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1QUOTIENTBASEDMULTIRESOLUTIONIMAGEFUSIONOFTHERMALANDVISUALIMAGESUSINGDAUBECHIESWAVELETTRANSFORMFORHUMANFACERECOGNITIONMRINALKANTIBHOWMIK1,DEBOTOSHBHATTACHARJEE2,MITANASIPURI2,DIPAKKUMARBASU2ANDMAHANTAPASKUNDU21DEPARTMENTOFCOMPUTERSCIENCEANDENGINEERING,TRIPURAUNIVERSITYACENTRALUNIVERSITYSURYAMANINAGAR,TRIPURA799130,INDIAMKB_CSEYAHOOCOIN2DEPARTMENTOFCOMPUTERSCIENCEANDENGINEERING,JADAVPURUNIVERSITYKOLKATA,WESTBENGAL700032,INDIAAICTEEMERITUSFELLOWDEBOTOSHINDIATIMESCOM,MITANASIPURIGMAILCOM,DIPAKKBASUGMAILCOM,MKUNDUCSEJDVUACINABSTRACTTHISPAPERINVESTIGATESTHEMULTIRESOLUTIONLEVEL1ANDLEVEL2QUOTIENTBASEDFUSIONOFTHERMALANDVISUALIMAGESINTHEPROPOSEDSYSTEM,THEMETHOD1NAMELY“DECOMPOSETHENQUOTIENTFUSELEVEL1”ANDTHEMETHOD2NAMELY“DECOMPOSERECONSTRUCTTHENQUOTIENTFUSELEVEL2”BOTHWORKONWAVELETTRANSFORMATIONSOFTHEVISUALANDTHERMALFACEIMAGESTHEWAVELETTRANSFORMISWELLSUITEDTOMANAGEDIFFERENTIMAGERESOLUTIONANDALLOWSTHEIMAGEDECOMPOSITIONINDIFFERENTKINDSOFCOEFFICIENTS,WHILEPRESERVINGTHEIMAGEINFORMATIONWITHOUTANYLOSSTHISAPPROACHISBASEDONADEFINITIONOFANILLUMINATIONINVARIANTSIGNATUREIMAGEWHICHENABLESANANALYTICGENERATIONOFTHEIMAGESPACEWITHVARYINGILLUMINATIONTHEQUOTIENTFUSEDIMAGESAREPASSEDTHROUGHPRINCIPALCOMPONENTANALYSISPCAFORDIMENSIONREDUCTIONANDTHENTHOSEIMAGESARECLASSIFIEDUSINGAMULTILAYERPERCEPTRONMLPTHEPERFORMANCESOFBOTHTHEMETHODSHAVEBEENEVALUATEDUSINGOTCBVSANDIRISDATABASESALLTHEDIFFERENTCLASSESHAVEBEENTESTEDSEPARATELY,AMONGTHEMTHEMAXIMUMRECOGNITIONRESULTIS100KEYWORDSDISCRETEWAVELETTRANSFORM,INVERSEDISCRETEWAVELETTRANSFORM,QUOTIENTFUSEDIMAGE,PRINCIPALCOMPONENTANALYSISPCA,MULTILAYERPERCEPTRONMLP,FACIALRECOGNITION,CLASSIFICATION,OTCBVSANDIRISDATABASE1INTRODUCTIONFACERECOGNITIONISAVITALPROBLEMINCOMPUTERVISIONTHOUGHFACERECOGNITIONSYSTEMSSHOWCONSIDERABLEIMPROVEMENTINSUCCESSIVECOMPETITIONS12,STILLITISCONSIDEREDUNSOLVED3FACERECOGNITIONNEEDSHIGHDEGREEOFACCURACYASITSMOSTAPPLICATIONSAREINPUBLICSECURITY,LAWENFORCEMENTANDCOMMERCE,SUCHASMUGSHOTDATABASEMATCHING,IDENTITYAUTHENTICATIONFORCREDITCARDORDRIVERLICENSE,ACCESSCONTROL,INFORMATIONSECURITYANDINTELLIGENTSURVEILLANCE4THEREAREALOTOFFACTORSLIKE,ILLUMINATIONVARIATION,POSEVARIATION,FACIALEXPRESSIONCHANGESETCWHICHAFFECTTHEFACERECOGNITIONPERFORMANCEAMONGALLTHESE,ILLUMINATIONPROBLEMHASRECEIVEDMUCHATTENTIONINRECENTYEARSQUOTIENTIMAGINGTECHNIQUEISONEOFTHESOLUTIONTOTHISPROBLEMTHISMETHODISSIMPLEANDSIGNIFICANTQUOTIENTIMAGEISANIMAGERATIOBETWEENATESTIMAGEANDALINEARCOMBINATIONOFTHREEIMAGESILLUMINATEDBYNONCOPLANARLIGHTS,DEPENDSONLYONTHEALBEDOINFORMATION,ANDTHEREFOREISILLUMINATIONFREE5THEQUOTIENTIMAGECANBECONSIDEREDASFUSEDQUOTIENTIMAGEASBOTHTHEVISUALANDITSCORRESPONDINGTHERMALIMAGESHAVEBEENUSEDTOGENERATEITTHEPROCESSINGSTEPSOFTHETWOMETHODSUSEDTOGENERATEQUOTIENTIMAGESARESHOWNINTHEFIG1AANDFIG1BINBOTHTHETWOMETHODSFORIMAGEDECOMPOSITIONPURPOSEDISCRETE2DWAVELETTRANSFORMHASBEENUSEDFORBOTHTHEVISUALANDTHERMALIMAGESBUTINMETHOD2FORRECONSTRUCTIONPURPOSETHEINVERSEDISCRETE2DWAVELETTRANSFORMHASBEENUSEDINMETHOD1,DECOMPOSITIONHASBEENDONEATLEVEL1TOGENERATETHEFUSEDQUOTIENTIMAGE,ALLTHECOEFFICIENTSOFTHEDECOMPOSEDIMAGEHAVEBEENUSEDINCASEOFMETHOD2,DISCRETE2DWAVELETTRANSFORMHASBEENUSEDATLEVEL2TODECOMPOSETHEVISUALANDTHERMALIMAGESBUTTOREGENERATETHEIMAGESONLYAPPROXIMATIONCOEFFICIENTSHAVEBEENUSEDWITHTHENEWRECONSTRUCTEDVISUALANDTHERMALIMAGESTHEQUOTIENTIMAGESHAVEBEENGENERATEDINTERMSOFDESIGNINGAFACIALRECOGNITIONSYSTEMWITHHIGHACCURACYLEVEL,THEMAINCRUCIALPOINTISTHECHOICEOFFEATUREEXTRACTORINTHISCONNECTION,PRINCIPALCOMPONENTANALYSISPCAHASBEENUSEDFORDIMENSIONREDUCTIONPURPOSEPRINCIPALCOMPONENTANALYSISPCAISBASEDONTHESECONDORDERSTATISTICSOFTHEINPUTIMAGE,WHICHTRIESTOATTAINANOPTIMALREPRESENTATIONTHATMINIMIZESTHEIJCSIINTERNATIONALJOURNALOFCOMPUTERSCIENCEISSUES,VOL7,ISSUE3,MAY2010WWWIJCSIORG2RECONSTRUCTIONERRORINALEASTSQUARESSENSEEIGENVECTORSOFTHECOVARIANCEMATRIXOFTHEFACEIMAGESCONSTITUTETHEEIGENFACESTHEDIMENSIONALITYOFTHEFACEFEATURESPACEISREDUCEDBYSELECTINGONLYTHEEIGENVECTORSPOSSESSINGSIGNIFICANTLYLARGEEIGENVALUES25THEEIGENFACESWHICHARETHESETOFEIGENVECTORSISTHENUSEDTODESCRIBEFACEIMAGES6THESEEIGENFACESARETHENCLASSIFIEDUSINGMULTILAYERPERCEPTRONMLPDIFFERENTEXISTINGILLUMINATIONINVARIANTMETHODSHAVEBEENDISCUSSEDRESEARCHERSHAVEPROPOSEDDIFFERENTSOLUTIONSTOILLUMINATIONPROBLEM,WHICHINCLUDEINVARIANTFEATUREBASEDMETHOD7,3DLINEARILLUMINATIONSUBSPACEMETHOD8,LINEAROBJECTCLASS9,ILLUMINATIONANDPOSEMANIFOLD10,ILLUMINATIONCONES13,HARMONICSUBSPACE17,LAMBERTIANREFLECTANCEANDLINEARSUBSPACE14ANDINDIVIDUALPCACOMBININGTHESYNTHESIZEDIMAGES1516THEORETICALLYTHEILLUMINATIONCONEMETHODILLUSTRATEDTHATFACEIMAGESDUETOVARYINGLIGHTINGDIRECTIONSFORMANILLUMINATIONCONE1INTHISALGORITHM,BOTHSELFSHADOWANDCASTSHADOWWERECONSIDEREDANDITSEXPERIMENTALRESULTSOUTPERFORMEDMOSTEXISTINGMETHODSRAMAMOORTHI1719ANDBASRI2021INDEPENDENTLYDEVELOPEDTHESPHERICALHARMONICREPRESENTATIONTHISORIGINALREPRESENTATIONEXPLAINEDWHYTHEIMAGESOFANOBJECTUNDERDIFFERENTLIGHTINGCONDITIONSCANBEDESCRIBEDBYLOWDIMENSIONALSUBSPACEINSOMEPREVIOUSEMPIRICALEXPERIMENTS2324AMONGALLTHESEALGORITHMSTHEQUOTIENTIMAGEMETHODISSIMPLEANDPRACTICALLYUSEFULALSOQUOTIENTIMAGEBYSHASHUAANDRIKLINRAVIVISMAINLYDESIGNEDFORDEALINGWITHILLUMINATIONCHANGESINFACERECOGNITION262728JACOBSETAL30INTRODUCEDANOTHERCONCEPTOFQUOTIENTIMAGE,WHICHISTHERATIOOFTWOIMAGESJACOBSSMETHODCONSIDERSTHELAMBERTIANMODELWITHOUTSHADOWANDASSUMESTHESURFACEOFTHEOBJECTISSMOOTH5RETINEX,WHICHISACOMBINATIONOFTHEWORDSRETINAANDCORTEX,ISANALGORITHMTOMODELTHEHUMANVISUALSYSTEM22THOUGHITSORIGINALPURPOSEISFORCOLORCONSTANCY,BUTPERFORMSWELLASACONTRASTENHANCEMENTALGORITHMTOOAFAMOUSALGORITHMCALLEDFRANKLEMCCANNVARIATIONHASBEENINTRODUCEDBYMCCANNANDFRANKLE33ANDTHISALGORITHMWORKSBYOPERATINGONTHEIMAGEPIXELSINTHELOGDOMAINTHISINVOLVESFOURBASICSTEPSRATIO,PRODUCT,RESETANDAVERAGE29INTHISAPPROACHTHEMAINCONTRIBUTIONISTHEGENERATIONOFFUSEDQUOTIENTIMAGESI/JFROMBOTHTHECOEFFICIENTSOFVISUALIANDTHERMALJIMAGESINTHISPAPER,FIRSTTIMETHEAUTHORSHAVECONTRIBUTEDTHEQUOTIENTBASEDMULTIRESOLUTIONIMAGEFUSIONOFTHERMALANDVISUALIMAGESUSINGDAUBECHIESWAVELETTRANSFORMFORHUMANFACERECOGNITIONTHEPAPERISORGANIZEDASFOLLOWSSYSTEMOVERVIEWHASBEENGIVENINSECTION2WHICHINCLUDESTHEDESCRIPTIONOFVISUALANDTHERMALFACEIMAGES,MULTIRESOLUTIONANALYSIS,THEIMAGEDECOMPOSITIONANDRECONSTRUCTIONPROCESS,QUOTIENTIMAGINGMETHOD,PRINCIPALCOMPONENTANALYSISPCAANDARTIFICIALNEURALNETWORKSECTION3SHOWSANDANALYSESTHEEXPERIMENTALRESULTSUSINGOTCBVSANDIRISDATABASESTHECOMPARISONBETWEENDIFFERENTQUOTIENTIMAGINGMETHODSARESHOWNINSECTION4ANDFINALLYTHECONCLUSIONISMADEINSECTION52SYSTEMOVERVIEWHERE,ATECHNIQUEFORHUMANFACERECOGNITIONUSINGQUOTIENTIMAGESHASBEENPRESENTTHEBLOCKDIAGRAMOFTHESYSTEMISGIVENINFIG1AFORMETHOD1ANDINFIG1BFORMETHOD2ALLTHEPROCESSINGSTEPSTOGENERATEQUOTIENTIMAGESUSEDINTWOMETHODSARESHOWNINTHECORRESPONDINGBLOCKDIAGRAMSINCASEOFMETHOD1INFIRSTSTEPSINGLELEVELDECOMPOSITIONHASBEENDONEFORBOTHTHEVISUALANDTHERMALIMAGESQUOTIENTIMAGESAREGENERATEDFROMALLTHECOEFFICIENTSAPPROXIMATIONANDDETAILSCOEFFICIENTSOFDECOMPOSEDVISUALANDTHERMALIMAGESMETHOD2ISSLIGHTLYDIFFERENTFROMMETHOD1INTHEFIRSTSTEP,DECOMPOSITIONOFBOTHTHETHERMALANDVISUALIMAGESUPTOLEVEL2HASBEENDONEUSINGDAUBECHIESWAVELETTHEREASONBEHINDUSINGLEVEL2DECOMPOSITIONISTHATTHEHIGHERTHEDECOMPOSITIONLEVELSARETHEMOREADVANTAGEOUSBECAUSETHENUMBEROFHIGHERANDLOWERFREQUENCYSUBBANDSWILLINCREASEINTHISCONNECTIONTHESIZEOFTHEIMAGEWILLDECREASEANDTHUSTHEPROCESSINGSPEEDWILLINCREASE38THENTHEIMAGESARERECONSTRUCTEDFROMTHECORRESPONDINGAPPROXIMATIONCOEFFICIENTSINCASEOFBOTHVISUALANDTHERMALIMAGESTHENQUOTIENTIMAGESAREGENERATEDWITHTHESECOEFFICIENTSTHESETRANSFORMEDIMAGESARESEPARATEDINTOTWOGROUPSNAMELYTRAININGSETANDTESTINGSETTHEPCAISCOMPUTEDUSINGTRAININGIMAGESALLTHETRAININGANDTESTINGIMAGESAREPROJECTEDINTOTHECREATEDEIGENSPACEANDNAMEDASQUOTIENTFUSEDEIGENFACESONCETHESECONVERSIONSAREDONETHENEXTTASKISTOUSEMULTILAYERPERCEPTRONMLPTOCLASSIFYTHEMAMULTILAYERFEEDFORWARDNETWORKISUSEDFORCLASSIFICATION21MULTIRESOLUTIONANALYSISINCOMPUTERVISION,ITISDIFFICULTTOANALYZETHEINFORMATIONCONTENTOFANIMAGEDIRECTLYFROMTHEGRAYLEVELINTENSITYOFTHEIMAGEPIXELSINDEED,THISVALUEDEPENDSUPONTHELIGHTINGCONDITIONSGENERALLY,THESTRUCTURESWEWANTTORECOGNIZEHAVEVERYDIFFERENTSIZESHENCE,ITISNOTPOSSIBLETODEFINEAPRIORIANOPTIMALRESOLUTIONFORANALYZINGIMAGESFUSEDQUOTIENTVISUALIMAGEDECOMPOSEDVISUALIMAGEWITHLEVEL1DWTIJCSIINTERNATIONALJOURNALOFCOMPUTERSCIENCEISSUES,VOL7,ISSUE3,MAY2010WWWIJCSIORG3FIG1BLOCKDIAGRAMOFTHESYSTEMPRESENTEDHEREFORAMETHOD1ANDBMETHOD2WAVELETDECOMPOSITIONISTHEMOSTWIDELYUSEDMULTIRESOLUTIONTECHNIQUEINIMAGEPROCESSING34INTHISWORK,2DDISCRETEWAVELETTRANSFORMHASBEENUSEDTOEXTRACTMULTIPLESUBBANDFACEIMAGESTHESESUBBANDIMAGESCONTAINAPPROXIMATIONCOEFFICIENTSMATRIXANDDETAILSCOEFFICIENTSMATRICESLIKEHORIZONTAL,VERTICALANDDIAGONALCOEFFICIENTSOFFACESATVARIOUSSCALESONELEVELWAVELETDECOMPOSITIONOFAFACEIMAGEISSHOWNINFIG2FIG2SAMPLEONELEVELWAVELETDECOMPOSEDIMAGEINFIG2,FORBOTHTHEMETHODSA1ISTHEAPPROXIMATIONCOEFFICIENT,V1,H1ANDD1ARETHEVERTICAL,HORIZONTALANDDIAGONALDETAILSCOEFFICIENTSRESPECTIVELYSINGLELEVELDECOMPOSITIONISUSEDINBOTHVISUALANDTHERMALIMAGESFORMETHOD1AN80100PIXELSIMAGEISTAKENASINPUTANDAFTERDECOMPOSITIONFOUR4050PIXELSRESOLUTIONSUBBANDIMAGESA1,H1,V1ANDD1AREOBTAINEDINCASEOFMETHOD2,BOTHTHEINPUTIMAGESVISUALANDTHERMALAREOFSIZE80100AFTERSINGLELEVELDECOMPOSITION,ALLTHEGENERATEDCOEFFICIENTSA1,H1,V1ANDD1AREOFSIZE4050AGAINDECOMPOSITIONATLEVEL2HASBEENAPPLIEDONLYINAPPROXIMATIONCOEFFICIENTA1ANDAFTERTHAT,USINGONLYAPPROXIMATIONCOEFFICIENT,GETTINGAFTERLEVEL2DECOMPOSITION,THEQUOTIENTIMAGESOFSIZE4050HASBEENGENERATED22DAUBECHIESWAVELETTRANSFORMINTHISWORKDAUBECHIESDB1WAVELETHASBEENUSEDTODECOMPOSETHEIMAGESASWELLASTORECONSTRUCTTHEIMAGESALSODAUBECHIESDB1WAVELETISTHESAMEASHAARWAVELETSOTHEDISCUSSIONOFTHEHAARWAVELETISESSENTIALTOUNDERSTANDTHECONCEPTOFDAUBECHIESDB1WAVELETINMATHEMATICS,THEHAARWAVELETISACERTAINSEQUENCEOFFUNCTIONSTHISSEQUENCEWASPROPOSEDIN1909BYALFRDHAARHAARUSEDTHESEFUNCTIONSTOGIVEANEXAMPLEOFACOUNTABLEORTHONORMALSYSTEMFORTHESPACEOFSQUAREINTEGRABLEFUNCTIONSONTHEREALLINE18THEHAARWAVELETSMOTHERWAVELETFUNCTIONTCANBEDESCRIBEDAS101/2,11/21,0TTTOTHERWISE1ANDITSSCALINGFUNCTIONTCANBEDESCRIBEDAS101,0TTOTHERWISE2DAUBECHIESWAVELETTRANSFORMHASBEENUSEDINTHISWORKDAUBECHIESWAVELETSAREAFAMILYOFORTHOGONALWAVELETSA1V1H1D1IJCSIINTERNATIONALJOURNALOFCOMPUTERSCIENCEISSUES,VOL7,ISSUE3,MAY2010WWWIJCSIORG4DEFININGADISCRETEWAVELETTRANSFORMANDCHARACTERIZEDBYAMAXIMALNUMBEROFVANISHINGMOMENTSFORSOMEGIVENSUPPORTTHISKINDOF2DIMENSIONALDISCRETEWAVELETTRANSFORMDWTAIMSTODECOMPOSETHEIMAGEINTOAPPROXIMATIONCOEFFICIENTSCAANDDETAILEDCOEFFICIENTSCH,CVANDCDHORIZONTAL,VERTICALANDDIAGONALOBTAINEDBYWAVELETDECOMPOSITIONOFTHEINPUTIMAGEXTHE2DIMENSIONALDISCRETEWAVELETTRANSFORMDWTFUNCTIONSUSEDINMATLAB7ARESHOWNINEQUATION3ANDEQUATION4CA,CH,CV,CDDWT2X,WNAME3CA,CH,CV,CDDWT2X,LO_D,HI_D4INEQ3,WNAMEISTHENAMEOFTHEWAVELETUSEDFORDECOMPOSITIONINTHISWORKDB1HASBEENUSEDINCASEOFWNAMEEQ4LO_DDECOMPOSITIONLOWPASSFILTERANDHI_DDECOMPOSITIONHIGHPASSFILTERWAVELETDECOMPOSITIONFILTERSTHISKINDOFTWODIMENSIONALDWTLEADSTOADECOMPOSITIONOFAPPROXIMATIONCOEFFICIENTSATLEVELJINFOURCOMPONENTSTHEAPPROXIMATIONATLEVELJ1,ANDTHEDETAILSINTHREEORIENTATIONSHORIZONTAL,VERTICAL,ANDDIAGONALTHEFIG3DESCRIBESTHEALGORITHMICBASICDECOMPOSITIONSTEPSFORIMAGEWHERE,ABLOCKWITHADOWNARROWINDICATESDOWNSAMPLINGOFCOLUMNSANDROWSANDCA,CH,CVANDCDARETHECOEFFICIENTVECTORS373839CONSEQUENTLYTHERECONSTRUCTIONPROCESSISPERFORMEDUSINGINVERSEOFDWTIDWTWEHAVERECONSTRUCTEDTHEIMAGESBASEDONTHEAPPROXIMATIONCOEFFICIENTMATRIXCAFINALLYTHERECONSTRUCTEDIMAGEISUSEDASTHEINPUTTOPCAFORDIMENSIONREDUCTIONTHE2DIMENSIONALINVERSEDISCRETEWAVELETTRANSFORMIDWTFUNCTIONSUSEDINMATLAB7ARESHOWNINEQUATION5ANDEQUATION6XIDWT2CA,CH,CV,CD,WNAME5XIDWT2CA,CH,CV,CD,LO_R,HI_R6INVERSEDISCRETEWAVELETTRANSFORMIDWTUSESTHEWAVELETWNAMETOCOMPUTETHESINGLELEVELRECONSTRUCTIONOFANIMAGEX,BASEDONAPPROXIMATIONMATRIXCAANDDETAILEDMATRICESCH,CVANDCDHORIZONTAL,VERTICALANDDIAGONALRESPECTIVELYINTHEFIG4WEHAVESHOWNTHEALGORITHMICBASICRECONSTRUCTIONSTEPSFORANIMAGERESPECTIVELYTHEABOVECONCEPTSOFDISCRETEWAVELETTRANSFORMDWTFUNCTIONANDINVERSEDISCRETEWAVELETTRANSFORMIDWTFUNCTIONHAVEBEENUSEDFROMWAVELETTOOLBOXOFMATLAB7FIG3STEPSFORDECOMPOSITIONOFANIMAGEFORMETHOD1ANDMETHOD2FIG4STEPSFORRECONSTRUCTIONOFANIMAGEFORMETHOD223THEQUOTIENTFUSEDIMAGEOFTHERMALANDVISUALIMAGEIFTWOOBJECTSAREAANDB,WEDEFINETHEQUOTIENTIMAGEQBYTHERATIOOFTHEIRALBEDOFUNCTIONSAANDBCLEARLY,QISILLUMINATIONINVARIANTINTHEABSENCEOFANYDIRECTACCESSTOTHEALBEDOFUNCTIONS,ITHASBEENSHOWNTHATQCANNEVERTHELESSBERECOVERED,ANALYTICALLY,GIVENACOLUMNSCAJO_DI_D11ROWSO_DI_D22COLUMNSCAJ1CHJ1O_DI_D22COLUMNSCOLUMNSCVJ1HORIZONTALVERTICALCDROWSHORIZONTALDIAGONALAJ1ROWS1ROWSI_RO_RKEEPVERTICAL2HO_R2COLUMNSCOLUMNSCOLUMNSCOLUMNS22I_RO_RI_RCAJ1CHJ1CVJ1CDJ1WHERE,21O_RI_RUPSAMPLECOLUMNSINSERTZEROSATODDINDEXEDCOLUMNSUPSAMPLEROWSINSERTZEROSATODDINDEXEDROWSRECONSTRUCTIONLOWPASSFILTERDECOMPOSITIONHIGHPASSFILTERIJCSIINTERNATIONALJOURNALOFCOMPUTERSCIENCEISSUES,VOL7,ISSUE3,MAY2010WWWIJCSIORG5BOOTSTRAPSETOFIMAGESONCEQISRECOVERED,THEENTIREIMAGESPACEUNDERVARYINGLIGHTINGCONDITIONSOFOBJECTACANBEGENERATEDBYQANDTHREEIMAGESOFOBJECTBTHEDETAILSAREGIVENBELOWLET,STARTWITHTHECASEN1,IE,THEREISASINGLEOBJECT2IMAGESINTHEBOOTSTRAPSETLETTHEALBEDOFUNCTIONOFTHATOBJECTABEDENOTEDBYA,ANDLETTHETWOIMAGESBEDENOTEDBYA1,A2THEREFORE,AJANTSJ,WHERE,J1,2LETYBEANOTHEROBJECTOFTHECLASSWITHALBEDOYANDLETYSBEANIMAGEOFYILLUMINATEDBYSOMELIGHTINGCONDITIONS,IE,YSYNTSTHEQUOTIENTIMAGEQYOFOBJECTYAGAINSTOBJECTAISDEFINEDBY,YYAUVUVUVQ7WHEREU,VRANGEOVERTHEIMAGETHUS,THEIMAGEQYDEPENDSONLYONTHERELATIVESURFACETEXTUREINFORMATION,ANDTHUSISINDEPENDENTOFILLUMINATION40THEQUOTIENTIMAGEUSEDINTHISEXPERIMENTISTHEQUOTIENTOFTHEVISUALANDTHERMALIMAGEOFANOBJECTLET,THEVISUALIMAGEBEIANDTHETHERMALIMAGEBEJ,THENWECANCONSIDERTHEQUOTIENTIMAGECASFI/FJTHEABOVEMENTIONEDQUOTIENTIMAGINGTECHNIQUEISSAMEFORBOTHTHEMETHODSMETHOD1ANDMETHOD2BUTFIANDFJAREDIFFERENTFORMETHOD1ANDMETHOD2FORMETHOD1,FIRSTBOTHTHEVISUALANDTHERMALIMAGESHAVEBEENDECOMPOSEDATLEVEL1THEQUOTIENTIMAGESHAVEBEENGENERATEDUSINGALLTHEFOURCOEFFICIENTSOFTHEDECOMPOSEDIMAGESAPPROXIMATIONCOEFFICIENTANDDETAILSCOEFFICIENTSINTHREEORIENTATIONSHORIZONTAL,VERTICAL,DIAGONALINCASEOFMETHOD2,FIRSTTHEVISUALANDTHERMALIMAGESAREDECOMPOSEDATLEVEL2ANDAFTERTHATBOTHTHEIMAGESARERECONSTRUCTEDUSINGTHEAPPROXIMATECOEFFICIENTSTHESEIMAGESAREDECOMPOSEDANDRECONSTRUCTEDUSINGWAVELETDECOMPOSITIONANDRECONSTRUCTIONFUNCTIONFINALLYTHEQUOTIENTIMAGEISGENERATEDFROMBOTHTHERECONSTRUCTEDVISUALANDTHERMALFUNCTIONS24IMAGEFUSIONRULESATTHETIMEOFGENERATINGFUSEDIMAGESOFCOEFFICIENTSAPPROXIMATEANDDETAILS,THEABSOLUTEMAXIMUMOFTHERMALANDVISUALIMAGESWASSELECTEDTHEFUSIONMETHODUSEDTOGENERATEFUSEDIMAGEOFWAVELETTOOLBOXISPRESENTINTHEEQ8DABSTABSVCTDVD8WHERE,DISTHEABSOLUTEMAXIMUMMATRIXOFTTHERMALIMAGEANDVVISUALIMAGE,ABSTANDABSVARETHEABSOLUTEMATRICESOFTANDVANDCISTHEGENERATEDFUSEDIMAGEOFTANDVNOWATTHETIMETOFINDTHEABSOLUTEVALUEOFCORRESPONDINGTHERMALANDVISUALCOEFFICIENTSITWILLCALCULATETHEINTENSITYOFTHEEACHPIXELINCASEOFEQUATION8,ITWILLCHECKTHAT,XYXYTB,THENFORTHEFUSEDIMAGEOFCOEFFICIENTITWILLDOTHEFOLLOWINGOPERATIONGIVENINEQ9XYXYXYFTV9WHEREFXYISTHEPIXELVALUEOFTHEFUSEDIMAGECANDTHEMETHODSHOWNINEQ9ISTHEPROCESSTOCALCULATETHEPIXELVALUEFORFUSEDIMAGEOFTANDV25COMPARISONBETWEENQIANDSQIINTHISSECTION,ACOMPARISONANALYSISOFQUOTIENTIMAGEQIANDSELFQUOTIENTIMAGESQIHASBEENPRESENTEDACCORDINGTOTHECONCEPTPROPOSEDBYHAITAOWANG,STANZLIANDYANGSHENGWANG25SQIISDEFINEDASTHERATIOOFTHEINPUTIMAGEANDITSSMOOTHVERSIONSTHESELFQUOTIENTIMAGEQOFIMAGEICANBEEXPRESSEDASIIQIFI10WHEREISTHESMOOTHEDVERSIONOFIFISTHESMOOTHINGKERNELWECANCONSIDERTHESQIASONEKINDOFQIWHICHISDERIVEDFROMTHESAMEIMAGEIITSELFTHEDEFINITIONOFTHEQUOTIENTIMAGEPROVIDESANINVARIANTREPRESENTATIONOFFACEIMAGESUNDERDIFFERENTLIGHTINGCONDITIONS26PRINCIPALCOMPONENTANALYSISTHEPRINCIPALCOMPONENTANALYSISPCA41,42,43USESTHEENTIREIMAGETOGENERATEASETOFFEATURESANDDOESNOTREQUIRETHELOCATIONOFINDIVIDUALFEATUREPOINTSWITHINTHEIMAGEWEHAVEIMPLEMENTEDTHEPCATRANSFORMASAREDUCEDFEATUREEXTRACTORINOURFACERECOGNITIONSYSTEMHERE,EACHOFTHEQUOTIENTFUSEDFACEIMAGESAREPROJECTEDINTOTHEEIGENSPACECREATEDBYTHEEIGENVECTORSOFTHECOVARIANCEMATRIXOFALLTHETRAININGIMAGESREPRESENTEDASCOLUMNVECTORHERE,WEHAVETAKENTHENUMBEROFEIGENVECTORSINTHEEIGENSPACEAS40,BECAUSEEIGENVALUESFOROTHEREIGENVECTORSARENEGLIGIBLEINCOMPARISONTOTHELARGESTEIGENVALUES44454627ANNUSINGBACKPROPAGATIONWITHMOMENTUMNEURALNETWORKS,WITHTHEIRREMARKABLEABILITYTODERIVEMEANINGFROMCOMPLICATEDORIMPRECISEDATA,CANBEUSEDTOEXTRACTPATTERNSANDDETECTTRENDSTHATARETOOCOMPLEXTOBENOTICEDBYCOMPUTERTECHNIQUESATRAINEDNEURALNETWORKCANBETHOUGHTOFASAN“EXPERT“INTHECATEGORYOFINFORMATIONITHASBEENGIVENTOANALYZETHEBACKPROPAGATIONLEARNINGALGORITHMISONEOFTHEMOSTIJCSIINTERNATIONALJOURNALOFCOMPUTERSCIENCEISSUES,VOL7,ISSUE3,MAY2010WWWIJCSIORG6HISTORICALDEVELOPMENTSINNEURALNETWORKSITHASREAWAKENEDTHESCIENTIFICANDENGINEERINGCOMMUNITYTOTHEMODELINGANDPROCESSINGOFMANYQUANTITATIVEPHENOMENAUSINGNEURALNETWORKSTHISLEARNINGALGORITHMISAPPLIEDTOMULTILAYERFEEDFORWARDNETWORKSCONSISTINGOFPROCESSINGELEMENTSWITHCONTINUOUSDIFFERENTIABLEACTIVATIONFUNCTIONSSUCHNETWORKSASSOCIATEDWITHTHEBACKPROPAGATIONLEARNINGALGORITHMAREALSOCALLEDBACKPROPAGATIONNETWORKS471225353EXPERIMENTSANDDISCUSSIONEXPERIMENTSAREPERFORMEDTOEVALUATEQUOTIENTIMAGEQIFORFACERECOGNITION,USINGIRISDATABASETHISWORKHASBEENSIMULATEDUSINGMATLAB7INAMACHINEOFTHECONFIGURATION213GHZINTELXEONQUADCOREPROCESSORAND1638400MBOFPHYSICALMEMORYASTHEBOTHRECONSTRUCTEDVISUALANDTHERMALIMAGESHASBEENUSEDTOGENERATEQUOTIENTFUSEDIMAGES,SOFIRSTOFALLORIGINALIMAGESARECROPPEDMANUALLY31OTCBVSDATABASETHEEXPERIMENTSWEREPERFORMEDONTHEFACEDATABASEWHICHISOBJECTTRACKINGANDCLASSIFICATIONBEYONDVISIBLESPECTRUMOTCBVSBENCHMARKDATABASECONTAININGASETOFTHERMALANDVISUALFACEIMAGESTHISISAPUBLICLYAVAILABLEBENCHMARKDATASETFORTESTINGANDEVALUATINGNOVELANDSTATEOFTHEARTCOMPUTERVISIONALGORITHMSTHEBENCHMARKCONTAINSVIDEOSANDIMAGESRECORDEDINANDBEYONDTHEVISIBLESPECTRUMITCONTAINSDIFFERENTSETSOFDATALIKEOSUTHERMALPEDESTRIANDATABASE,IRISTHERMAL/VISIBLEFACEDATABASE,OSUCOLORTHERMALDATABASE,TERRAVICFACIALIRDATABASE,TERRAVICWEAPONIRDATABASEANDCBSRNIRFACEDATASETAMONGALLOFTHESEDIFFERENTDATASETS,MAINLY,VISUALIMAGESFROMIRISTHERMAL/VISIBLEFACEDATASETHAVEBEENUSEDINTHISDATASET,THEREARE2000IMAGESOFVISUALAND2000THERMALIMAGESOF16DIFFERENTPERSONSINCASEOF