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New Information Theoretic Distance Measures and Algorithms for Multimodality Image Registration

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FirstlyIextendmythankstomyadvisorDr.AnandRangarajanforhisexcellentacademicguidanceandopen-mindedresearchsupport.ItwaspleasurebuttoughtopursuemyPhDdegreeunderhisadvisingandpressing.Workingwithhimfor5yearswasworthyandfruitful,fromwhichmyfuturewillbenet.IalsoexpressmythankstoDr.ArunavaBanerjee,Dr.YunmeiChen,Dr.JorgPetersandDr.BabaC.Vemurifortheirwillingnesstoserveonmycommitteeandtheirvaluablecommentstothedissertation.IalsothankmyfellowstudentsHongyuGuo,FeiWang,BinJian,EricSpellman,SanthoshKodipakaandAjitRajwadefortheirhelpandsupportinstudyingandresearch.AndIalsoextendmythankstomyfriends:XiaohuiGao,WeihongGuo,QingguoZeng,HongchaoZhangandothers,whohelpedandsupportedmeinmylifeandstudyingatUF.FinallyIwouldexpressmyappreciationstomyparentsandsisterfortheirunderstandingandencouragementinmylife. iv

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page ACKNOWLEDGMENTS ............................. iv LISTOFTABLES ................................. viii LISTOFFIGURES ................................ x ABSTRACT .................................... xiv CHAPTER 1INTRODUCTION .............................. 1 1.1WhatisRegistration? ......................... 2 1.2ContributionsoftheDissertationWork ............... 4 1.2.1ABayesianMultimodalityNonrigidImageRegistrationMethod ............................. 4 1.2.2AUniedFeature-basedRegistrationMethodforMulti-modalityImages ........................ 5 1.2.3MultimodalityImageRegistrationUsinganExtensibleIn-formationMetricandHighDimensionalHistogramming .. 5 1.3OutlinesoftheDissertation ..................... 6 2RELATEDPREVIOUSWORK ....................... 9 2.1Feature-basedMethods ........................ 9 2.1.1Point-basedRegistration ................... 9 2.1.2Surface-basedRegistration .................. 10 2.1.3Edge-basedRegistration ................... 12 2.1.4OtherFeature-basedRegistration .............. 12 2.2Intensity-basedRegistration ..................... 12 2.2.1MutualInformation ...................... 13 2.2.2NormalizedCrossCorrelation ................. 14 2.2.3EntropyofDierenceImageandPatternIntensity ..... 14 2.2.4JointEntropyandJointProbability ............. 15 2.2.5OtherMeasures ........................ 16 2.3MultimodalityImageRegistration .................. 16 2.3.1MutualInformation ...................... 16 2.3.2JensenDivergence ....................... 18 2.3.3MinimumEntropyofBadPrediction(MEBP) ....... 19 v

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.......... 20 3.1ConditionalDensityEstimation ................... 20 3.2BayesianNon-rigidRegistration ................... 21 3.3ConvergenceoftheBayesianMAPMinimizerintheGeneralSet-ting ................................... 23 4AUNIFIEDFEATURE-BASEDREGISTRATIONMETHODFORMUL-TIMODALITYIMAGES ........................... 29 4.1FeatureCombination ......................... 30 4.2AneImageRegistrationwiththe\Best"FeatureImages .... 31 5SIMULTANEOUSMULTIMODALITYIMAGEREGISTRATIONUS-INGANEXTENSIBLEINFORMATIONMETRICANDHIGHDI-MENSIONALHISTOGRAMMING ..................... 32 5.1MultimodalityRegistrationUsingtheExtensibleMetric ...... 33 5.1.1MetricDenition ....................... 33 5.1.2RelationshipbetweentheInformationMetricandMutualInformation .......................... 34 5.1.3AneRegistrationbyMinimizingtheMetric ........ 35 5.1.4NormalizedVersionsofourMetric .............. 36 5.2ExtensiontotheMultimodalityCase ................ 37 5.3ComputingtheEntropyofMultipleRandomVariables ...... 40 5.4AnotherMeasureforMultimodalityImageRegistration ...... 43 6NONRIGIDMULTIMODALITYIMAGEREGISTRATION ....... 46 6.1NonrigidMultimodalityImageRegistration ............. 46 6.2B-SplinesforFlowFieldRepresentation ............... 47 6.3MultiresolutionOptimizationoverB-Spline ............. 48 7EXPERIMENTALRESULTS ........................ 52 7.1ExperimentalResultsontheBayesianMultimodalityNonrigidImageRegistration .......................... 52 7.1.1ExperimentsonSimpleMultimodalityShapeImages .... 53 7.1.2ExperimentsonSimulatedT1andT22DMRImages ... 54 7.2ExperimentalResultsontheUniedFeature-basedRegistrationMethodforMultimodalityImages .................. 56 7.2.1RobustnessofFeatureImagestoNoise ........... 56 7.2.2AneRegistrationofPDandT22DImageSlices ..... 57 7.2.3BootstrappingtheFeatureCombinationWithImperfectRegistration .......................... 61 7.3ExperimentalResultsontheAneImageRegistrationUsingtheUpperBoundoftheInformationMetric ............... 63 vi

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... 63 7.3.2MatchingFaceImagesObtainedunderDierentIllumina-tions .............................. 66 7.4ExperimentalResultsontheAneMultimodalityImageRegis-trationusingtheInformationMetricandHighDimensionalHis-togramming .............................. 69 7.4.1Multimodalityvs.Intermodality:SimultaneousRegistra-tionof3ImagesandPair-wiseRegistrationonSyntheticPD,T2andT1MRImages .................. 69 7.4.2UnbiasedMultimodalityImageRegistrationofVisibleHu-manData ........................... 74 7.4.3MultimodalityImageRegistrationonSyntheticMRData 80 7.5ExperimentalResultsontheNonrigidMultimodalityImageReg-istrationUsingtheInformationMetricandHighDimensionalHis-togramming .............................. 82 7.5.1ValidityofMultiresolutionOptimizationAlgorithmsoverB-Spline ............................ 82 7.5.1.1Validityofintermodalityregistrationwithsyn-theticPDandT23DMRimages ......... 82 7.5.1.2ValidityofmultimodalityregistrationwithVisi-bleHumanDataincluding2Danatomicalphoto,CTandMRPD ................... 85 7.5.2Intermodalityvs.Multimodality:ComparisonofSimul-taneousMultimodalityRegistrationandPair-wiseInter-modalityRegistrationof3DImages ............. 89 7.5.3UnbiasedNonrigidRegistrationon3DMRImages ..... 93 8CONCLUSIONSANDFUTUREWORK .................. 96 APPENDIX:PROOFSOFTHETRIANGLEINEQUALITYOFTHEMET-RIC ......................................... 98 REFERENCES ................................... 101 BIOGRAPHICALSKETCH ............................ 108 vii

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Table page 7{1Registrationresultsof2DsagittalPDandT2slicesusingintensityandbestfeaturepair ............................ 59 7{2Registrationresultsof2DcoronalPDandT2slicesusingintensityandbestfeaturepair ............................ 60 7{3Registrationresultsof2DaxialPDandT2slicesusingintensityandbestfeaturepair .............................. 60 7{4Registrationresultsof2DsagittalPDandT2slicesbeforeandafterbootstrap .................................. 61 7{5Registrationresultsof2DcoronalPDandT2slicesbeforeandafterbootstrap .................................. 62 7{6Registrationresultsof2DaxialPDandT2slicesbeforeandafterboot-strap .................................... 62 7{7Resultsof2Dslicealongsagittaldirection ................ 63 7{8Resultsof2Dslicealongcoronaldirection ................ 65 7{9Resultsof2Dslicealongaxialdirection ................. 66 7{10Resultsunderdierentlightingconditions(leftlighton,rightlighton,andnolighton)andwearingsunglasses .............. 67 7{11Resultsunderdierentlightingconditions(leftlighton,rightlighton,andnolighton)andwearingascarf ................ 68 7{12Resultsunderdierentlightingconditions(leftlighton,rightlighton,andnolighton)andwearingsunglassesorascarf ........ 69 7{13Meanerrorsondierentaneparametersintherstexperimentwithnoise0.1 .................................. 72 7{14MeanerrorsofdierentaneparametersinthesecondexperimentwithGaussiannoisewithmean0andstd.0.2 .............. 73 7{15Resultsofunbiasedregistrationofanatomicalslice,CT,MRPD,T1andT2images.[Datasetindex:VHD#1080.] ............. 76 viii

