M;Mbeingthenumberofswarma
nd
d=1,2,3,…..Nisthedimensionofaswarm;
α
and
β
are
the positive constants, called cognitive parameter
and
social parameter respectively. These indicate the r
elative
influence of the local and global positions.
1
r
and
2
r
are
the random numbersdistributeduniformly in[0 1];
and
k

=1,2,3…
is the iteration step. 
ω

is called inertia weight.
InordertoapplyPSOapproachtothefusionproble
m,we
takethefirstNdimensionstobesensorthresholds

i
λ
that
are continuous and (N+1)
th
 dimensionforthe fusionrule,
( 1)
i N i
X R
+
=
. With this each particle will have (N+1)
dimensions; so that
1 2
(,,...,,)
i i i iN i
X R
λ λ λ
=
. This is an
integermodelbecause
i
R

takesanintegervalue.Itsuffers
from slow convergence hence the need for binary PSO

algorithmwhereF
AR
areevolvedinsteadofthresholdsfor
each of the sensors, i.e.,
(,)
i
i AR i
X F R
=
. The thresholds
arecomputedusingF
AR
.ThebinaryPSOnotonlyleadsto
the optimal convergence with high accuracy but is a
lso
capableofmakingbinarydecisions[12]unlikeothe
rs.


5.2. Binary PSO
TheoriginalPSOisforcontinuouspopulationbuti
slater
extended by Kennedy and Eberhart [13] to the discre
te
valued population. In the binary PSO thus emerged,
the
particles are represented by binary values (0 or 1)
. The
velocityandparticleupdatingforbinaryPSOaret
hesame
as in the case of continuous one. However, the fina
l
decisionsaremadeintermsof0or1.Sigmoidfunc
tionin
[15]isusedtorestrictthedecisionintherange
[0,1]:

1
1
1

1
k
k
ri
v
v
e
+
+

=
+
(17)
Theparticleschangepositionscalledstatesfrom0
to1or
viceversasatisfyingthecondition:

1
1
k
i
X
+
=
if
1
k
ri
r v
+
<

 =0otherwise. 
(18)
where,
r
 isthe randomnumber generatedinthe range[0,
1]. Now the binary fusion rule comes handy to fuse
the
decisions given by the individual matchers. The opt
imal
fusionruleisselectedwiththeuseofbinaryPSO
thatsets
theappropriateparameters.Wewillnowdiscussthe
effect
ofparametersonthealgorithm.

5.3. Parameters of PSO

The convergence and performance of PSO are largely
dependentuponparameterschosen.
ω
istermedasinertia
weight[15]andisincorporatedinthealgorithmto
control
theeffectofthepreviousvelocityvectorofthes
warmon
the new one. It facilitates the trade&off between t
he local
andtheglobalexplorationabilitiesoftheswarma
ndmay
result in less number of iterations of the algorith
m while
searching for an optimal solution. It is experiment
ally
found that inertiaweight
ω
intherange[0.8,1.2]yields
abetterperformance[14].Itisinitiallysetto1
.2andthen
decreased to zero during the subsequent iterations.
 This
scheme of decreasing inertia weight is found to be
better
thanthefixedone[18].Itcontrolstherapidmoti
onofthe
particle while searching for optimum from region to

region.Thevelocityliesintherange[&
V
max ,
V
max
]where
787
787
786
786
786
&
V
max
denotes the lower range and
V
max
  is the upper
rangeofthemotionoftheparticle.
The roles of 
α
× )(×
β
)<λ× ∧−× ∧× <∏−∏)× ∏× −∑λ×
∧λ<λλ×∧∨×"#ϕ×∑∧+λλ<ϕ×)×α∏−)$+×∑∧λ×)(×
∨∏λ×
−αλ(× )αλ× )× λ)(× −∧× )× ∨)−λ<× ∧λ<λλ× ∧∨× −∑λ
×
)∧<∏−∑ω∀××(λ∨)α−×)αλ×∧∨×
α
G
β
G×/×∏×αλ−λ(×∨∧<×
λλ<)× ≤α<≤∧λϕ× $α−× ∧ωλ+∑)−× $λ−−λ<× <λα−× )<λ× ∨∧
α(×
+∏−∑×
α

β
×G×:∀0×'(B)∀×>∧+λλ<ϕ×−∑λ×)αλ×∧∨×∧∏−∏λ×
≤)<)ωλ−λ<ϕ×
α
× )<λ<× −∑)× −∑λ× ∧∏)× ≤)<)ωλ−λ<×
β
× )<λ×
≤<λ∨λ<<λ(× ∨<∧ω× −∑λ× ≤λ<∨∧<ω)λ× ≤∧∏−× ∧∨× ∏λ+× +∏−∑× −
∑λ×
∧−<)∏−×
α
×O
β
×

