WRIGHTET
AL.:ROBUSTFACERECOGNITIONVIASPARSEREPRESENTATION223
Fig.12.Recognitionundervaryinglevelofcontiguousocclusion.Left,toptworows:(a)30percentoccludedtestfaceimagesyfromExtended
^1,red(darker)entriescorrespondtotrainingimagesofthesameperson.YaleB.(b)Estimatedsparseerrors,^e1.(c)Estimatedsparsecoefficients,x
(d)Reconstructedimages,yr.SRCcorrectlyidentifiesbothoccludedfaces.Forcomparison,thebottomrowshowsthesametestcase,withtheresultgivenbyleastsquares(overdetermined‘2-minimization).(e)Therecognitionrateacrosstheentirerangeofcorruptionforvariousalgorithms.SRC(redcurve)significantlyoutperformsothers,performingalmostperfectlyupto30percentcontiguousocclusion(seetablebelow).
occlusioniscertainlyaworsetypeoferrorsforthealgorithm.Notice,though,thatthealgorithmdoesnotassumeanyknowledgeaboutthenatureofcorruptionorocclusion.InSection4.6,wewillseehowpriorknowledgethattheocclusioniscontiguouscanbeusedtocustomizethealgorithmandgreatlyenhancetherecognitionperformance.Thisresulthasinterestingimplicationsforthedebateovertheuseofholisticversuslocalfeaturesinfacerecognition[22].IthasbeensuggestedthatbothICAIandLNMFarerobusttoocclusion:sincetheirbasesarelocallyconcentrated,occlusioncorruptsonlyafractionofthecoefficients.Bycontrast,ifoneuses‘2-minimization(orthogonalprojection)toexpressanoccludedimageintermsofaholisticbasissuchasthetrainingimagesthemselves,allofthecoefficientsmaybecorrupted(asinFig.12thirdrow).Theimplicationhereisthattheproblemisnotthechoiceofrepresentingthetestimageintermsofaholisticorlocalbasis,butratherhowtherepresentationiscomputed.Properlyharnessingredundancyandsparsityisthekeytoerrorcorrectionandrobustness.Extractinglocalordisjointfeaturescanonlyreduceredundancy,resultingininferiorrobustness.
4.5RecognitionDespiteDisguise
WetestSRC’sabilitytocopewithrealpossiblymaliciousocclusionsusingasubsetoftheARFaceDatabase.Thechosensubsetconsistsof1,399images(14each,exceptforacorruptedimagew-027-14.bmp)of100subjects,50maleand50female.Fortraining,weuse799images(about8persubject)ofunoccludedfrontalviewswithvaryingfacialexpression,givingamatrixBofsize4,980Â5,779.WeestimateP¼convðÆBÞisapproximately577neighborly,indicatingthatperfectreconstructionispossibleupto11.6percentocclusion.OurMatlabimplementationrequiresabout75secondspertestimageonaPowerMacG5.
Weconsidertwoseparatetestsetsof200images.Thefirsttestsetcontainsimagesofthesubjectswearingsunglasses,whichoccluderoughly20percentoftheimage.
Fig.1ashowsasuccessfulexamplefromthistestset.Noticethat^e1compensatesforsmallmisalignmentoftheimageedges,aswellasocclusionduetosunglasses.Thesecondtestsetconsideredcontainsimagesofthesubjectswearingascarf,whichoccludesroughly40percentoftheimage.SincetheocclusionlevelismorethanthreetimesthemaximumworstcaseocclusiongivenbytheneighborlinessofconvðÆBÞ,ourapproachisunlikelytosucceedinthisdomain.Fig.13ashowsonesuchfailure.Noticethatthelargestcoefficientcorrespondstoanimageofabeardedmanwhosemouthregionresemblesthescarf.
ThetableinFig.13leftcomparesSRCtotheotherfivealgorithmsdescribedintheprevioussection.Onfacesoccludedbysunglasses,SRCachievesarecognitionrateof87percent,morethan17percentbetterthanthenearestcompetitor.Forocclusionbyscarves,itsrecognitionrateis59.5percent,morethandoubleitsnearestcompetitorbutstillquitepoor.Thisconfirmsthatalthoughthealgorithmisprovablyrobusttoarbitraryocclusionsuptothebreakdownpointdeterminedbytheneighborlinessofthetrainingset,beyondthatpoint,itissensitivetoocclusionsthatresembleregionsofatrainingimagefromadifferentindividual.Becausetheamountofocclusionexceedsthisbreakdownpoint,additionalassumptions,suchasthedisguiseislikelytobecontiguous,areneededtoachievehigherrecognitionperformance.
4.6ImprovingRecognitionbyBlockPartitioningThusfar,wehavenotexploitedthefactthatinmanyrealrecognitionscenarios,theocclusionfallsonsomepatchofimagepixelswhichisaprioriunknownbutisknowntobeconnected.Asomewhattraditionalapproach(exploredin[57]amongothers)toexploitingthisinformationinfacerecognitionistopartitiontheimageintoblocksandprocesseachblockindependently.Theresultsforindividualblocksarethenaggregated,forexample,byvoting,whilediscard-ingblocksbelievedtobeoccluded(using,say,theoutlier