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........ 77 7{17Resultsofunbiasedregistrationofanatomicalslice,CT,MRPD,T1andT2images.[Datasetindex:VHD#1110.] ............. 77 7{18Numberofpixelsinnonoverlapregionofsegmentedimagesbeforeandafterregistration.Uppertriangleisbeforeregistrationandlowertri-angleisafterregistration.[Datasetindex:VHD#1110.] ....... 78 7{19Resultsofunbiasedregistrationofanatomicalslice,CT,MRPD,T1andT2images.[Datasetindex:VHD#1165.] .............. 79 7{20Numberofpixelsinnonoverlapregionofsegmentedimagesbeforeandafterregistration.Uppertriangleisbeforeregistrationandlowertri-angleisafterregistration.[Datasetindex:VHD#1165.] ....... 79 7{21SSDsofintensityofpairwiseMRPDimagesbeforeandafterregistra-tion.uppertriangleisbeforeregistrationandlowertriangleisafterregistration ................................. 82 7{22DDF,ADFandSSDofintermodalityregistrationofsynthetic3DMRPDandT2imagesbeforeandafterregistration. ............ 83 7{23Crosscorrelationoftheimagesbeforeandafterregistration.Uppertriangleisbeforeregistrationandlowertriangleisafterregistration.[Datasetindex:VHD#1080.] ....................... 86 7{24Numberofpixelsinnonoverlapregionofsegmentedimagesbeforeandafterregistration.Uppertriangleisbeforeregistrationandlowertri-angleisafterregistration.[Datasetindex:VHD#1080.] ........ 87 7{25DDFsandSSDsofSimultaneousregistrationof3imagesvs.pair-wiseregistrationonsyntheticPD,T2andT13DMRimagesbeforeandafterregistration.Therstrowistheerrorsbeforeregistration,thesecondrowistheerrorsafterintermodalityregistrationandthethirdrowistheerrorsaftermultimodalityregistration. ......... 90 7{26SSDsbeforeregistrationandafterunbiasedmultimodalityregistra-tionof3MR3Dimages.Uppertriangleisbeforeregistrationandlowertriangleisafterregistration. ....................... 93 ix

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Figure page 1{1Examplesofmultimodalitybrainimages:thephotographsintherstrowfromlefttorightareMRT2,SPECTandPETbrainimages,whichcomefromTheWholeBrainAtlas(http://www.med.harvard.edu/AANLIB/home.html);thesecondrowfromlefttorightareanatomicalphotograph,CTandMRPDBrainimages,whicharefromAtlasoftheVisibleHumanMale. .................... 1 1{2Multimodalityimageregistration .................... 2 2{1DenitionsofmutualinformationandmodiedMIofthreeimages(shadedareas) ............................... 17 5{1Venndiagramfortworandomvariables ................. 34 5{2ThemetricandmutualinformationbetweenPDandrotatedandscaledT2images ............................. 35 5{3,MIandMMIwithrotation(2ndrow)andscaling(3rdrow)ofMRPD,MRT2andMRT1images .................. 39 5{4withrotationandscalingofPD,rotatedT2androtatedT1images 45 7{1Leftandmiddle:twosimpleshapeimages.Right:nalregistrationresult. ................................... 53 7{2Thechangesini)log-likelihood,ii)mutualinformation,iii)jointprob-abilityandiv)negativejointentropywhenminimizingtheBayesianMAPobjectivefunction. ......................... 54 7{3Leftmost:transverseT2image.Leftmiddle:transverseT1image.Middle:DeformedT1.Rightmiddle:IntensitydierencebetweenoriginalT1anddeformedT1priortoregistration.Right:UnwarpednalT1image ............................... 54 7{4Thechangesini)log-likelihood,ii)mutualinformation,iii)jointprob-abilityandiv)negativejointentropywhenminimizingtheBayesianMAPobjectivefunction. ......................... 55 x

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................................ 55 7{6Leftmost:OriginalT1image,Leftmiddle:deformedT1image.Mid-dle:IntensitydierencebetweenoriginalT1anddeformedT1beforeregistration.Rightmiddle:IntensitydierencebetweenoriginalT1andunwarpedT1afterregistration.Right:UnwarpednalT1im-age.ThebeforeandafterSSDswere647and59respectively. ..... 56 7{7Left:Fromtoptobottom,NMIbetweentheoriginalintensitypairwithrotation.Right:Fromtoptobottom,NMIbetweenthebestfeatureimagepairwithrotation.Therotationrangeisfrom-20de-greesto20degrees.Fromtoptobottom:addedGaussiannoisewithmean0anddeviation0,0.1,0.2and0.4. ................ 58 7{8Sagittal2Dslices ............................. 59 7{9Coronal2Dslices ............................. 59 7{10Axial2Dslices ............................... 60 7{11Sagittal2Dslice .............................. 64 7{12Coronal2Dslice ............................. 65 7{13Axial2Dslice ............................... 66 7{14Imagesunderdierentlightingconditions(leftlighton,rightlighton,andnolighton)andwearingsunglasses .............. 67 7{15Imagesunderdierentlightingconditions(leftlighton,rightlighton,andnolighton)andwearingascarf ................ 68 7{16Imagesunderdierentlightingconditionsandwearingsunglassesorscarf .................................... 69 7{17Plotsofsumof^T1T1+^T2T2of30trialsrecoveredbytenmeasuresintherstexperimentwithnoisestd.0.1.Numbers1to10represent,,,,,,mMI,pMI,mNMIandpNMI|thetenreg-istrationmeasures. ............................ 72 7{18Plotsofsumof^T1T1+^T2T2of30trialsrecoveredbytenmeasuresinthesecondexperimentwithnoise0.2.Numbers1to10represent,,,,,,mMI,pMI,mNMIandpNMI|thetenregis-trationmeasures. ............................. 73 xi

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....... 76 7{20Segmentedimagesbefore(1strow)andafter(2ndrow)registration.[Datasetindex:VHD#1080.] ...................... 76 7{21Therstrowisthesetofimagespriortoregistration;thesecondrowisthesetafterregistration.[Datasetindex:VHD#1110.] ....... 77 7{22Segmentedimagesbefore(1strow)andafter(2ndrow)registration.[Datasetindex:VHD#1110.] ...................... 78 7{23Therstrowisthesetofimagesbeforeregistration;thesecondrowisthesetafterregistration.[Datasetindex:VHD#1165.] ....... 78 7{24Segmentedimagesbefore(1strow)andafter(2ndrow)registration.[Datasetindex:VHD#1165.] ...................... 79 7{25Therstrowaretheimagesbeforeregistrationand2ndrowistheimagesafterregistration. ........................ 81 7{26CorrespondingMRPDimagesbeforeandafterregistration. ..... 81 7{27Someslicesof3DMRPDandT2imagesbeforeregistration. ..... 84 7{28Someslicesof3DMRPDandT2imagesafterregistration. ...... 84 7{29Anatomicalphotoandoverlapof3imagesbeforeandafterregistration. 85 7{30CTimagebeforeandafterregistrationanddeformedgridwithdis-placementeld. .............................. 86 7{31PDimagebeforeandafterregistrationanddeformedgridwithdis-placementeld. .............................. 86 7{32Segmentedimagesbeforeregistration. ................. 87 7{33Segmentedimagesafterregistration. .................. 87 7{34Someslicesof3DMRT2images(targetintheregistration). ..... 91 7{35Someslicesof3DMRT1andPDimagesbeforeregistration. ..... 91 7{36Someslicesof3DMRT1andPDimagesafterregistration. ...... 92 7{37Deformedgridwithdisplacementeldsof3DMRT1andPDimagesinregistration. ............................... 92 7{38SomeslicesofthreeMR3Dimagesbeforeregistration. ........ 94 7{39SomeslicesofthreeMR3Dimagesafterregistration. ......... 94 xii

