The Role of Statistics in Biometric Authentication Based on Facial Images

nauseatingcynicalSecurity

Feb 22, 2014 (3 years and 5 months ago)

60 views

TheRoleofStatisticsinBiometricAuthentication
BasedonFacialImages
SinjiniMitra
DepartmentofStatistics&CyLab
CarnegieMellonUniversity
smitra@stat.cmu.edu
Collaborators:
StephenE.Fienberg
AnthonyBrockwell
B.V.K.VijayaKumar(ECE)
MariosSavvides(ECE)
YanxiLiu(RoboticsInstitute,CS)
CarnegieMellonp.1/19
WhatisBiometricAuthentication?
Biometrics
refertotheuniquebiologicaltraits(physicalorbehavioral)ofindividualsthatcan
beusedforidenti?cation
Physical:retinal/irisscan,?ngerprint,face,palm-print
Behavioral:voice-print,gait,gesture
face?ngerprintirisscanpalm-printvoiceprint
BiometricAuthentication
Technologyforveri?cationofaperson’sidentitybasedonhis/herbiometrics
?Somethingyouare?versus?somethingyouknow?(passwords)or?somethingyoupossess?
(IDcard)
Bettersecurityandreliability:cannotbestolenorforgottenandlesspronetofraud
Applications
Forensics,homelandsecurity,accesstoATMsandcomputernetworks
CarnegieMellonp.2/19
FacialBiometrics
Fairlyaccurate,non-intrusiveanduserfriendly
Analyzesfacialcharacteristicsfromanimage
Examples:
Positionrelationshipsbetweeneyes,nose,mouthandchin
Verychallenging-sensitivetoexternalfactors
Afaceauthenticationsystemhas3components:(i)Enrollment,(ii)Identi?cation,(iii)
Decision:authenticorimpostor?
Matching
Face
Database
Camera
Pre−processing
(feature extraction)
(Verification/identification)
Authentication
CarnegieMellonp.3/19
TheFaceRecognitionVendorTest(FRVT)2002
Provideperformancemeasuresforassessingtheabilityof10commerciallyusedautomatic
facerecognitionsystemstomeetreal-worldrequirements
Participantstestedonlargedatanotpreviouslyseen-121;589imagesof37;437people
Effectofdemographics(sex,age),imageproperties(location,resolution,pose,
illumination),timedifferencebetweenenrollmentandtesting
Performancedegradedwithincreasingdatabaseand?watch-list?size
Drawback:
Impressiveresultsbutbasedonobservationalstudiesandareempiricalinnature-
nostatisticalbasis(modeling,ROCcurves)andscopeforvalidinference
CarnegieMellonp.4/19
MyResearchGoals
I.Statisticalanalysisandevaluationofexistingauthenticationsystems
II.Explorenewapproachestobuildingstatisticalmodel-basedauthenticationsystems
III.Exploreotherwaystodevelopdistortion-tolerantauthenticationsystems
Motivation:M
inimum
A
verage
C
orrelation
E
nergy
(MACE)
Filter
IntroducedbyKumar,etal.(2002)
Easilydetectedfeaturesfordistinguishingauthenticsandimpostors
Alinear?lterandreportsimpressiveresults
Objective:
UseMACEasabaselinefordevelopingstatisticalmethodsofanalysisandevaluationofface
authenticationsystems,inordertomakethemmorerigorousandusefulinpractice
CarnegieMellonp.5/19
I.TheMACEFilter
