224IEEETRANSACTIONSONPATTERNANALYSISANDMACHINEINTELLIGENCE,VOL.31,NO.2,FEBRUARY
2009
WeverifytheefficacyofthisschemeontheARdatabaseforfacesdisguisedwithsunglassesorscarves.Wepartitiontheimagesintoeight(4Â2)blocksofsize20Â30pixels.Partitioningincreasestherecognitionrateonscarvesfrom59.5percentto93.5percentandalsoimprovestherecogni-tionrateonsunglassesfrom87.0percentto97.5percent.ThisperformanceexceedsthebestknownresultsontheARdataset[29]todate.Thatworkobtains84percentonthesunglassesand93percentonthescarfs,ononly50subjects,usingmoresophisticatedrandomsamplingtechniques.Alsonoteworthyis[16],whichaimstorecognizeoccludedfacesfromonlyasingletrainingsamplepersubject.OntheARdatabase,thatmethodachievesalowercombinedrecogni-tionrateof80percent.24
Fig.13.(a)-(d)Partitionschemetotacklecontiguousdisguise.ThetoprowvisualizesanexampleforwhichSRCfailedwiththewholeimage(holistic).Thetwolargestcoefficientscorrespondtoabeardedmanandascreamingwoman,twoimageswhosemouthregionresemblestheoccludingscarf.Iftheocclusionisknowntobecontiguous,onecanpartitiontheimageintomultiplesmallerblocks,applytheSRCalgorithmtoeachoftheblocksandthenaggregatetheresultsbyvoting.Thesecondrowvisualizeshowthispartition-basedschemeworksonthesametestimagebutleadstoacorrectidentification.(a)Thetestimage,occludedbyscarf.(b)Estimated
^1.(d)Reconstructedsparseerror^e1.(c)Estimatedsparsecoefficientsx
image.(e)TableofrecognitionratesontheARdatabase.Thetableshowstheperformanceofallthealgorithmsforbothtypesofocclusion.SRC,itsholisticversion(righttop)andpartitionedversion(rightbottom),achievesthehighestrecognitionrate.
rejectionruleintroducedinSection2.4).Themajordifficultywiththisapproachisthattheocclusioncannotbeexpectedtorespectanyfixedpartitionoftheimage;whileonlyafewblocksareassumedtobecompletelyoccluded,someoralloftheremainingblocksmaybepartiallyoccluded.Thus,insuchascheme,thereisstillaneedforrobusttechniqueswithineachblock.
WepartitioneachofthetrainingimagesintoLblocksofsizeaÂb,producingasetofmatricesAð1Þ;...;AðLÞ2IRpÂn,
:
wherep¼ab.Wesimilarlypartitionthetestimageyintoyð1Þ;...;yðLÞ2IRp.WewritethelthblockofthetestimageasasparselinearcombinationAðlÞxðlÞoflthblocksofthetrainingimages,plusasparseerroreðlÞ2IRp:yðlÞ¼AðlÞxðlÞþeðlÞ.WecanrecovercanagainrecoverasparsewðlÞ¼½xðlÞeðlÞ 2IRnþpby‘1minimization:
hi
ðlÞ:ðlÞðlÞ^1¼argminkwksubjecttoAIw¼y:ð24Þw1
w2IRnþpWeapplytheclassifierfromAlgorithm1withineachblock23
andthenaggregatetheresultsbyvoting.Fig.13illustratesthisscheme.
23.Occludedblockscanalsoberejectedvia(15).Wefindthatthisdoesnotsignificantlyincreasetherecognitionrate.
4.7RejectingInvalidTestImages
Wenextdemonstratetherelevanceofsparsityforrejectinginvalidtestimages,withorwithoutocclusion.Wetesttheoutlierrejectionrule(15)basedontheSparsityConcentra-tionIndex(14)ontheExtendedYaleBdatabase,usingSubsets1and2fortrainingandSubset3fortestingasbefore.Weagainsimulatevaryinglevelsofocclusion(10percent,30percent,and50percent)byreplacingarandomlychosenblockofeachtestimagewithanunrelatedimage.However,inthisexperiment,weincludeonlyhalfofthesubjectsinthetrainingset.Thus,halfofthesubjectsinthetestingsetarenewtothealgorithm.Wetestthesystem’sabilitytodeterminewhetheragiventestsubjectisinthetrainingdatabaseornotbysweepingthethreshold througharangeofvaluesin[0,1],generatingthereceiveroperatorcharacteristic(ROC)curvesinFig.14.Forcomparison,wealsoconsideredoutlierrejectionbythresholdingtheeuclideandistancebetween(featuresof)thetestimageand(featuresof)thenearesttrainingimageswithinthePCA,ICA,andLNMFfeaturespaces.ThesecurvesarealsodisplayedinFig.14.Noticethatthesimplerejectionrule(15)performsnearlyperfectlyat10percentand30percentocclusion.At50percentocclusion,itstillsignificantlyoutperformstheotherthreealgorithmsandistheonlyoneofthefouralgorithmsthatperformssignificantlybetterthanchance.Thesupplementaryappen-dix,whichcanbefoundontheComputerSocietyDigitalLibraryathttp://www.77cn.com.cn/10.1109/TPAMI.2008.79,containsmorevalidationresultsontheARdatabaseusingEigenfaces,againdemonstratingsig-nificantimprovementintheROC.
4.8DesigningtheTrainingSetforRobustness
Animportantconsiderationindesigningrecognitionsys-temsisselectingthenumberoftrainingimages,aswellastheconditions(lighting,expression,viewpoint,etc.)underwhichtheyaretobetaken.Thetrainingimagesshouldbeextensiveenoughtospantheconditionsthatmightoccurinthetestset:theyshouldbe“sufficient”fromapatternrecognitionstandpoint.Forinstance,Leeetal.[59]showshowtochoosethefewestrepresentativeimagestowellapproximatetheilluminationconeofeachface.ThenotionofneighborlinessdiscussedinSection2providesadifferentquantitativemeasureforhow“robust”thetrainingsetis:theamountofworstcaseocclusionthealgorithmcantolerateisdirectlydeterminedbyhowneighborlytheassociatedpolytopeis.Theworstcaseisrelevantinvisualrecognition,
24.Fromourownimplementationandexperiments,wefindtheirmethoddoesnotgeneralizewelltomoreextremeilluminations.