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............................. 94 xiii

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Accuratecomparisonandalignmentofmultimodalityimagesgivevitalintegratedinformationtocliniciansandresearcherswhichhasapayoinclinicalpractice.Acriticalstageinthisprocessisthealignmentorregistrationoftheimages,whichisthetopicofmydissertation. First,wepresentaBayesianmultimodalitynon-rigidimageregistrationmethod.WeprovethatthedisplacementeldwhichminimizestheBayesianmax-imumaposteriori(MAP)objectivealsomaximizesthetruemutualinformation(withasmalldeformationpenalty)asthenumberofpixelstendstoinnity.Thecriterionimposesanupperboundonthenumberofpermissiblecongurationsofthedisplacementeld. Second,weproposeanewregistrationmethodformultimodalityimages,whichcombinesfeaturesandintensitiesoftheimagesinregistration.Wemaximizethenormalizedmutualinformation(NMI)overthe\bestfeatures"oftwoimagesinsteadofjustusingintensityasafeature.The\bestfeature"isachievedbyndingthebestprojectionontoasinglefeatureimagebymaximizingtheNMIbetweenthetworegisteredimages(trainingsets)w.r.t.theprojectionweights. xiv

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Finally,wepresentanextensibleinformationmetricformultimodalityimageregistration.Anditsnormalizedversionisstillapseudometricandisequivalenttonormalizedmutualinformationintheintermodalitycase.Whencomparedtomutualinformation,itiseasiertoextendourmetrictotheregistrationofmultipleimages.Afterusinganewtechniquetoecientlycomputehighdimensionalhistograms,themetriccanbeecientlycomputedeveninthemultipleimagecase.Andweusethemetricandhighdimensionalhistogramtoaneandnonrigidmultimodalityimageregistration.Innonrigidregistration,displacementeldisrepresentedbyB-Splineandthemultiresolutionoptimizationalgorithmsareusedfornonrigidintermodalityandmultimodalityimageregistration.Wecomparetheresultsofdirectmultimodalityregistrationusinghigh-dimensionalhistogrammingwithrepeatedintermodalityregistration.Wendthatregistering3imagessimultaneouslywiththenewmetricismoreaccuratethanpair-wiseregistrationontheimagesobtainedfromsyntheticmagneticresonance(MR)protondensity(PD),MRT2andMRT13DvolumesfromBrainWeb.Weperformtheunbiasedaneregistrationof5multimodalityimagesofanatomy,CT,MRPD,T1andT2fromVisibleHumanMaleDataandtheunbiasednonrigidregistrationofthreeMR3Dimagesofthebrainwiththenormalizedmetricandhigh-dimensionalhistogramming.Ourresultsdemonstratetheecacyofthemetricsandhigh-dimensionalhistogramminginaneandnonrigidmultimodalityimageregistration. xv

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Medicalimageanalysisisgettingmoreandmoreimportantfordiagnosis,treatment,surgeryandhealthcare.Andmedicalimageanalysistechniquescanbeusedinneuroscienceandbioengineeringdomains.Fourimportantradiologicalimagingmodalitiesarecomputedtomography(CT),magneticresonanceimaging(MRI),singlephotonemissioncomputedtomography(SPECT)andpositronemissiontomography(PET).Generallyspeaking,structuresareimagedwithCTandMRI,whereasfunctionismeasuredwithSPECTandPETandfunctional (a)MRT2 (b)SPECT (c)PET (d)anatomicalphoto (e)CT (f)MRPD Figure1{1. Examplesofmultimodalitybrainimages:thephotographsintherstrowfromlefttorightareMRT2,SPECTandPETbrainimages,whichcomefromTheWholeBrainAtlas(http://www.med.harvard.edu/AANLIB/home.html);thesecondrowfromlefttorightareanatomicalphotograph,CTandMRPDBrainimages,whicharefromAtlasoftheVisibleHumanMale. 1

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MRI(fMRI).Inadditiontotheseimagingmodalities,thereareotherimportantin-vivomodalitiessuchasX-ray,ultrasound,traditionalprojectionradiographs,digitalportallms,etc.Figure 1{1 showssomeexamplesofdierentbrainimagemodalities. Accuratecomparisonandoverlayofthesemultimodalityimageswillgiveintegratedinformationtocliniciansandresearchersinmedicineandbiology.Acriticalstageinthisprocessofcomparisonand/oroverlayisthealignmentorregistrationoftheimages,whichisthetopicofmydissertation. Figure1{2. Multimodalityimageregistration

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registrationisamappingTortransformationbetweenthecoordinatesystemsoftwoimagesI(1)andI(2)suchthatimageI(1)andtransformedimageI(2)(T)withthetransformationThavesimilarstructures/featuresatthesameposition.Sinceitturnsouttobequitediculttodeneimagesimilarity,wecallthisaquasi-formaldenition.Informally,wecallitalignmentofimages. ForexamplewhenweregistertwoimagesattherstrowinFigure 1{2 ,weknowthepointPintherstimageshouldcorrespondtothepointQinthesecondimage.HencewelookforatransformationTsuchthatT(xq;yq)=(xp;yp).AfterwendthepropertransformationT,weusethetransformationTtotransformthesecondimagetothebottomimageinFigure 1{2 .Thisistheprocessofregistration. Formostcurrentapplicationsofmedicalimageregistration,atransformationTisamappingfrom2Dspaceto2Dspaceorfrom3Dspaceto3DspacebutsomespecialcasesrequireTtobefrom3Dspaceto2Dspace,suchastheregistrationof3DCTto2Ddigitalradiography.Dependingonthepurposeofregistrationandthepropertyofimages,thetransformationTcanbearigidtransformation,anetransformationornonrigidtransformation.Forarigidtransformation,therearethreefreeparametersinamappingfrom2Dspaceto2Dspace:onerotationandtwotranslations.Forarigidmappingfrom3Dspaceto3Dspace,therearesixfreeparameters:threerotationsandthreetranslations.Ananetransformationhasmorefreeparameters:scalingandshearbesidesrotationandtranslation.Eachanetransformationhassixfreeparametersinmappingfrom2Dspaceto2Dspaceincludingonescaling,oneshear,tworotationsandtwotranslationsorhastwelvefreeparametersinmappingfrom3Dspaceto3Dspace.Hence,arigidtransformationisananetransformationwithoutscalingandshear.IfThasmoreparametersthanananetransformation(for2D-2Dorfor3D-3D),wecallitanonrigidtransformation.

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Inthenextsection,wereviewsomerelatedworksinmultimodalityimageregistra-tion. InChapter2,wereviewsomerelatedpreviousworkonmultimodalityimageregistration.Dependingonwhatisusedintheregistration,theworksarecatego-rizedintotwogroup:intensity-andfeature-basedmethods.Inthefeature-basedmethods,wereviewsomepaperswhichusefeaturessuchaspoints,edges,curvesorsurfaceinmultimodalityimageregistration.Intheintensity-basedmethods,were-viewsomepaperswhichusedierentintensitysimilaritymeasuresinmultimodalityimageregistration.Wealsoreviewsomepaperswheremultipleimageareregisteredinsametime. InChapter3,wepresentaBayesianmultimodalitynon-rigidimageregis-trationmethod.Sincethelikelihoodisunknowninthegeneralmultimodalitysetting,weuseadensityestimatorasadropinreplacementforthetruelikeli-hood.Thepriorisastandardsmalldeformationpenaltyonthedisplacementeld.Sincemutualinformation-basedmethodsareinwidespreaduseformul-timodalityregistration,weattempttorelatetheBayesianapproachtomutualinformation-basedapproaches.Tothisend,wederiveanewcriterion|asucientcondition|which,whensatised,guaranteesthatthedisplacementeldwhichminimizestheBayesianmaximumaposteriori(MAP)objectivealsomaximizesthetruemutualinformation(withasmalldeformationpenalty)asthenumberofpixelstendstoinnity.Thecriterionimposesanupperboundonthenumberofpermissiblecongurationsofthedisplacementeld.