hMACE
=D1
X(X
T
D
1
X)1
c;
D:adiagonalmatrix(ave.powerspectrum),c:acolumnvectorofones
N Training Images
12
........
N
2D FFTvectorize
.
.
.
.
.
.
image 1
FFT
array
X
2
d x d
d x d
(d x N)
image 2
d x d
image N
.
.
. ..
.
. . .
d x d
column vector of
2
d x 1()
FFT array
x 1)
2
(d
x 1)(d2
ObtainedbyminimizingtheaveragecorrelationplaneenergyE
ave
=h0
Dhwhilesatisfying
X
+
h=c(constraintattheorigin)
Suchadesignforcestheoutputplanetohavelowvalueseverywhereexceptattheorigin
facilitateseasydistinction
CarnegieMellonp.6/19
Filter-basedAuthentication
OneMACE?lterissynthesizedperperson
Filterappliedtoeachtestimageviaconvolution(frequencydomain)
InverseFouriertransformyields?nalspatialoutput
Peak-to-SidelobeRatio(PSR):
Quantitativemeasureforauthentication
origin
5 x 5 central
mask
20 x 20 sidelobe
region
{
output plane
peak
(height)
PSR=
peak-
x
s
Authentication:
Highforauthenticsandlowforimpostors
CarnegieMellonp.7/19
TheDatabases
I.Cohn-KanadeAU-CodedFacialExpressionDatabase
:
55
subjects
expressingneutral,joy,angeranddisgust
II.CMU-PIEDatabase
:
65
subjectsunderdifferentilluminationconditions
CarnegieMellonp.8/19
MyAuthenticationResults
Authentic
(Subject1)
Impostor
(Subject2)
TestImageTestImage
Filter1Output(Subject1)Filter1Output(Subject2)
PSR:30.6360PSR:8.8697
CarnegieMellonp.9/19
PropertiesandDistortionTolerance
Easytoimplementandhasattractivefeatures
Shift-invariance,tolerancetoilluminationandpartialocclusion(SavvidesandKumar,2003),
butsensitivetootherdistortionslikenoise,expressions,pose,etc.
Manyheuristicsinvolved:(i)trainingimages,(ii)PSRthreshold
Distortion-tolerantMACE
Obtainedbyminimizingthe
compromisecriterion
(Kumar,1992):
Eave
+
2
=h0
Dh+h0
h=h0
(D+Id
)h,where
2
:noisevariance,:tuning
parameter
ReplaceDinhMACE
byD+I,sothat
hnoise
=(D+Id
)1
X[X
T
(D+Id
)1
X]1
c:
Reasonableperformanceunderdistortions-lowerfalsealarms
Drawback:
Nodeterministicwayofchoosing:?brute-force?andad-hoc,andno?xed
optimalvalue
CarnegieMellonp.10/19
StatisticalAnalysisofMACE
MACEisnotamodel-basedtechnique
ModelvariationinPSRvalueswithchangesinimageproperties(noise,resolution),?lter
designparameters(sidelobedimension,)anddemographics(age,sex)
Performanceevaluationandinference:
Con?denceintervalsandhypothesistestsforPSRanderrorrates
PredictPSRvaluesanderrorratesforunobservedlargenewdata
Modelperformancestatisticsasafunctionofdatabaseand?watch-list?sizes
ExploratoryAnalysis
Moretrainingimagesrequiredinpresenceofdistortions
Oftenbetterauthenticationwith(i)fewertrainingimages,(ii)lowerresolutionimages,(iii)
smallersidelobedimension
CarnegieMellonp.11/19
PerformanceEvaluation:TheLiterature
Adecision-theoreticframework:amatchscoreTandathreshold
T>:match(authentic),T:mismatch(impostor)
TypeIerror:FNR=P(TjT2Authentic)=
R

