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1、Sing1eImageSubspaceforFaceRecognitionJun1iu,SongcanChen,Zhi-HuaZh0u2,andXiaoyangTani1DepartmentofComputerScienceandEngineering,NanjingUniversityofAeronauticsandAstronautics,China,j.1iu,s.chen,x.iang2Nationa1Key1aboratoryforNove1SoftwareTechno1ogy,NanjingUniversity,ChinazhouzhAbstract.Sma11samp1esize
2、andseverefacia1variationaretwocha11engingprob1emsforfacerecognition.Inthispaper,weproposetheSIS(Sing1eImageSubspace)approachtoaddressthesetwoprob1ems.Todea1withtheformerone,Werepresenteachsing1eimageasasubspacespannedbyitssynthesized(shifted)samp1es,andemp1oyanew1ydesignedsubspacedistancemetrictomea
3、surethedistanceofsubspaces.Todea1withthe1atterone,wedivideafaceimageintosevera1regions,computethecontributionscoresofthetrainingsamp1esbasedontheextractedsubspacesineachregion,andaggregatethescoresofa11theregionstoyie1dtheu1timaterecognitionresu1t.Experimentsonwe11-knownfacedatabasessuchasAR,Extende
4、dYA1EandFERETshowthattheproposedapproachoutperformssomerenownedmethodsnoton1yinthescenarioofonetrainingsamp1eperperson,buta1sointhescenarioofmu1tip1etrainingsamp1esperpersonwithsignificantfacia1variations.1 IntroductionOneofthemostcha11engingprob1emsforfacerecognitionistheso-ca11edSma11Samp1eSize(SS
5、S)prob1em18,25,i.e.,thenumberoftrainingsamp1esisfarsma11erthanthedimensiona1ityofthesamp1es.Meanwhi1e,thefacerecognitiontaskbecomesmoredifficu1twhenthetestingsamp1esaresubjecttoseverefacia1variationssuchasexpression,i11umination,occ1usion,etc.Todea1withtheSSSprob1em,weproposetorepresenteachsing1e(tr
6、aining,testing)imageasasubspacespannedbyitssynthesizedimages.Theemp1oyedsynthesizedimagesaretheshiftedimagesoftheorigina1sing1efaceimageandthuscanbeefficient1yobtainedwithoutadditiona1computationandstoragecosts.Tomeasurethedistancebetweensubspaces,wedesignasubspacedistancemetricthatisapp1icab1etosub
7、spaceswithunequa1dimensions.Moreover,toimprovetherobustnesstotheaforementionedfacia1variations,wedivideafaceimageintoregions,computethecontributionscoresofthetrainingsamp1esbasedontheextractedsubspacesineachregion,andfina11yaggregatethescoresofa11theregionstoyie1dtheu1timatec1assificationresu1t.Sinc
8、etheproposedapproachgeneratesasubspaceforeachimage(orapartitionedregionofanimage),itisnamedasSIS(Sing1eImageSubspace).Experimentsonsevera1we11-knowndatabasesshowthattheproposedSISapproachachievesbetterc1assificationperformancethansomerenownedmethodsinthescenariosofbothonetrainingsamp1eperpersonandmu
9、1tip1etrainingsamp1esperpersonwithsignificantfacia1variations.Inwhatfo11ows,wewi11brief1yreviewthere1atedworkinSection2,proposetheSISapproachinSection3,reportonexperimenta1resu1tsinSection4,andconc1udethispaperwithsomediscussioninSection5.2 Re1atedWorkIndea1ingwiththeSSSprob1em,thefo11owingtwoparadi
10、gmsareoftenemp1oyed:1)performingdimensiona1ityreductionto1owerthesamp1edimensiona1ity,and2)synthesizingvirtua1samp1estoen1argethetrainingset.Amongthemanyexistingdimensiona1ityreductionmethods,PCA(Principa1ComponentAna1ysis,Eigenfaces)20and1DA(1inearDiscriminantAna1ysis,Fisherfaces)Iarewe11-knownandh
11、avebecomethede-factobase1ines.1ateradvancesonPCAand1DAinc1udeBayesianIntraZExtrapersona1C1assifier(BIC)13,DiscriminantCommonVectors(DCV)4,9,etc.OurproposedSISapproachworksa1ongthesecondparadigm,i.e.,synthesizingvirtua1samp1es,whoseeffectivenesshasbeenverifiedinquiteafewstudies3,11,16,19,23.In3,Beyme
12、randPoggiosynthesizedvirtua1samp1esbyincorporatingpriorknow1edge,andyie1dedac1assificationaccuracyof82%withonerea1and14virtua1imagescomparedto67%withon1yrea1samp1esonadatabaseof62persons.Niyogieta1.14showedthatincorporatingpriorknow1edgeismathematica11yequiva1enttointroducingaregu1arizerinfunction1e
13、arning,thusimp1icit1yimprovingthegenera1izationoftherecognitionsystem.In23,WuandZhouenrichedtheinformationofafaceimagebycombiningthefaceimagewithitsprojectionmap,andthenapp1iedPCAtotheenrichedimagesforfacerecognition.Theyreported3-5%higheraccuracythanPCAthroughusing10-15%fewereigenfaces.Martinez11pr
14、oposedthe1oca1Probabi1isticSubspace(1PS)method.Specifica11y,Martinezsynthesizedvirtua1samp1esbyperturbationanddividedafaceimageintosevera1regionswheretheeigenspacetechniquewasapp1iedtothegeneratedvirtua1samp1esforc1assification.Goodperformanceof1PSwasreportedontheAR12facedatabase.In16,Shaneta1.propo
15、sedtheFace-SpecificSubspace(FSS)method.Theysynthesizedvirtua1samp1esbygeometricandgray-1eve1transformation,bui1tasubspaceforeverysubject,andc1assifiedthetestingsamp1ebyminimizingthedistancefromtheface-specificsubspace.TheeffectivenessofFSSwasverifiedonfacedatabasessuchasYA1EB6.Torreeta1.19generatedv
16、irtua1samp1esbyusing15()1inearandnon-1inearfi1ters,andbui1tanOrientedComponentAna1ysis(OCA)c1assifieroneachrepresentation.Bycombiningtheresu1tsofthe15()OCAc1assifiers,theyachievedgoodperformanceontheFRGCv1.()dataset.Thesynthesizedsamp1esareusua11yexp1oitedforgeneratingasubspace.Therearerough1ythreesty1esforgeneratingthesubspace:1)generatingasubspacefromthewho1een1argedtrainingset,e.g.,3,11,23,2)generatingasubspacefro
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