×8×'(D)∀××−∑λ×≤<λλ−×+∧<%ϕ×+λ×∨∏;×
α
G×:∀B× )(×
β
× G× (∀× ∑λ× ≤)<)ωλ−λ<×
1
r
gbv
2
r
M.wlvMimM
yghbighbMislMvhIlpwhifMmoMislMtmt.agihmbMhbM)NCE-M
McslM hytalylbigihmbM moM islM xhbgpfM:RTM hwM gM xhiM
vhoolplbiMopmyMislM mbihb.m.wMmbl-MRmMwAhi shbeMmIl
pMimM
xhbgpfM:RTMplz.hplwMpl0wliihbeMmoMislMtgpgylilpw-Mc
shwMhwM
xl g.wlMislMsheslpMIga.lMmoM
V
max
works well for better
exploration in the case of continuous PSO whereas t
he
lowervalueof
V
max
willdothesameinthecaseofbinary
PSO [15]. To overcome this situation we take
V
max
= 1
thus specifying the range [&1, 1] for the motion of
 the
particleinthesearchspace.




5.4. Hybrid PSO
Forbiometricfusionweneedoptimizeddecisionsfr
om
different sensors and a fusion rule to combine them
. As
thefusionrulesare binaryweneedbinaryPSOfor
better
convergence. However we use a hybrid type of PSO
algorithm to reap benefits from both types. The
continuousPSOisusedforcalculating theupdates
ofthe
positionandvelocityofaparticleandthebinary
PSOfor
the purpose of arriving at a fusion rule. Next the
global
errorratesarecalculatedusingthefusionrule.T
heseerror
rates are further used to calculate the weighted su
m
serving as the objective function. The error rates
and the
fusion rule corresponding to the minimum weighted s
um
ofallthesensorsconstitutetheoutputofthealg
orithm.

5.5. Decision Rule
Once the optimal sensor points (error rates) are
selectedbytheoptimizationtechniques,thenexts
tepisto
makeuseofdecisionmakingusingthesepointsasi
nputs.
Here we use Chair&Varshney fusion rule for decision

making,whichisdefinedas:
1
1
log (1 )log log
1 2
i i
i
i
N
RR RR
FA
i i
AR AR FA
i
F F
C
s s
F F C
=


   

 


   
+ −
 
 
   
− −


 
   



¤
(19)
Theweighted sumgiven by(19)isthen comparedwit
h a
threshold on the r.h.s. The output decision is 1 if
 the
weighted sum is greater than the threshold and 0
otherwise. A user is authenticated if the output is
 1
otherwise rejected. For 3 modalities Eqn. (19) has
to be
repeated with
1
i
R
gbvM
3
s
xfM ig1hbeM islM Iga.lwM moM
1 1 1
,,
i i
AR RR FA
F F C
-RhyhagpMhwMislM gwlMAhisM5Mymvgahihlw-M
cslM omaamAhbeM gaemphisyMgvgtihIlafM wlal iwM islMAlhe
siwM
w. sMisgiMislM mwiMo.b ihmbMhwMyhbhyh”lv-MM
Adaptive Multimodal Biometric Management (AMBM)
algorithm
1.

Calculate the error rates (F
AR
 & F
RR
) by fixing 1000
thresholdsforeachmodality.
2.

Initialize the error rates and costs (C
FA
 and C
FR
) to
feedintothePSOalgorithmforoptimalvalues.
3.

Runthe PSOalgorithm tilltheoptimaldecisionsan
d
thecorrespondingfusionrulesareobtained.
4.

Fuse the decisions using Chair&Varshney fusion rule

foreachofthecost.
5.

Repeat the process till the desired performance is
achieved.
6. Results of Implementation

Theproposedfusionapproachisimplementedonreal
data
consisting of palmprint and hand geometry images. T
he
database is made up of 100 users, each providing 10

images. For the experimental evaluation the first f
ive
images from each user are taken as a training set a
nd the
rest five as a testing set. We have generated the g
enuine
and imposter scores using distance similarity. The
error
ratesaregeneratedbysettingsomethresholds.The
seerror
rates along with the random numbers are treated as
particles in PSO optimization technique and optimiz
ed
using the algorithm. We have considered 10 particle
s for
optimization.

Fig. 1
.TheCombinedROCofPalmandHandGeometry

Figure1showstheperformanceofboththemodaliti
es
on the same curve.  The objective function for the
PSO
algorithm is given in (14). We vary the cost of C
FA
 from
0.1 to 1.9 and run the PSO algorithm 100 times for
the
samecostwith1000iterationsperrun.Itisobse
rvedthat
if C
FA
 is less than 1, the OR rules is selected by the
algorithm most of the times. On the other hand for
C
FA

788
788
787
787
787
morethan1.5ANDruleisselectedmostofthetime
s.For
the costs between 1 and 1.5 both AND and OR rules a
re
selected equally, indicating that for this cost bot
h rules
perform equally well. Figure 2 shows ROC due to bot
h
ANDandORrules.

