Robust Face Recognition via Sparse Representation(11)

220IEEETRANSACTIONSONPATTERNANALYSISANDMACHINEINTELLIGENCE,VOL.31,NO.2,FEBRUARY

2009

Fig.8.RecognitionratesonExtendedYaleBdatabase,forvariousfeaturetransformationsandclassifiers.(a)SRC(ourapproach).(b)NN.(c)NS.(d)SVM(linearkernel).

28DontheYalefacedatabase,bothusingNN.In[32],Leeetal.reported95.4percentaccuracyusingtheNSmethodontheYaleBdatabase.

4.1.2ARDatabase

TheARdatabaseconsistsofover4,000frontalimagesfor126individuals.Foreachindividual,26picturesweretakenintwoseparatesessions[60].Theseimagesincludemorefacialvariations,includingilluminationchange,expres-sions,andfacialdisguisescomparingtotheExtendedYaleBdatabase.Intheexperiment,wechoseasubsetofthedatasetconsistingof50malesubjectsand50femalesubjects.Foreachsubject,14imageswithonlyilluminationchangeandexpressionswereselected:thesevenimagesfromSession1fortraining,andtheothersevenfromSession2fortesting.Theimagesarecroppedwithdimension165Â120andconvertedtograyscale.Weselectedfourfeaturespacedimensions:30,54,130,and540,whichcorrespondtothedownsampleratios1/24,1/18,1/12,and1/6,respectively.Becausethenumberofsubjectsis100,resultsforFisherfacesareonlygivenatdimension30and54.

ThisdatabaseissubstantiallymorechallengingthantheYaledatabase,sincethenumberofsubjectsisnow100,butthetrainingimagesisreducedtosevenpersubject:fourneutralfaceswithdifferentlightingconditionsandthreefaceswithdifferentexpressions.ForNS,sincethenumberoftrainingimagespersubjectisseven,anyestimateofthefacesubspacecannothavedimensionhigherthan7.WechosetokeepallsevendimensionsforNSinthiscase.Fig.9showstherecognitionratesforthisexperiment.With540Dfeatures,SRCachievesarecognitionratebetween92.0percentand94.7percent.Ontheotherhand,thebestratesachievedbyNNandNSare89.7percentand90.3percent,respectively.SVMslightlyoutperformsSRConthisdataset,achievingamaximumrecognitionrateof95.7percent.However,theperformanceofSVMvariesmore

withthechoiceoffeaturespace—therecognitionrateusingrandomfeaturesisjust88.8percent.Thesupplementaryappendix,whichcanbefoundontheComputerSocietyDigitalLibraryathttp://www.77cn.com.cn/10.1109/TPAMI.2008.79,containsatableofdetailednumer-icalresults.

BasedontheresultsontheExtendedYaleBdatabaseandtheARdatabase,wedrawthefollowingconclusions:1.

ForboththeYaledatabaseandARdatabase,thebestperformancesofSRCandSVMconsistentlyexceedthebestperformancesofthetwoclassicalmethodsNNandNSateachindividualfeaturedimension.Morespecifically,thebestrecognitionrateforSRContheYaledatabaseis98.1percent,comparedto97.7percentforSVM,94.0percentforNS,and90.7percentforNN;thebestrateforSRContheARdatabaseis94.7percent,comparedto95.7percentforSVM,90.3percentforNS,and89.7percentforNN.Theperformancesoftheotherthreeclassifiersdependsstronglyonagoodchoiceof“optimal”features—Fisherfacesforlowerfeaturespacedimen-sionandLaplacianfacesforhigherfeaturespacedimension.WithNNandSVM,theperformanceofthevariousfeaturesdoesnotconvergeasthedimensionofthefeaturespaceincreases.

Theresultscorroboratethetheoryofcompressedsensing:(18)suggeststhatd%128randomlinearmeasurementsshouldsufficeforsparserecoveryintheYaledatabase,whiled%88randomlinearmeasurementsshouldsufficeforsparserecoveryintheARdatabase[44].Beyondthesedimensions,theperformancesofvariousfeaturesinconjunctionwith‘1-minimizationconverge,withconventionalandunconventionalfeatures(e.g.,Randomfacesanddownsampledimages)performingsimilarly.When

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