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inastandardpatternrecognitionalgorithmtofindwhichofanumberofpredefinedfaceclasses,ifany,bestde-scribestheface.ThesimplestmethodfordeterminingwhichfaceclassprovidesthebestdescriptionofaninputfaceimageistofindthefaceclasskthatminimizestheEuclidiandistancewhereahisavectordescribingthekthfaceclass.Thefaceclassesaiarecalculatedbyaveragingtheresultsoftheeigenfacerepresentationoverasmallnumberoffaceimages(asfewasone)ofeachindividual.Afaceisclassifiedasbelonging.toclasskwhentheminimumQisbelowsomechosenthreshold0,.Otherwisethefaceisclassifiedasunknown,andoptionallyusedtocreateanewfaceclass.Becausecreatingthevectorofweightsisequivalenttoprojectingtheoriginalfaceimageontothelow-dimen-sionalfacespace,manyimages(mostofthemlookingnothinglikeaface)willprojectontoagivenpatternvector.Thisisnotaproblemforthesystem,however,sincethedistanceEbetweentheimageandthefacespaceissimplythesquareddistancebetweenthemean-adjustedinputimage@=I'-*and@f=c::,oiui,itsprojectionontofacespace:Thustherearefourpossibilitiesforaninputimageanditspatternvector:(1)nearfacespaceandnearafaceclass,(2)nearfacespacebutnotnearaknownfaceclass,(3)distantfromfacespaceandnearafaceclass,and(4)distantfromfacespaceandnotnearaknownfaceclass.Inthefirstcase,anindividualisrecognizedandiden-tified.Inthesecondcase,anunknownindividualispres-ent.Thelasttwocasesindicatethattheimageisnotafaceimage.Casethreetypicallyshowsupasafalsepos-itiveinmostrecognitionsystems;inourframework,however,thefalserecognitionmaybedetectedbecauseofthesignificantdistancebetweentheimageandthesubspaceofexpectedfaceimages.Figure4showssomeimagesandtheirprojectionsintofacespaceandgivesameasureofdistancefromthefacespaceforeach.SummaryofEigenfaceRecognitionProcedureTosummarize,theeigenfacesapproachtofacerecogni-tioninvolvesthefollowingsteps:1.Collectasetofcharacteristicfaceimagesoftheknownindividuals.Thissetshouldincludeanumberofimagesforeachperson,withsomevariationinexpres-sionandinthelighting.(Sayfourimagesoftenpeople,soM=40.)2.Calculatethe(40X40)matrixL,finditseigenvec-torsandeigenvalues,andchoosetheM'eigenvectorswiththehighestassociatedeigenvalues.(LetM'=10inthisexample.)3.Combinethenormalizedtrainingsetofimagesac-cordingtoEq.(6)toproducethe(M'=10)eigenfacesuk.4.Foreachknownindividual,calculatetheclassvec-tor0sbyaveragingtheeigenfacepatternvectors0[fromEq.(8)]calculatedfromtheoriginal(four)imagesoftheindividual.Chooseathreshold0,thatdefinesthemaxi-mumallowabledistancefromanyfaceclass,andathreshold0,thatdefinesthemaximumallowabledis-tancefromfacespace[accordingtoEq.(9)).5.Foreachnewfaceimagetobeidentified,calculateitspatternvector0,thedistanceseitoeachknownclass,andthedistanceEtofacespace.Iftheminimumdistance~k0,andthedistanceE0,,classifytheinputfaceastheindividualassociatedwithclassvectornk.Iftheminimumdistance~k0,butdistancee0,,thentheimagemaybeclassifedasunknown,andoptionallyusedtobeginanewfaceclass.6.Ifthenewimageisclassifiedasaknownindividual,thisimagemaybeaddedtotheoriginalsetoffamiliarfaceimages,andtheeigenfacesmayberecalculated(steps1-4).Thisgivestheopportunitytomodifythefacespaceasthesystemencountersmoreinstancesofknownfaces.Inourcurrentsystemcalculationoftheeigenfacesisdoneofflineaspartofthetraining.Therecognitioncurrentlytakesabout400msecrunningratherineffi-cientlyinLisponaSun4,usingfaceimagesofsize128x128.Withsomespecial-purposehardware,thecurrentversioncouldrunatclosetoframerate(33msec).Designingapracticalsystemforfacerecognitionwithinthisframeworkrequiresassessingthetradeoffsbetweengenerality,requiredaccuracy,andspeed.Ifthefacerecognitiontaskisrestrictedtoasmallsetofpeople(suchasthemembersofafamilyorasmallcompany),asmallsetofeigenfacesisadequatetospanthefacesofinterest.Ifthesystemistolearnnewfacesorrepresentmanypeople,alargerbasissetofeigenfaceswillberequired.TheresultsofSirovichandKirby(1987)andKirbyandSirovich(1990)forcodingoffaceimagesgivessomeevidencethatevenifitwerenecessarytorepresentalargesegmentofthepopulation,thenumberofeigen-facesneededwouldstillberelativelysmall.LocatingandDetectingFacesTheanalysisintheprecedingsectionsassumeswehaveacenteredfaceimage,thesamesizeasthetrainingimagesandtheeigenfaces.Weneedsomeway,then,tolocateafaceinascenetodotherecognition.Wehavedevelopedtwoschemestolocateandlortrackfaces,us-ingmotiondetectionandmanipulationoftheimagesinfacespace.76JournalofCognitiveNeuroscienceVolume3,NumberIfaceview,sideviews,at-f45,andrightandleftprofileviews.Undermostviewingconditionstheseseemtobesufficienttorecognizeafaceanywherefromfrontaltoprofileview,becausetherealviewcanbeapproximatedbyinterpolationamongthefixedviews.EXPERIMENTSWITHEIGENFACESToassesstheviabilityofthisapproachtofacerecogni-tion,wehaveperformedexperimentswithstoredfaceimagesandbuiltasystemtolocateandrecognizefacesinadynamicenvironment.Wefirstcreatedalargeda-tabaseoffaceimagescollectedunderawiderangeofimagingconditions.Usingthisdatabasewehavecon-ductedseveralexperimentstoassesstheperformanceunderknownvariationsoflighting,scale,andorienta-tion.Theresultsoftheseexperimentsandearlyexperi-encewiththenear