1
fA
(x)dx
TypeIIerror:FPR=P(T>jT2Impostor)=
R
1

gI
(y)dy
Trade-offbetweenFPR,FNRandtheirbehaviorwithcanberepresentedbya
Receiver
OperatingCharacteristic(ROC)
curve
Errorratesestimatedempiricallybysampleproportions
Con?denceintervalsandhypothesistestsforerrorrateestimates:binomialdistributionand
bootstrapping(Bolleetal,2000),beta-binomialdistribution(Schuckers,2003)
Drawback:
Basedonmanyassumptions-independence,equalityofvariances,whichseldom
holdinpracticeforrealimagedata
ROCcurveshelpinevaluationofscoredistributions-IshwaranandGatsonis(2000)used
hierarchicalmodelsforclustereddata
Myapproach:
UseROCcurvestostudythescoredistributionsandusetherobustmodelingapproach
CarnegieMellonp.12/19
InferenceforNewData
Goal:
PredictPSRvaluefornewlargefacedata,estimatetheexpectederrorratesandmodel
variationasafunctionofdatabaseand?watchlist?size
RandomEffectsHierarchicalModel
(Gelfand,etal.JASA1990)
Yij
ind:
N(i
+
PM
m=1

m
i
x(m)
ij
;2
),
i
(i
;1
i
;:::;
M
i
)T
MVN(0
(0
;
1
0
;:::;
M
0
)T
;);2
IG(a;b)
Conjugatehyperpriorsfor0
,andMCMC-basedposteriorsimulation
Inferencebasedon0
andposteriorpredictivedistributionsp(yij
jy)
PSRistheMACE?score?,soY:log(PSR),covariatesx
ij
:
Imageproperties
Filterparameters
Databaseproperties
Authentic/Impostor(binary)
#trainingimages
size
Distortions(categorical)

?watch-list?size
Imageresolution
sidelobedimension
Modeltheoddsoffalsealarm(FPR,FNR)inalogisticregressionframework
Modelchecksforvalidityofassumptions:linearity,independence,homoscedasticity
CarnegieMellonp.13/19
II.StatisticalModel-basedSystems
Spatialmodels(2DAR,MRF)
inadequateforbuildingmodel-basedclassi?cationtools
Spectralmodels:
Myapproach
Noonehasmodeledtheimagespectrumdirectly
TheFouriertransformofanimagex(n
1
;n2
)isde?nedas:
X(j;k)=
1
N
2
1
N1
1
X
n1
=0
N1
1
X
n2
=0
x(n1
;n2
)ei2(n1
j=N1
+n2
k=N1
)
(polarform)
=jX(j;k)j
|
{z
}
magnitude
ei
phase
z
}|
{
x
(j;k)
;j;k=0;1;:::;N1
1
Wewillmodelmagnitudeandphase
Magnitude:
0
20
40
60
80
100
120
140
0
50
100
150
0
1000
2000
3000
4000
5000
6000
Phase:
0
20
40
60
80
100
120
140
0
50
100
150
−4
−3
−2
−1
0
1
2
3
4
CarnegieMellonp.14/19
SpectralModeling
Phasecapturesmostofafaceimageidenti?ability(Hayes,1982)
Subject1Subject2Mag1+Phase2Mag2+Phase1
DifcultiesinPhaseModeling:
Nostationarityassumptionswork-?wrappingaround?property
Hardtoisolatelocationofdiscriminatinginformationinphase
Variesconsiderablywithanykindofdistortion
ModelSelection:
Idea:
Generatemodelsforan?optimal?numberofFouriercoef?cientsbypreserving
identi?ability-dimensionreduction
Animageofgoodqualitycanbereconstructedusingfewlowfrequencycomponents
(highenergy)whilehigherones(lowenergy)represent?nerfacialdetails
original40%16%3%
CarnegieMellonp.15/19
MixtureModels
Flexiblesemi-parametricframeworkformodelingunknowndistributionalshapes
Mixturesrepresentdifferentilluminationconditionsforeachperson
Modellog-magnitudeandphaseforpixelswithina5050gridaroundorigin:
Yj
=
0
@
Lk;j
s;t
P
k;j
s;t
1
A
BVN
k
s;t
;k
s;t

Mixturemodel:
f(yj
; )=
Pg
i=1
i
(yj
;i
;i
)
Onemixturemodelperpixelperperson:f
s;t
(yj
; jk)
GibbsSamplerusedforparameterestimationviaposteriorsimulation,usingconjugatepriors
for,i
andi
Newtestimage(x=(Ls;t
;Ps;t
))classi?edbyMAPestimatebasedonposteriorlikelihood:
C=argmaxk
g(kjL;P)argmaxk
g(L;Pjk)p(k)
whereg(L;Pjk)=s
t
fs;t
(x; jk),p(k)=1=k
Inferencebasedonlikelihoods,possiblyusingsimilarrandomeffectsmodelsasbefore
Possibletoclassifytheilluminationtypeofanimageofaperson
CarnegieMellonp.16/19
Summary
Presentedarigorousstatisticalframeworkforanalysisandevaluationofexisting
authenticationsystemswhichhelpsinbypassingtheneedfortheempiricalsystemevaluation
toolsmostlyusedtoday
Shownsigni?canceofstatistically-basedsystems:
inferenceforlargenewdata
guidelinestousersofexistingsystems,makingthemmorereliable
Exploitingthekeyroleofphaseinfaceidenti?cationforbuildingmodelsinthespectral
domainisapromisingnovelapproachwithasimpleclassi?cationscheme
Currentresearchagendaconsistsofimplementingallthesetechniquesinthecontextofthe
MACE?ltersystemandthespectralmodel-basedsystem(afterdevelopment)
FutureDirections:
SpectralModels:
Modelallpixelstogetherusinginter-pixelcorrelations,increasealgorithm
ef?ciency
OtherMethods:
FacialAsymmetry-potentialfordevisingdistortion-tolerantauthentication
systems(Liuetal.2003)
OtherBiometrics:
Fingerprints,Multi-modalsystems
CarnegieMellonp.17/19
References
Bolle,R.M.,Pankanti,S.andRatha,N.K.(2000).EvaluationTechniquesforbiometrics-based
authenticationsystems(FRR).InProceedingsofICPR2000,pages2831-2837.
Gelfand,A.E.,Hills,S.E.,Racine-Poon,A.,Smith,A.F.M.(1990).IllustrationofBayesian
InferenceinNormalDataModelsUsingGibbsSampling.JASA,85(412):972-985.
Hayes,M.H.(1982).TheReconstructionofaMultidimensionalSequencefromthePhaseor
MagnitudeofitsFourierTransform.IEEETransactionsonAcoustics,SpeechandSignal
Processing,30(2):140-154.
Ishwaran,H.andGatsonis,C.(2000).Ageneralclassofhierarchicalordinalregressionmodels
withapplicationstocorrelatedROCanalysis.TheCanadianJournalofStatistics,28:731:750.
Liu,Y.,Schmidt,K.,Cohn,J.,Mitra,S.(2003).FacialAsymmetryQuanti?cationfor
Expression-invariantHumanIdenti?cation.ComputerVisionandImageUnderstanding
Journal,91(1/2):138-159.
Savvides,M.andVijayaKumar,B.V.K.(2003).Ef?cientDesignofadvancedcorrelation
?ltersforrobustdistortion-tolerantfaceidenti?cation.ProceedingsoftheIEEEInternational
ConferenceonAdvancedVideoandSignal-basedSurveillance(AVSS),pages45-52.
Schuckers,M.E.(2003).UsingtheBeta-BinomialDistributiontoAssessPerformanceofa
BiometricIdenti?cationDevice.InternationalJournalofImageGraphics,3(3):523-529.
CarnegieMellonp.18/19
References(cont.d)
VijayaKumar,B.V.K.,Savvides,M.,Venkataramani,K.,Xie,C.(2002).SpatialFrequency
DomainImageProcessingForBiometricRecognition.ProceedingsoftheInternational
ConferenceonImageProcessing(ICIP),Rochester,NY.
VijayaKumar,B.V.K.(1992).Tutorialsurveyofcomposite?lterdesignsforoptical
correlators.AppliedOptics,31(23):4773-4801.
Acknowledgment
:
FundinginpartbytheArmyResearchOf?cecontractDAAD19-02-1-3-0389toCyLab.
CarnegieMellonp.19/19