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InChapter4,weproposeanewregistrationmethodformultimodalityimages,whichcombinesfeaturesandintensitiesoftheimagesinregistration.Wemaximizethenormalizedmutualinformation(NMI)overthe\bestfeatures"oftwoimagesinsteadofjustusingintensityasafeature.The\bestfeature"isachievedbyndingthebestprojectionontoasinglefeatureimagebymaximizingtheNMIbetweenthetworegisteredimages(trainingsets)w.r.t.theprojectionweights.Thenweusethesameprojectioncoecientsonnewtestimagestoobtaintheir\bestfeatures."Weshowthatusingthenewbest\feature"ismorenoiseresistantthanusingimageintensityasthedefaultfeature.Andweextendtheideatothebootstrapcase,whereinthebestfeaturecombinationiscomputedusingtheimperfectlyregisteredpairofimages(obtainedbyusingNMIontheoriginalintensitypair)asatrainingset. InChapter5,wepresentanextensibleinformationmetricformultimodalityimageregistration.Fortheintermodality(2-image)case,givenimagesAandB,thepseudometricusedhereisthesumoftheconditionalentropiesH(AjB)andH(BjA).Andweshowthatthenormalizedversionofthepseudometric[thepseudometricdividedbythejointentropyH(A;B)]isstillapseudometricandisequivalenttonormalizedmutualinformationintheintermodalitycase.Weshowthatwhencomparedtomutualinformationwhichcanevenbecomenegativeinthemultipleimagecase,itiseasiertoextendourmetrictotheregistrationofmultipleimages.Afterusinganewtechniquetoecientlycomputehighdimensionalhistograms,weshowthatthemetriccanbeecientlycomputedeveninthemultipleimagecase. InChapter6,weusethenormalizedmetricandhighdimensionalhistogram-mingtothenonrigidregistrationofmultimodalityimages.Forrecoveringlocaldeformation,wewilluseB-SplinestorepresentoweldsofpixelsbecauseB-SplineshavegoodlocalapproximationaslongasthegridsofB-Splinesarene

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enough.Andwealsoproposemultiresolutionoptimizationalgorithmfornonrigidmultimodalityimageregistration. InChapter7,wepresenttheexperimentstosupportmeasuresandalgorithmsproposedinpreviouschapters.ThemostdatausedinexperimentsareBrain-websyntheticMRT1,T2andPDimagesandVisibleHumanDataincludinganatomicalphoto,CT,MRT1,T2andPDdata. InChapter8,wedrawtheconclusionforourworksandproposesomepossibledirection,whichcanbedoneinthefuture.

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Afundamentaldistinctionmadebymanyresearchersworkinginmultimodalityimageregistration[ 1 2 3 ]isbetweenintensity-andfeature-basedmethods.Wewillreviewsomerelatedworksinthesetwocategories. 4 ],Alkeretal.[ 5 ]andWorzandRohr[ 6 ]. Giventwopointsetswiththesamecardinalityandwithknowncorrespon-dence,ifthedesiredtransformationisrigid,theproblemisaclassicalProcrustesproblem(Small[ 7 ]).Thetransformationcanbesolvedusingsingular-valuede-compositions(SVD)(DrydenandMardia[ 8 ]).Ifthetransformationisane,theproblemisastandardleastsquaresproblem(GolubandLoan[ 9 ]).Fornonrigidtransformations,theproblemgetsharder.Thinplatesplines(TPS)areusedinChuiandRangarajan[ 10 ]andBelongieetal.[ 11 ].AnddieomorphismsareusedinJoshiandMiller[ 12 ]. 9

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Foragiventransformation,thecorrespondenceproblembecomesalinearassignmentproblem,whichcanbesolvedusingaHungarianmethod(Papadim-itriouandSteiglitz[ 13 ])ormoreecientlyusingtheShortestAugmentingPathAlgorithm(JonkerandVolgenant[ 14 ]). Apopularalgorithmforpointmatchingistheiterativeclosestpointsalgo-rithm(ICP)(BeslandMcmay[ 15 ]),whichalternativelysolvesforcorrespondencebyndingtheclosestpointinonepointsetforeachpointinanotherpointsetandusesthestandardleastsquaressolutionforthetransformation.TheICPalgorithmiswidelyusedinmedicalimagingapplications(Cuchetetal.[ 16 ],Declercketal.[ 17 ],andMaureretal.[ 18 ]).However,ICPcanbequitesensitivetochangesinfeaturelocationsandfalsepositivesindetectionofclosestpoints.Thisproblemwaspartiallyxedintheadaptive-thresholdworkofFeldmarandAyache[ 19 ].Inaddition,ChuiandRangarajan([ 10 ])notedtheproblemswithrobustnesstonoiseandoutliersandproposedanewnonrigidpointmatchingalgorithmbasedonclusteringandsoftassignmentknownasrobustpointmatching(RPM)whichtheyusedtoregister3Dcorticalanatomicalstructures[ 20 ].Shapecontexts[ 11 ]arealsousedinnonrigidpointmatchingalthoughitcontributesmoreinobjectrecognition.Theshapecontextsapproachdenesanewenergyfunctionwith2distanceofhistogramsofradiusandangleforeachpointinsteadofusingEuclideandistancesbetweenpoints,whichmakesuseofthegeometricinformationoftheneighborhoodofeachpointandhasgoodperformanceinmatchingandrecognition.

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Pelizzariandcolleagues[ 21 22 ]proposedasurfacettingtechniqueforregis-trationofimagesoftheheadthatbecameknownasthehead-and-hatalgorithm.Twosurfacesareextractedfromtwoimages.Oneiscalledtheheadsurface.Anotheriscalledthehatsurface.Thetransformationisiterativelysolvedbytransformingthehatsurfaceuntilthesquareofthedistancebetweenapointonthehatandthenearestpointontheheadachievesitslocalminimum.ThePowellmethodwasusedforoptimization.Becauseofthedeformationoftwosurfaces,thenearestpointdoesnotalwayslieinthedirectionoftheheadcentroid.Thusthisalgorithmisnotrobusttocaseswithhighdeformation.Usingadistancetransformtoprelabelallvoxelsintheimagewiththeirdistancefromthesurfaceoftheobjectcanreducecomputationcostinthealgorithm;Jiangetal.[ 23 ]andElsen[ 24 ]usethechamferlter[ 25 ]asadistancetransformationforrigidregistration.HuangandMitchell[ 26 ]usedEuclideandistancetransformstoachievethesamegoal. Recently,apromisingsurfacematchingalgorithmwasproposedbyGuetal[ 27 ],inwhichallsurfacesaretreatedasRiemannsurfaces.Thatmeansallsurfaceshaveintrinsicconformalstructuresandareinvariantsunderglobeconformaltransformationgroups.Asurfacecanbetransformedwithaconformalmappingtoasphereorplaneafterwhichsubsequentmatchingonsphereorplaneisrelativelyeasier.Thisapproachwasusedforcorticalsurfacematching[ 28 ]. Inthe2Dcase,contoursorcurvesarealsousedinregistration.Lietal.[ 29 ]proposedtwocontour-basedmethodswhichuseregionboundariesandotheredgesasfeatures.Theyusecorrelationandothershapesimilaritycriteriatoregisterthesefeatures.Recently,Klassenetal.[ 30 ]proposedanewcurve-basedmethod(closedcurve).Theyproposednewrepresentationsofcurvesusingtheirdirectionfunctionsandcurvaturefunctions.Thecurvesarematchedbysolvingforthetangentthatconnectsanytwoshapesviaageodesicintheshapespace.

