基于Gabor变换与流形学习理论的人脸识别算法

华中科技大学硕士学位论文基于Gabor变换与流形学习理论的人脸识别算法姓名：朱冠卫申请学位级别：硕士专业：计算数学指导教师：李红20090501IIsomapLLELELTSALSDAGaborGaborGaborGaborGaborGaborGLSDAORLYaleGaborGLLTSAORLGaborIIAbstractRecently,anewkindofdimensionalityreductionalgorithm,namedmanifoldlearning,hasdrawnmuchattention.Manifoldlearningtheoryassumesthathigh-dimensionaldatalieonalow-dimensionalsubmanifold,itsalgorithmsattempttoembedtheoriginaldataintoasubmanifoldbypreservingthelocalgeometrystructure.Inthispaper,weintroducesomerepresentativealgorithmsincludeIsomap,LLE,LE,LTSA,LSDAandsoon,andthenstresstheapplicationofthesealgorithmsinthefieldoffacerecognition.Facerecognitionisanimportantareaofcomputerpatternrecognitionresearch.Whilehumansarehighlyeasyinrecognizingfaces,thistaskremainsasignificantchallengeformachines.Inthefieldoffacerecognition,theGaborwavelet,whosekernelsaresimilartothe2Dreceptivefieldprofilesofthemammaliancorticalsimplecells,canachievetheminimumoftheHeisenberguncertaintyprinciple,thushasthebesttime-frequencyresolution.Gaborfilterhasbeensuccessfullyusedinfeatrueextactionappliedinmachinevision,imageprocessingandsoon.ThispaperpresentsanovelGabor-basedmanifoldlearnningmethodforfacerecogniton.Themaintasksare:Firstly,BecauseoftheMuti-resolutioncharacteristicoftheGaborfilter,WefirstapplyaseriesofGaborfilterstofaceimagetoextracttheimagefeaturesfromdifferentdirectionandscale.Thentheprocessingofthefeaturessuchassampling,arangementcanbedonetogetafeaturevector.Asweallknow,lowdimensionalityisespeciallyimportantforlearning.ThedimensionalityoftheGaborvectorisveryhigh,thusweapplymanifoldlearningalgriothmstoreducethesehigh-dimensionalfeatures,thenrecognitionworkcanbedoneinthelow-dimensionalsubspace.Inthisarticle,weinctroduceanovelmethodcalledGabor-basedLocalitySensitiveDiscriminantAnalysis(GLSDA),WeassesstheperformanceofourGLSDAmethodonfacerecognitiontask,usingdatasetsfromtheORLandYaledatabase.Comparativeperformanceiscarriedoutagainstotherfacerecognitionmethodsandtheexperimentalresultsshowthatourmethodhashigherrecognitionratethanthatofothermethodsinthefacerecognition.Secondly,consideringthatLocalitySensitiveDiscriminantAnalysisisasuperviseddimensionalityreducealgriothm,andcannotbeappliedwhenthesamples’labelinformationisunkown.Thus,here,weintroduceanewmethodcalledGLLTSA,whichcombinetheGaborwaveletandunsupervisedmanifoldlearningmethodLinearLocalTangentSpaceAlignment.OurmethodcanlearnalinearprojectionwhichcouldmapnewIIIdatatothereducedrepresentationspace.AccordingtotheexperimentalresultsonORLdatabase,