Face Detection in Color Images Using PCA | Principal Component Analysis | Eigenvalues And Eigenvectors

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FACE DETECTION IN COLOR IMAGES USING PRINCIPAL COMPONENTS ANALYSIS B. Menser and F. Muller Aachen University of Technology (RWTH), Germany ABSTRACT In this paper we present a face detection algorithm for color images with complex background. We include color information into a face detection approach based on principal components analysis (PCA). A skin color probability image is generated by doing a color analysis and the PCA is performed on this new image instead of the luminance image. Experim
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  FACEDETECTIONINCOLORIMAGES USINGPRINCIPALCOMPONENTSANALYSIS  B.MenserandF.M uller AachenUniversityofTechnology(RWTH),Germany ABSTRACT  Inthispaperwepresentafacedetectionalgo-rithmforcolorimageswithcomplexbackground.Weincludecolorinformationintoafacedetec-tionapproachbasedonprincipalcomponentsanal-ysis(PCA).Askincolorprobabilityimageisgen-eratedbydoingacoloranalysisandthePCAis performedonthisnewimageinsteadofthelumi-nanceimage.Experimentsshowthatcolorinforma-tionimprovestherobustnessofthedetectionsignif-icantly. INTRODUCTION  Intherecentpastthereisagrowinginterestin imagecontentanalysis,givenalargenumberof applicationslikeimageretrievalindatabases,face recognitionorcontent-basedimagecoding.The automaticdetectionofhumanfacesinimageswith complexbackgroundisanimportantpreliminary taskfortheseapplications(seeforexampleChellapa etal1]).Aproblemcloselyrelatedtofacedetectionisface recognition.Oneofthebasicapproachesinface recognitionistheeigenspacedecomposition(e.g.Turk andPentland8]).Theimageunderconsidera-tionisprojectedintoalowdimensionalfeaturespace thatisspannedbytheeigenvectorsofasetoftestfaces.Fortherecognitiontask,theresultingco-ecients(principalcomponents)arecomparedto thoseofimagesinthedatabase.Principalcompo-nentsanalysis(PCA)canalsobeusedforthelocal-izationofafaceregion.Animagepatternisclas-siedasafaceifitsdistancetothefacespaceis smallerthanacertainthreshold.However,ourex-perimentsshowthatthebackgroundleadstoasig-nicantnumberoffalseclassicationsifthefacere-gionisrelativelysmall.Forthedetectionoffacialregionsincolorimages,severaltechniqueshavebeenproposedsofar,using texture,shapeandcolorinformation,e.g.Sobottka andPitas6],SaberandTekalp5],Wangand Chang9].Duetothefactthatcoloristhe mostdiscriminatingfeatureofafacialregion,the rststepofmanyfacedetectionalgorithmsisa pixel-basedcolorsegmentationtodetectskin-colored regions.Theperformanceofsuchahierarchicalsystemishighlydependentontheresultsofthis initialsegmentation.Thesubsequentclassication basedonshapemayfailifonlypartsoftheface aredetectedorthefaceregionismergedwithskin-coloredbackground.Inthispaperweincorporatecolorinformation intoafacedetectionschemebasedonprincipalcomponentsanalysis.Insteadofperforminga pixel-basedcolorsegmentation,wecreateanew imagewhichindicatestheprobabilityofeachimage pixelbelongingtoaskinregion(skinprobability image).Usingthefactthattheoriginalluminance imageandtheprobabilityimagehavesimilargrey-leveldistributionsinfacialregions,weemploya principalcomponentsanalysistodetectfacialregions