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31 ]usedseveraledgeorridgedetectorsforCTandMRimagesandusedcross-correlationtoregisterthefeatureimages.MoredetailontheirmethodscanbefoundinElsen[ 24 ]. 32 ]presentalocalfrequencybasedregistrationmethod.ThelocalfrequencyimagerepresentationisobtainedbylteringtheimageswithaGaborltertunedtoacertainfrequency/orientationandthencomputingthegradientofthephaseofthelteredimages.Tomatchthelocal-frequencyrepresentationsoftheimagepair,theyminimizetheintegralofthesquarederrorbetweenaGaussianmodeloftheresidualanditstruedensityfunction.Theresidualisthedierencebetweenthelocalfrequencyrepresentationsofthetransformedsourceandtargetimages.TheyregisterthemisalignedMRbrainimagesusingdierentprotocols.Thismethodhasgoodperformanceonimageswithlargenonoverlapregion. Heroandhiscolleagues[ 33 34 ]usefeaturesextractedbyindependentcompo-nentanalysis(ICA)inregistration.Theyusetheminimumspanningtree(MST)toestimatethe-entropyafterwhichtheyminimizethe-JensendivergenceoftwoICAfeaturesets.TheyappliedtheirmethodtoMRbrainimages.Sincethisisreallyanintensity-basedsimilaritymeasure,wedeferdiscussionofthistothenextsection.

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importantneedinintensity-basedmethodsisagoodimageintensitysimilaritymeasure.Forintermodalityregistrationofimages,thereareseveralgoodmeasuresthathavebeenproposed.Insharpcontrast,formultimodalityregistrationwhichrequirestheregistrationofmorethantwoimages,therearenotmanygoodmeasures. 35 ]andCollignonetal.[ 36 ]usedmutualinformationinimageregistration,therehavebeenhundredsofpapers[ 37 ]onimageregistrationusingmutualinformation. ThedenitionofmutualinformationfortworandomvariablesXandYis whereH(X)andH(Y)aremarginalentropiesofXandYandH(X;Y)isthejointentropyofXandYanddenedasH(X)=E(log(p(X)),wherep(X)istheprobabilitymassfunction(PMF)ofX,andE()denotestheexpectationofarandomvariable. Thedenitionofnormalizedmutualinformation[ 38 ]fortworandomvariablesXandYis MutualinformationisnowusedinnonrigidintermodalityimageregistrationalongwithdeformationmodelssuchasTPSasusedinKimetal([ 39 ]),elasticdeformationasusedinMaintzetal.([ 40 ])andHataetal.([ 41 ]),B-Splineorfreeformdeformation(FFD)asusedinRueckertetal.([ 42 ])andRohlngetal.([ 43 ]),andGaussiankernelsasusedinGaensetal.([ 44 ]).

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45 46 ]) Thedenitionofnormalizedcrosscorrelationis r PiI(1)iI(1)2r PiI(2)iI(2)2;(2{3) whereI(k)iistheintensityvalueofimageI(k)atlocationi[pixelposition(x;y;z)],k=1;2,i=1;:::;N,whereNisthetotalnumberofpixelsineachimageandI(k)isthemeanvalueoffI(k)igNi=1. withtheentropybeing Ahistogramisformedfromthedierenceimageandp(a)denotestheprobabilityofobtainingthepixelintensityvalueainI(d).Thismeasurehasbeenusedin2Dregistrationbetweenimagesofadigitalsubtractionangiography(DSA)sequencein[ 47 ]. Anothermeasureusingthedierenceimageispatternintensity.

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wherepixeljisaneighborofpixeliwithinaradiusrandisaconstantusedtoweighthemeasuresothatsmalldeviationsinintensityresultinthemeasureremainingnearitsmaximumvalue.Thevalueschosenfortheconstantswere=10andr=3pixelsinregistrationofanX-rayimagetoaCTimage[ 48 ].Thescalingfactorsforthecreationofthedierenceimageshouldbechosensothatthedierenceimagehastheleastcontrast.Notethataconstantshiftbetweentheimageintensitiesdoesnotaectthesimilaritymeasure,asitonlyassessesdierencesinthedierenceimages. whereaandbareintensityvaluesofimageI(1)andI(2)respectivelyandp(a;b)isthejointprobabilitymassfunctionofthetwoimages.Jointentropywassimulta-neouslyproposedforintermodalityimageregistrationbyStudholmeetal.[ 49 ]andCollignonetal.[ 50 ]. AsimilarmeasureisthejointprobabilityasusedinregistrationbyLeventonandGrimso[ 51 ]. wherep(I(1)i;I(2)i)isthejointprobabilityofintensityI(1)iatpixeliandintensityI(2)iforimageI(2).AGaussianmixturemodelwasusedtoestimatethejointprobabilitymassfunction.

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52 ]presentanewmeasureforintermodalityimageregistrationcalledcrosscumulativeresidualentropy(CCRE): where"(X)=R10Pr(x>)logPr(x>)d,"(YjX)=R10Pr(y>jX)logPr(y>jX)dandE("(YjX))istheexpectationof"(YjX).TheyappliedthismethodtorigidMRbrainimageregistrationandgotbetterresultsthanmutualinformation. Heroetal.[ 33 ]usethe-JensendivergenceintheirMRbrainimageregistra-tion. Letf0andf1betwodensitiesand2[0;1]beamixtureparameter.The-Jensendivergenceisthedierencebetweenthe-entropiesofthemixturef=f0+(1)f1andthemixtureofthe-entropyoff0andf1: H(;f0;f1)=H(f0+(1)f1)H(f0)(1)H(f1);(2{10) whereHisthe-entropyofadensityanddenedas 1logZf(x)dx:(2{11) Moredetailedcomparisonofthesemeasuresmaybefoundin[ 53 ].

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(a)MutualInformation (b)modiedMutualInformation Figure2{1. DenitionsofmutualinformationandmodiedMIofthreeimages(shadedareas) variablesisnon-negative,thisisnottruewhenmorethantworandomvariablesareinvolved.Themutualinformationmeasurebetween(morethantwo)randomvariablescanevenbecomenegativeCoverandThomas[ 54 ]. Twonotablefactsemergeaftersurveyingtheliterature.Thereisalmostnopriorworkonusinganentropy-basedimagesimilaritymetricaswehavedonehereandthereareconsiderabledierencesofopinionontheextensionofmutualinformationfromtheintermodality(twoimages)casetothemultimodality(morethantwoimages)case.InCoverandThomas[ 54 ],mutualinformationofthreerandomvariablesX,YandZisdenedasMI(X;Y;Z)=H(X)+H(Y)+H(Z)H(X;Y)H(X;Z)H(Y;Z)+H(X;Y;Z)((a)ingure 2{1 ).Unfortunately,MI(X;Y;Z)isnotnecessarilynonnegative,whichrendersitinadequateasanimagesimilaritymeasure.InStudholmeetal.[ 55 ]andBoesandMeyer[ 56 ],adierentdenitionisproposed:mMI(X;Y;Z)=H(X)+H(Y)+H(Z)H(X;Y;Z)((b)ingure 2{1 )).Thisdenitionisnonnegativebutitisnotanaturalextensionofthemutualinformationoftworandomvariables.InLynchetal.[ 57 ],threeimagesareregisteredusingyetanotherdierentdenitionofmutualinformation.However,allthesedenitionsdonotembodythetrue(in