wealsofindthatourmethodGLLTSAhashigherrecognitionratethanthatofotherunsupervisemanifoldlearningmethodsinthefacerecognition.KeyWords:ManifoldLearning,GaborFilter,FeatureExtraction,LocalitySensitiveDiscriminantAnalysis,FaceRecognition,LocalTangentSpaceAlignment,SupervisedLearning,UnsupervisedLearning□_____□“√”111.12000SeungTenenbaumRoweisScience1.1.1WebGoogleN256256×65536NN65536×N20001.1.22PrincipalComponentAnalysisPCA[1][2]LinearDiscriminantAnalysisLDA[1][3]“SwissRoll”SSeungLee2000Science[4]TenenbaumRoweisScienceIsometircMappingIsomap[5]LocallyLinearEmbeddingLLE[6]IsomapMultidimensionalScalingMDS[7]LLELLEDonohoHessianHessian-basedLocallyLinearEmbeddingHLLE[8]LLEChangH.LLE[9]BelkinLaplacianLaplacianEigenmapLE[10][11]LELaplacianLocalTangentSpaceAlignmentLTSA[12]3LTSA[13]−XLEELELTSAHeLELocalityPreservingProjectionsLPP[14]PangZhengLLENeighborhoodPreservingProjectionsNPP[15]ZhangT.LinearLocalTangentSpaceAlignmentLLTSA[16]IsomapLLELELocalitySensitiveDiscriminantAnalysisLSDA[17]DengcaiLSDA1.2GaborIsomapLLELELTSAGaborGaborGaborGLSDAORLYaleGabor4GaborLLTSAGLLTSAORL52PCA[1][2]LDA[1][3]Isomap[5]LLE[6]LaplacianLE[10][11]LTSA[12]{}DiNRxxxxX∈=,,,,21ΛdDd2.1PCAPCAPCAPCATnkTkkxXxXExxxxS)()())((1−−=−−=∑=(2.1)xnPCAPCAPCA2.2LDAPCALDAFisher1936Fisher[3]6caSaaSaLBTWTaminarg=(2.2)∑∑==−−=cimjTiijiijWixxS11)))(((µµTiciiiBmS))((1µµµµ−−=∑=aWSWithinClassScaterMatirx)BS(BetweenClassScaterMatrix)ijxijiµiµimi(2.2)aaSaSWBλ=LDALDALSDA2.3IsomapMDSMDSTenenbaumJ.B.MDSIsomapMDSMDSIsomap2.1Isomap2.1Isomap[5]7Isomap[5][18]Step1Gix−k∈∈otherwiseGxNxorxNxifxxdxxGjkiikjjiji)()(),(,−εotherwiseGxxdifxxdxxGjijijiε),(),(,Step2Dijkstra∞=otherwiseGifxxdxxdjijiG),(),(Nk,,2,1Λ={}),(),(),,(min),(jkGkiGjiGjiGxxdxxdxxdxxd+=),(jiGxxdixjxNjijiGGxxdD1,2)],([==Step3GDMDSMDS[7]IsomapIsomapIsomapIsomap“”IsomapIsomap2.4LLERoweisS.T.SaulL.K.2000SciencePCALDAIsomapLLELLEix8[6]LLEjxiNj∈ixLLE2.3ijw2)(∑∑∈−=iNjjijiixwxWε(2.3)ijwjxjxixijwix∑∈=iNjijw122)(∑∑∈∈−=−iiNjjiijNjjijixxwxwx(2.4)(2.4)ijwdiRy∈DiRx∈LLEdiRy∈∑∑−=ijjijiywyYE2)((2.5){}diNRyyyyY∈=,,,,21Λ2.5))()(()(YWIWIYtraceYETT−−=(2.6))()(WIWIT−−=Φdduu,,1ΛTduuuY],...,,[21=2.2LLE92.2[6]LLELLELLELLELLELLE[19]LLE[20][21]2.5LaplacianLELaplacianLE[10]LLELE∈∈otherwiseGxNxorxNxifwxxGjkiikjijji)()(,1=ijwHeatkernel)/exp(22σjiijxxw−−={}Nyyy,...,,21{}DiNRxxxxX∈=,,,,21Λ10LE∑−ijijjiwyy2)((2.7)2.7LyyyWDyywyyDyywyywywyyywyyyyyywyyTTjijijiiiiiijijijiijijiiijijjiiijijjijjiiijijji=−=−=−=−=+−−=−∑∑∑∑∑∑∑∑)()())(()()(21)(212222)(iiDdiagD=∑=jijiiwDWDL−=Laplacian1=DyyTTDyyyLyT1minarg=(2.8)2.8DyLyλ=(