intheprobabilityimage.Theutilizationofcolor informationinaPCAframeworkresultsinarobustfacedetectioneveninthepresenceofcomplexand skincoloredbackground.Ourdetectionalgorithm ndsfrontalviewsofhumanfacesincolorimages overarangeofscales. COLORANALYSIS  Thecolorofhumanskinisdistinctivefromthe colorofmanyothernaturalobjects,hencecoloris averyimportantfeaturethatcanbeusedforface detection.Analyzingtheskin-tonecolorstatistics,oneobservesthatskincolorsaredistributedovera smallareainthechrominanceplaneandthemajor dierencebetweenskintonesisintensity.Thus,the imageisrstconvertedintoacolorspacewhich providesaseparationintoaluminancechanneland twochrominancecomponentsliketheYCbCrcolor space.Let w  ij denotethevectorwhichisformedby thechrominancecomponentsofthepixelatsite ( ij  ).Theconditionalprobabilityfunctionof  w  ij belongingtotheskinclass  S  ismodeledbyatwo-dimensionalGaussian   p  ( w  ij j S  )= exp ;  12 ( w  ij ;    S  ) T    ;  1 S  ( w  ij ;    S  )]2    j   S  j 12 : (1)Themean    S  andthecovariancematrix    S  ofthe distributionareestimatedfromatrainingset.The gaussianapproachcanbeveriedbyanonparamet-ricdensityestimation(parzenestimate).Usually,theconditionalpdfisusedforaclassica-tionoftheimagepixels.In5]athresholdisse-  Figure1:Luminaceimage(salesman#1)lectedtodecidewhetherapixelbelongstotheskin classornot.In6]and9]apixelisclassiedasa skin-tonepixelifitschromaticityfallswithinaprede-nedregionofthecolorspace.Thesubsequentanal-ysisofthefacecandidatesisregion-basedandmay failifafaceisnotcorrectlyextractedintoonesin-gleregion.Insteadofdoingabinarysegmentation,wepreserve thecontinuousinformationgivenby   p  ( w  ij j S  ).We createasocalledskinprobabilityimage    whichin-dicatestheprobabilityofeachimagepixelbelong-ingtotheskinclass  S  :   ( ij  )    p  ( w  ij j S  ) : (2)Fig.1and2showstheluminancecomponentofthe imagesalesman#1andtheskinprobabilityimage    ,respectively.Thetestimagehascomplexbackgroundwithobjects coloredsimilartohumanskin.Theexampleshows thatitisdiculttondathresholdsuchthatthe wholefaceisrepresentedbyasingleregionwhichis notconnectedwithbackgroundobjects.Animportantobservationisthattheprobability imageresemblestheoriginalluminanceimagein facialregions.Forexample,partsofthefacewhich donothaveskincolorliketheeyesappearasdark holesinbothluminanceimageandskinprobability image.Ontheotherhand,imageregionswith dierentcolor(background)aresuppressedinthe skinprobabilityimage.Generallyspeaking,thegrey-leveldistributionofafaceregionisverysimilarin theoriginalluminanceimageandtheskinprobability image.Sincetheimportantglobalfeaturesof aface(e.g.shape,eyes,mouth)arepreserved,wesuggesttoapplyafacedetectionalgorithm basedonprincipalcomponentsanalysistotheskin probabilityimageinsteadoftheluminanceimage.Themajorbenetofusingtheskinprobabilityimage isthatafacialregionisenhancedcomparedtothe Figure2:Skintoneprobabilityimage background.Furthermore,theinuenceofdierentlightingconditionsisdrasticallyreducedsincethe skinprobabilitydependsnotontheluminance.AsimilarapproachhasbeenpresentedbyDaiand Nakano2],whereafacetexturemodeloriginally developedforgrey-levelimagesisappliedtotheI-componentofanimageintheYIQcolorspace. PRINCIPALCOMPONENTANALYSIS  Mostfacedetectionschemescanbedividedintotwo