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oureyes)spiritofmutualinformation:sharedinformationbetweenmultipleimages.Henceusingmutualinformationtosimultaneouslyregistermultipleimagesisnotappropriatedespitethefactthatmutualinformationisaverygoodmeasure(thoughnotametric)forregisteringtwoimages.Finally,evenifwehadanonnegativeandnaturaldenitionformultimodalitymutualinformation,anecientcomputationtechniqueofhighdimensionalentropyisstillneededincomputingmulti-variableentropyinmutualinformation. InordertocomputetheShannonentropyofmultiplerandomvariables,weneedtoestimatethehighdimensionalprobabilitymassfunction(PMF)ofmultiplerandomvariables.Duetothecurseofdimensionality,andespeciallywhenderivativesofthePMFarerequired,itisdiculttoaccuratelyestimateahighdimensionalprobabilitydistribution.ThesimplestPMFestimationapproachishistogrammingandhasbeenusedindatabaseresearchsuchasmultiple-attribute-dataqueryinPoosalaandIoannidis[ 58 ].Inmultimodalityimageregistration,despitethefactthatweonlyneedtoestimatetheentropy(oftheformplogp)fromthePMF,highdimensionalhistogrammingisnotprevalentandduetothis,thereisalmostnopreviousworkonsimultaneous,multimodalityimageregistration. 2.2.5 .ButthereisnopaperextendingJensondivergencetomultimodalityimageregistration.ApossibleextensionisthatforthreeimagesX,YandZ,computingJensondivergencebetweenp(X;Y;Z)andp(X)p(Y)p(Z)orH(;p(X;Y;Z);p(X)p(Y)p(Z))=H(p(X;Y;Z)+(1)p(X)p(Y)p(Z))H(p(X;Y;Z))(1)H(p(X)p(Y)p(Z));

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whereHisthe-entropyofadensityand2[0;1].ActuallyJensendivergencehassameintuitionasKullback-Leiblerdistance.Theyallaremeasureofthedistanceoftwodensity.SomaximizingJensendivergencebetweenp(X;Y;Z)andp(X)p(Y)p(Z)isequivalenttomaximizingKullback-Leibler(KL)distanceoftheminsomeextent.AndKLdistanceofp(X;Y;Z)andp(X)p(Y)p(Z)isthemodiedmutualinformationofthethreeimagesX,YandZ. 59 ],anewmethodisproposedfortheimagesequenceregistration.TheyneedapredictionfunctionPtocomputethepredictionerrorI=I(2)P(I(1)): 2.2.3 .Forthesequenceregistration,theyuseweightedleastsquaretocomputealinearregressionforprediction.Theyusedthemethodtoregistertheimagesequenceofrabbitbrain.Fromtheirresults,thismethodisbetterthandirectusingSSDbutnotgoodasmutualinformation.Actuallybecauseofneedingpredictionfunction,itishardtoextendthismethodtomultimodalityimageregistration.

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WepresentaBayesianmultimodalitynon-rigidimageregistrationmethod.Sincethelikelihoodisunknowninthegeneralmultimodalitysetting,weuseadensityestimatorasadropinreplacementforthetruelikelihood.Thepriorisastandardsmalldeformationpenaltyonthedisplacementeld.Sincemutualinformation-basedmethodsareinwidespreaduseformultimodalityregistration,weattempttorelatetheBayesianapproachtomutualinformation-basedapproaches.Tothisend,wederiveanewcriterion|asucientcondition|whichwhensatis-ed,guaranteesthatthedisplacementeldwhichminimizestheBayesianmaxi-mumaposteriori(MAP)objectivealsomaximizesthetruemutualinformation(withasmalldeformationpenalty)asthenumberofpixelstendstoinnity.Thecriterionimposesanupperboundonthenumberofpermissiblecongurationsofthedisplacementeld. 20

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becomemoreobviousasweproceed.Thebinnedintensityforeachimageis From( 3{1 ),weseethatthebinnedintensityvaluesareintegersinf1;:::;K(k)g.Weuse( 3{2 )tocomputetheconditionalprobabilityatlocationi: Pr(B(1)ijB(2)i)=Pr(B(1)i;B(2)i) Pr(B(2)i):(3{2) Pr(ujB(1);B(2))=Pr(B(1)jB(2);u)Pr(u) Pr(B(1)jB(2))(3{3) fromwhichweget logPr(ujB(1);B(2))=logPr(B(1)jB(2);u)+logPr(u)logPr(B(1)jB(2)):(3{4) SincetheprobabilityPr(B(1)jB(2))=Pu2Pr(B(1)jB(2);u)Pr(u)isindependentofu,wehave logPr(ujB(1);B(2))/logPr(B(1)jB(2);u)+logPr(u):(3{5)

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Consequently,fromaBayesianperspective,thenon-rigidregistrationproblembecomes ^u=argminuE(u)=argminulogPr(B(1)jB(2);u)logPr(u):(3{6) WeuseastandardsmalldeformationsmoothnessconstraintonuwhichcanbewrittenaslogPr(u)/kLuk2.SinceweuseadensityestimatorforPr(B(1)jB(2);u),weassumeconditionalindependenceofB(1)givenB(2)overthepixellocations.Thisassumptionisclearlynotnecessarysincetheimagepro-cessing/computervisionliteratureisrepletewithcorrelatedrandomeldimagemodels(rangingfromsimplistictobaroque)[ 60 61 ].However,mostrandomeldmodelsrequiretheestimationoffurtherparameterswhichincreasestheestimationburdenconsideringthatwearealreadysaddledwiththeproblemofestimatingu.Inaddition,EMI-basedregistrationmethodshavetraditionallyusedverysimpledensityestimationproceduressuchashistogramming[ 62 ]andParzenwindows[ 63 ]whichsetsaclearprecedentforus.Withthesesimplicationsinplace,weobtainthefollowingBayesianmaximumaposteriori(MAP)objectivefunction wherewehavenormalizedthenegativelog-likelihoodinthersttermof( 3{7 ).TheparameterisaregularizationparameterandListheregularizationoperator.Inthe2Dcase,wechoose whichisastandardthin-platespline[ 64 ]smalldeformationcost.

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3{7 )asthenumberofpixelsNtendstoinnity.Inthenon-rigidsetting,thecardinalityofuscaleslinearlywithNandasweshallsee,thiscomplicatestheconvergenceproof. WebeginbyassumingthatthechosendensityestimatorconvergestothetruedensityasNtendstoinnity.ThisisusuallytrueofhistogramandParzenwindowestimators.DenotethetruedensityofB(1);B(2)andthepair(B(1);B(2))byPr(B(1)),Pr(B(2))andPr(B(1);B(2))respectivelyandthecorrespondingestimateddensitiesby^Pr(B(1)),^Pr(B(2)),and^Pr(B(1);B(2)).Weassumethat limN!1^Pr(B(1))=Pr(B(1));limN!1^Pr(B(2))=Pr(B(2)) (3{9) and limN!1^Pr(B(1);B(2))=Pr(B(1);B(2)):(3{10) Withthisnotationinplace,wecanwritethetruemutualinformationas andtheempiricalmutualinformationas Theobjectivefunctionwewouldliketominimizeis Sinceweusetheframeworkofstatisticallearningtheory[ 65 ]throughoutthisdissertation,wecallEMI(u)theexpectedrisk.ThisobjectivefunctionisnotcomputablesincethetruedistributionPrisunknownandisonlyapproachedby

