Robust Face Recognition via Sparse Representation(14)

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

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