dierentstrategies.Therstmethodisbasedonthe detectionoffacialfeatures(e.g.YowandCippola 10]),whereasthesecondapproachtriestodetecta facepatternasawholeunit(e.g.SungandPoggio 7],MoghaddamandPentland4]).Followingthe secondapproach,eachimagepatternofdimension  I  by  J  canbeconsideredasavector  x  ina  N  =  IJ  dimensionalspace.Obviously,imagesof faceswillnotberandomlydistributedinthishigh dimensionalimagespace.Asuitablemeantoreduce thedimensionalityofthedatasetistheprincipalcomponentsanalysis(PCA).Thecentralideaofprincipalcomponentsanalysis istondalowdimensionalsubspace(thefeature space)whichcapturesmostofthevariationwithin thedatasetandthereforeallowsthebestleast-squareapproximation(Jollie3]).Whenused forfacedetectionandrecognition,thisprincipalsubspaceisoftencalledthe\facespace whichis spannedbythe\eigenfaces 8].Givenasetoftrainingvectors  f  x  g  (facesamples)withsamplecovariancematrix    ,theKLTbasiscan becomputedbysolvingtheeigenvalueproblem    =  P  T    P   (3)where  P  istheeigenvectormatrixof    and    the diagonalmatrixoftheeigenvalues.  Theorthogonalprojectionmatrix  P  M  intothe  M  -dimensionalprincipalsubspace( M    N  )isgiven bythe  M  eigenvectorscorrespondingtothelargesteigenvalues.Theseeigenvectors(\eigenfaces )form thecolumnsoftheprojectionmatrix  P  M  .Theprincipalcomponentsvector  y  isobtainedby projectingtheimage  x  intothefacespace: y  =  P  T  M  ( x  ;    x  )  (4)where   x  denotesthemeanfaceimage.Theclassicationoftheimagepatterncontaining  N  pixelsas\face or\non-face isonlybasedonits  M  principalcomponents  y  i .Theapproximationofafaceusing  M  \eigenfaces is givenby ^  x  =  P  M  y  +   x  .Theresidualreconstruction error    2   2 =  jj ( x  ;  ^  x  ) jj 2 =  jj ( x  ;    x  ) ;  P  M  y  jj 2 =  jj x  ;    x  jj 2 ;  M  X  i =1 y  2 i (5)indicateshowwellthetestpatterncanbeapproxi-matedinthefacespace.Thus,the\distancefrom facespace (DFFS)denedbyequation(5)can beusedtodetermineiftheimagepatternrepre-sentsaface8].Thedistancebetweentheprojectedimageandthe meanfaceimageinthefeaturespaceisgivenbythe normoftheprincipalcomponentvector.Sincethe varianceofaprincipalcomponent y  i isgivenbythe associatedeigenvalue    i ,thesquaredMahalanobis distance  d  2 providesasuitablemeasureofthe dierencebetweentheprojectionofthetestimage andthemeanface: d  2 =  y  T    ;  1 y  =  M  X  i =1 y  2 i   i (6)Forthedetectiontask,itiscustomarytouseonlythe DFFSforthedecisioncriterion8].Asshowninthe nextsection,theincorporationofthe\distancein facespace (DIFS)denedbyequation(6)improves therobustnessofthedetectionsignicantlyifthe detectionisperformedontheskinprobabilityimage. FACEDETECTIONUSINGPCA  Inourexperimentsweusea10-dimensionalprin-cipalsubspace( M  =10).Theprojectionma-trix  P  M  iscalculatedbyaneigenspacedecomposi-tionusingasetofluminancefacetestimages.Tolo-calizeafacialregioninanewimage,theerrorcri-terionmustbecomputedforeachpixelposition,re-sultinginadistancemap.Forthemoment,weuse asimpledetectorwhichisbasedonlyonthe\dis-tancefromfacespace (DFFS).Theglobalmini-mumofthedistancemapisthenselectedasthebestmatch.Whenusing  M  eigenvectors,thecomputa-tionoftheDFFSrequires  M  +1correlations(with the  M  \eigenfaces andthemeanimage)andanad-ditionalenergycalculation.Thecorrelationscanbe