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ourdensityestimator^PrasNtendstoinnity.Insteadofminimizingtheexpectedrisk,weminimizetheBayesianMAPobjectivefunction,a.k.a.theempiricalriskwhichisthesameas( 3{7 ): wherethelog-likelihoodLL(u)isdenedas In( 3{15 ),^Pr(B(1)ijB(2)i;u)istheestimateddistributionfromNsamples.Weareinterestedintherelationshipbetweentheminimizersof( 3{14 )and( 3{13 ). Lettheminimumoftheexpectedriskin( 3{13 )beachievedbythedisplace-menteldurandtheminimumoftheempiricalriskin( 3{14 )beachievedbythedisplacementeldue.Thefollowingquestionisourmainconcerninthisdissertation: 1. WhatisEMI(ue)EMI(ur),orhowcloseisthevalueoftheexpectedriskattainedbytheminimizeroftheBayesianMAPobjectivefunction(empiricalrisk)tothemaximumvalueofthetruemutualinformation(expectedrisk)whichisattainedbyur? Weanswerthisquestionbyprovingthefollowingtheorem.Itturnsoutthatthetheoremrequiresaspecicchoiceofthedensityestimator.Wepicktheestimatorusedin[ 61 ]whichiscloselyrelatedtohistogramming.Assumingani.i.d.densityforeachpixel,ourchosendensityestimatoris where()istheDiracdeltafunctionwithR+1(x)dx=1.Notethatp(I)in( 3{16 )isadensityfunctionandnotadiscretedistributionasrequired.Sincethe

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Diracdeltafunctionisnotdierentiable,weswitchtoacontinuousapproximation Thisapproximationisincreasinglyexactas!0andiscontinuousanddier-entiablefor>0.Finally,sinceweusebinnedintensitiesB,wenormalizetheabovedeltafunctionapproximationtogetthenaldensityestimatorusedinthisdissertation.Themarginalandjointprobabilitydistributionsare ^Pr(B(1)i)=PNj=1expf(B(1)iB(1)j)2 and ^Pr(B(1)i;B(2)i)=PNj=1expf(B(1)iB(1)j)2+(B(2)iB(2)j)2 withtheunderstandingthatwearedealingwithi.i.d.pixels. Asmentionedpreviously,=fugisthesetofallpossiblecongurationsofu.Forthenon-rigidregistrationproblemwithN-pixelimages,kk|thecardinalityof|isboundedfromabovebyNN,sinceeachpixelcanpotentiallymovetoanyotherlocation.SincetheupperboundforkkscaleswithN,weletkkbeafunctionofN: 3{18 )and( 3{19 ),andwiththetotalnumberofcongurationsofuasin( 3{20 ),theinequality Pr(supu2(K(1)Xa=1K(2)Xb=1Pr(a;bju)[log^Pr(ajb;u)]1

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isvalidwhereisanygivenpositivesmallnumber. 65 ]forreal-valuedboundedfunctionstoget Prfsupu2(K(1)Xa=1K(2)Xb=1Pr(a;bju)[log^Pr(ajb;u)]1 whichisthedesiredresult.From( 3{22 ),weobtainwithprobability1(wheredef=expf22N 22+log(K(1)K(2))g),theinequality AddingandsubtractingkLuek2tobothtermsontheleftsideof( 3{23 ),weget(aftercuttingafewcorners), Onceagain,fromHoeding'sinequality,wehave

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AddingkLurk2tobothsidesof( 3{25 )wecanstatemoresimplythat Sinceueistheminimizeroftheempiricalrisk(BayesianMAPobjectivefunction),EMAP(ur)EMAP(ue)andhence 0EMI(ue)EMI(ur)[EMI(ue)EMAP(ue)]+[EMAP(ur)EMI(ur)]:(3{27) Substituting( 3{24 )and( 3{26 )in( 3{27 ),weseethat 0EMI(ue)EMI(ur)[(K(1))2+(K(2))2 Ifweassumethat limN!1logg(N) thenwehave limN!1jEMI(ue)EMI(ur)j=0:(3{30) Wehaveshownthattheminimizersoftheexpectedrisk(truemutualinformation)andtheempiricalrisk(BayesianMAPobjectivefunction)coincideasthenumberofsamplesapproachesinnityprovidedthatasucientcondition( 3{29 )ismet. Itistimethatwetookacloserlookatg(N)whichisthecardinalityofthenumberofallowedcongurationsofu:Innon-rigidregistration,theupperboundofg(N)isNNifwealloweachpixeltomovetoanyotherlocation.Insharpcontrast,inrigidregistration,theupperboundofg(N)isC6in2Dwherewehaveassumed6freeparameters(ane)witheachparameterquantizedintoC(independentofN)bins.Itshouldbeobviousthatifg(N)=NN,wecannotconcludethatlimN!1jEMI(ue)EMI(ur)j=0.Clearly,fromthisproof'sviewpoint,allowingeverypixeltopotentiallyvisitanyotherlocationisunreasonableeveninlarge

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deformationsituations.Inthisdissertation,wealreadyhaveaBayesianpriorwhicheectivelyrestrictsutosmalldeformations(eventhoughtherearenoforbiddencongurations).Ifwesetanupperboundforg(N)tobeNDwhereDisaconstantindependentofN,thentheproofsgothroughandtheempiricalandexpectedriskminimizerscoincide.Consequently,asucientconditionisthatg(N)beO(ND).AnupperboundofO(ND)isequivalenttoD(independentofN)freeparametersinsteadof6asinthecaseofthe2DanewitheachparameterquantizedintoNbins.

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Whilemutualinformation-basedmethodshavebecomepopularforimageregistration,thequestionofwhatunderlyingfeaturetouseisrarelydiscussed.Instead,itisimplicitlyassumedthatintensityistherightfeaturetobematched.Wedepartfromthistraditionbyrstbeginningwithasetoffeatureimages|theoriginalintensityimageandthreedirectionalderivativefeatureimages.This\featureextraction"isperformedonbothimagesinatypicalintermodalityregistrationsetup.Assumingtheexistenceofatrainingsetofregisteredimages,wendthebestprojectionontoasinglefeatureimagebymaximizingthenormalizedmutualinformation(NMI)betweenthetwoimagesw.r.t.theprojectionweights.Afterdiscoveringthebestfeaturetomatchusingnormalizedmutualinformationasthecriterion,weusethesameprojectioncoecientsonnewtestimages.WeshowthataneNMI-basedregistrationofthetestimagesusingthenewbest\feature"ismorenoiseresistantthanusingimageintensityasthedefaultfeature.Sincetheassumptionofaregistered,trainingsetofimagesisproblematic,weextendtheideatothebootstrapcase,whereinweuseimperfectlyregisteredimages(obtainedbyusingNMIontheoriginalintensitypair)asatrainingset.Thebestfeaturecombinationiscomputedusingtheimperfectlyregisteredpairofimages.WeshowthatsubsequentNMI-basedregistrationofthebestfeatureimagepairisabletoimproveupontheoriginalimperfectregistration.Resultsareshownon2Dcoronal,axialandsagittalslicesdrawnfroma3DMRIvolumeofprotondensity(PD)andT2-weightedimages. 29

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and whereH(X)andH(Y)arethemarginalentropiesofXandYandH(X;Y)isthejointentropyofXandY. AssumethatwehavetwoimagesI(1)andI(2)whicharealreadyregistered.Letff(1)kgandff(2)kg,k=1;:::;KbeKfeatureimagescorrespondingtoI(1)andI(2):Thefeatureimagescorrespondtoasetofltersthatarerunonbothimages.Thereisnoapriorireasontousethesamesetofltersonbothimages.Asmentionedabove,giventhetwosetsoffeatureimages,wedetermineasetofprojectioncoecientsthatmapeachsetoffeatureimagesontoasingle\best"featureimage.Normalizedmutualinformation(NMI)[ 38 ]isusedasthecriteriontondthesingle,bestdimensionoffeatureprojection.Theobjectivefunctionusedis where(W(r))TisthetransposeofthecolumnvectorW(r)=266664w(r)1...w(r)K377775andF(r)=266664f(r)1...f(r)K377775,r=1;2.WedenotebyF(r);thesetoffeatureimagesofimage

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4{3 )ismaximizedtogetthebestpro-jectioncoecients(W(1);W(2)).Bymaximizing( 4{3 ),weobtainthebestlinearcombinationoffeatures. Asmentionedintheintroduction,wehavefoundthatMIisnotagoodcriteriontodeterminethebestfeaturecombination.MIisbiasedtowardimageswithhigherentropyandusuallyfavorstheoriginalintensityimageoranevennoisierimage!NMIdoesnotsuerfromthesamebias. 4{3 )onarepresentativetrainingset.ThenweregisterimagesI(1)andI(2)bymaximizingNMIbetweenthebestfeatureimages(W(1))TF(1)and(W(2))TF(2).ThisisastandardaneregistrationstepusingNMIasthecriterion. whereF(2)(T)isthesetoffeatureimagesofimageI(2)(T),whichistheanetransformedversionofimageI(2)withanetransformationT.