Fig.2
ThecombinedROCofANDandORrule

The ROC shown above has very less improvement in
terms of error rates. We recalculate the optimal se
nsor
pointsusingPSOandfusionstrategybyvaryingC
FA
.This
isdoneineachcasebycombingthemusingANDand
OR
rules.Fig.3showsthecombinedROCforallthe12
points
(0.1 to 1.9). It can be seen that in OR case the le
ast G
AR

(i.e.1&F
RR
)is96%whileforANDcasetheleastF
AR
is10
&
6
 %. Note that AND fusion rule improves G
AR
 but
deteriorates F
AR
 whereas OR rule improves F
AR
 but
deterioratesG
AR
ascanbeseenfromFig.3.Forthegiven
cost Chair&Varshney rule is verified thus demonstra
ting
the applicability of decision level fusion approach
 using
PSO. The calculated global F
AR
 and F
RR
 of both the
sensors are used as input to the Chair&Varshney dec
ision
rule.Thefinaldecisionissubjecttosatisfaction
offusion
rules.

Fig.3
ROCforANDandORrulewithdifferentC
FA.





7. Conclusions
A particle swarm optimization based decision level
fusion of palmprint and hand geometry biometrics is

presented.Thesensorpointsandfusionrulesserve
asthe
given input to the PSO algorithm. The algorithm
automaticallyselectstheoptimalsensorpointsand
oneof
the 16 described fusion rules to fuse the decisions
 made
by individual matchers. Further the global decision
s are
computed using Chair –Varshney rule. Extending the
fusiontomorethantwomodalitiesisthefuturewo
rk.

References
[1]

K.Nandkumar,“IntegrationofMultipleCuesinBiom
etric
Systems”,PHDThesis,MichiganStateUniversity,20
05.
[2]

K. Woods, K. Bowyer, and W.P. Kegelmeyer,
“CombinationofMultipleClassifiersusingLocalAc
curacy
Estimates”,
IEEE Trans. PAMI
,19(4):405–410,1997.
[3]

L.LamandC.Y.Suen,“ApplicationofMajorityVot
ingto
Pattern Recognition: An Analysis of Its Behavior an
d
Performance”,
IEEE Trans. SMC – Part A
,27(5):553–568,
1997.
[4]

P. K. Varshney, Distributed Detection and Data Fusi
on
,

NewYork:Springer,1997.
[5]

T. K. Ho, J. J. Hull, and S. N. Srihari, “Decision
CombinationinMultipleClassifierSystems”,
IEEE Trans.
PAMI
,16(1):66–75,January1994.
[6]

J. Daugman, “Combining Multiple Biometrics”,
<
http://www.cl.cam.ac.uk/users/jgd1000/combine/
>
[7]

R. W. Frischholz and U. Deickmann, “BioID: A
multimodal biometric identification system,”
IEEE
Computer
,vol.33,no.2,Feb.2000.
[8]

J. Kennedy, R. C. Eberhart, and Y. H. Shi,
Swarm
Intelligence
, CA
:MorganKaufmann,Jun.2001.
[9]

K. Veeramachaneni, L. Osadciw, and P.K. Varshney, “
An
Adaptive Multimodal Biometric Management Algorithm”
,
IEEE Trans. SMC —Part C
,vol.35,no.3,August2005.
[10]

R. Horst and H. Tuy,
Global Optimization –
Deterministic Approaches
,Springer,NewYork,1996.
[11]

T. Bäck, D. Fogel and Z. Michalewicz, Handbook of
Evolutionary Computation, IOP Publishing and Oxford

UniversityPress,NewYork,1997.
[12]

J.KennedyandR.C.Eberhart,“PSOoptimization,”
Proc.
IEEE Int. Conf. Neural Networks
,1995,pp.1941–1948.
[13]

R.C. Eberhart and J. Kennedy,” A New Optimizer Usin
g
Particle Swarm Theory”,
Proc. 6
th
Symposium on Micro
Machine and Human Science
,pp.39–43,1995.
[14]

Y. Shi and R.C. Eberhart, “A modified Particle Swar
m
Optimizer”,
Proc. IEEE Conference on Evolutionary
Computation
,1998.
[15]

M.A. Khanesar,M.Teshnehlab,andM.A.Shoorehdeli
“A
Novel Binary Particle Swarm Optimization”,
Proc. 15
th

Mediterranean Conference on Control and Automation
,
2007.
[16]

A.CarlisleandG.Dozier,“AnOff&The&ShelfPSO
”, Proc.
Particle Swarm Optimization Workshop
,pp.1–6,2001.
[17]

A. K. Jain, S. Prabhakar, and S. Chen, “Combining
multiple matchers for a high security fingerprint
verification system,”
Pattern Recognition Letters.
, vol.20,
no.11–13,pp.1371–1379,Nov.1999.
[18]

A.Kumar,D.C.M.Wong,HelenC.Shen,andA.K.J
ain,
“Personal authentication using hand images”,
Pattern
Recognition Letters
,vol.27,pp.1478&1486,Oct.2006.
[19]

A. Kumar and D. Zhang, “Palmprint authentication us
ing
multiple representation,”
Pattern Recognition
, vol. 38, pp.
1695&1704,Oct.2005.
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