ecientlycomputedusingtheFFT.FirstweanalyzethePCA-basedfacedetectionon greylevelimagesandpointouttheproblemscaused bytheimagebackground.Figure3:Distancemapfortheluminancecompo-nentusingDFFS(salesman#1)Fig.3showstheDFFSmapfortheluminanceimage salesman#1.Theglobalminimumismarkedby thewhitecircle.Thoughthereisalocalminimum atthetruefaceposition,thebestmatchisinthe backgroundregionleadingtoafalsedetection.The DFFSishighfornon-facialimageregionswitha highchangingintheintensity(e.g.theareathatincludespartsofthelight-coloredshirtandthe darkbackground).Ontheotherhand,theDFFS becomesrelativesmallinnon-facialregionswith littlevarianceintheintensitylikepartsofthe backgroundattherightsideofthetestimage.This isduetothefactthatanimagepatternthatcanbe modeledbynoisecanbebetterrepresentedbythe eigenfacesthananon-facialimagepatterncontaining astrongedge.Therefore,detectionbasedonthe DFFSbecomesdiculteveninimageswithasimple backgroundifthefaceregiondoesnotcoverthemain partofthetestimage.Wenowapplyaprincipalcomponentanalysistothe skinprobabilityimagedenedbyequation(2)using thesameprojectionmatrix.TheDFFSmapforthe skinprobabilityimageshowning.2isdisplayed ing.4a.Thetruefaceregionischaracterizedby alocalminimum.Similartotheluminancecase,theerrorcriterionisalsolowinbackgroundregions withlittlevariance.Theseregionsrepresentnon-skin-coloredbackground,sotheprobabilityimageis nearzerointheseareas.Fig.4bshowsthe\distance  in  facespace foreach   a)DFFS b)DIFS Figure4:Distancemapsfortheskinprobability image(salesman#1)spatialpositionwhichisdenedbytheweighted LS-normoftheprincipalcomponentvector.The projectionofanimageregionwithvaluesnear zerointothefacespaceresultsinlargeprincipalcomponents.Thus,theDIFScanbeemployed toeliminatetheinuenceofthenon-skin-colored background.Sincenoadditionalcorrelationis necessaryforthecalculationoftheDIFS,the computationalloadincreasesonlyslightly.Wedene anewerrorcriterionwhichisaweightedsumofthe DFFSandtheDIFS: e  =  d  2 +  c  2 (7)Sincetheprincipalcomponentsarescaledbythe correspondingeigenvaluesforthecalculationofthe DIFS,asimilarscalingisnecessaryfortheDFFS.Thus,wesetthescalingfactorto  c  =  1 k  M  where    M  denotesthesmallestcalculatedeigenvalueand  k  isasmallconstant( k  =1  ::: 5)determinedby a)Combinederrorcriterion b)Detectedfaceregion Figure5:FacedetectionusingDFFSandDIFS experiments.In4]theeigenspacedecompositionisusedtoesti-matethecompleteprobabilitydensityforacertain objectclass(e.g.thefaceclass).Assuminganormaldistribution,theestimatefortheMahalanobisdis-tanceisalsoaweightedsumoftheDFFSandthe DIFSsimilartoequation(7).Amaindierenceis thatourscalingfactor  c  ismuchsmallerthanthe oneusedin4]becausetheDIFSprovidesmorein-formationwhenusingtheskinprobabilityimagein-steadoftheluminanceimage.Thedistancemapus-ingthecombinederrorcriterionisshowning.5a.Theglobalminimum(markedbythewhitecircle)lies inthetruefaceregionandthefaceisdetectedcor-rectly.Fig.5bshowsthedetectedfaceregionsuper-imposedontheluminancecomponent.Todetectfacesatmultiplescales,thedetection algorithmisperformedonseveralscaledversionsof theskinprobabilityimageandtheglobalminimum oftheresultingmulti-scaledistancemapsisselected 
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