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Wepresentanextensibleinformationmeasureforsimultaneousmultimodal-ityimageregistration.Themeasureisapseudometricwhenrestrictedtotheintermodalitycasesinceitsatisestheproperties,i)non-negativity,ii)sym-metry,iii)triangleinequalityandisiv)zeroif(butnotonlyif)thetwoimageintensitiesareidentical.GivenimagesAandB,themetricusedhereisthesumoftheconditionalentropiesH(AjB)andH(BjA).Weshowthatthenormal-izedversionofthemetric[themetricdividedbythejointentropyH(A;B)]isstillametricandisequivalenttothenormalizedmutualinformation(NMI).Informationmetricsarerarelyusedinimageregistrationandnotably,mutualinformationisnotametric.Whencomparedtomutualinformationwhichcanevenbecomenegativeinthemultipleimagecase,itiseasiertoextendourmetrictotheregistrationofmultipleimages|themultimodalitycase.Theextensionisstraightforwardandcomesinnon-normalizedandnormalizedversions.GivenimagesA,B,andC,thenon-normalizedmeasureisthesumoftheconditionalentropiesH(AjB;C)+H(BjA;C)+H(CjA;B).Thenon-normalizedmeasurecanbenormalizedbyeitherthejointentropyH(A;B;C)orthesumofthemarginalentropiesH(A)+H(B)+H(C):Theconditionalentropiesareestimatedusinghigh-dimensionalhistogrammingwhich(formostlyculturalreasonswethink)israrelyusedinthemedicalimagingcommunity.Finally,weproposeanothernewmeasure|anupperboundofthenon-normalizedmeasure(alongwithitsnormalizedcounterparts)formultipleimageregistration,whichdoesnotneedthe 32

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estimationofhighdimensionalprobabilitymassfunctions.Wecomparetheregis-trationresultsusingthenewmeasure,thenormalizedmeasure,theupperboundofthemeasure,thenormalizedupperbound,modiedmutualinformationandmod-iednormalizedmutualinformationtosimultaneouslyregistermultiple2Dsliceimagesobtainedfromsyntheticmagneticresonance(MR)protondensity(PD),MRT2andMRT13DvolumesavailablefromtheBrainwebsimulator.Inaddition,wealsoperformunbiasedregistrationofmultipleimagesofanatomicalslices,CTandMRPDfromtheVisibleHumanMaleDatawiththenormalizedmetricandweshowtheunbiasedandsimultaneousregistrationresultsof9syntheticPD,T1andT2MRbrainimagesusingthenormalizedmeasurecomputedviahigh-dimensionalhistogramming.Ourresultsdemonstratetheecacyofthenewmeasuresandhigh-dimensionalhistogrammingforunbiased.ane,multimodalityimageregistration. 5.1.1MetricDenition Themetricisthesumoftwoconditionalentropiesanddenedin[ 54 ].FortworandomvariablesXandY, whereH()istheentropyofarandomvariableanddenedasH(X)=E(log(p(X)),wherep(X)istheprobabilitymassfunctionofX,andE()denotestheex-pectationofarandomvariable.HenceH(XjY)=E(log(p(XjY))andH(YjX)=E(log(p(YjX)). 54 ].

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Figure5{1. Venndiagramfortworandomvariables 1. 2. 3. 4. whereH(X)andH(Y)aremarginalentropiesofXandYandH(X;Y)isthejointentropyofXandY.Also, andH(YjX)=H(X;Y)H(Y):

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(a)PDimage (b)MRT2image (c)themetric Figure5{2. ThemetricandmutualinformationbetweenPDandrotatedandscaledT2images Hence InFigure 5{2 ,weplotthevaluesofthemetricandMIbetweenaprotondensity(PD)MRimageandarotatedandscaledMRT2image,wheretherotationanglerangesfrom-20degreesto20degreesandscalingrangesfrom-1to1.

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metric( 5{2 ). whereT=266664ab0cd0ef1377775isananetransformation.InT;thesubmatrix264abcd375canbedecomposedintoshear,scaleandrotationandthevectorefcontainsthexandytranslations.TheimageI(2)(T)isthetransformedimageofimageI(2)usingtheanetransformationT. 66 ].And0(X;Y)1,(X;Y)=0ifX=Y;(X;Y)=1ifXandYareindependent.Thesecondnormalizedversionofthemetric(X;Y)is And0(X;Y)1,(X;Y)=0ifX=Y;(X;Y)=1ifXandYareindependent.But(X;Y)doesnotsatisfythetriangleinequalityandhenceitisnotametric(orpseudometric).Wegivetheproofsofthetriangleinequalityofthemetric(X;Y)=H(XjY)+H(YjX)andthenormalizedmetric(X;Y)=H(XjY)+H(YjX) Fromthedenitionin( 5{1 ),weseethatisverysimilartomutualinfor-mation(MI)( 5{6 )inthe2-imagecaseexceptthatthemetrichasonemorejointentropyterm,whichmeansthemetricgivesjointentropymoreweightthanthemarginalentropyincomparisontomutualinformation

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2: Andwehavefoundthatminimizingthenormalizedmetricorisequivalenttomaximizingthenormalizedmutualinformation(NMI)[ 38 ]( 5{7 )inthe2-imagecase Consequently,fromourperspective,NMIisnotadhocsinceitisinverselypropor-tionaltoapseudometric. Nowwemovetoourmaintopic|multimodalityimageregistration. 5{1 ),wecaneasilyextendthemetrictomultiplerandomvariablesintwodierentways.Therstextension,fornrandomvariablesX1,X2,:::Xn, andthesecondis, AndafterdividingbyeitherthejointentropyH(X1;X2;:::;Xn)orbythesumofthemarginalsPni=1H(Xi),wegettheirnormalizedcounterparts. IfwewanttosimultaneouslyregisterthreeimagesI(1),I(2)andI(3),weobvi-ouslyneedtondmoretransformations.WedenethebiasedcaseasonewhereI(1)isthereferenceimageandxedintheregistrationandweseektwooptimalanetransformations|T2forimageI(2)andT3forimageI(3)byminimizingthe

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metric( 5{10 ). Wedenetheunbiasedcaseasonewherethereisnoreferenceimageandweseekthreeoptimalanetransformations|T1forimageI(1),T2forimageI(2)andT3forimageI(3)byminimizingthemetric( 5{11 ). whereI(1)(T1)isthetransformedimageofimageI(1)usinganetransformationT1,I(2)(T2)isthetransformedimageofimageI(2)usinganetransformationT2andI(3)(T3)isthetransformedimageofimageI(3)usinganetransformationT3.Equivalentminimizationscanbecarriedoutforthenormalizedcounterpartsofand. InFigure 5{3 ,weplotthevaluesof,MIandmodiedMI(MMI)foraPDimage,arotatedMRT2andarotatedMRT1image,wherebothrotationanglesrangefrom-10degreesto10degreesandthevaluesof,MIandMMIforaMRPDimage,scaledMRT2andscaledMRT1image,wherebothscalerangesarefrom-1to1.FromFigure 5{3 ,wecanseethatandMMIcanachievetheirminimumormaximumatthepointswhererotationorscaleiszero.OnceagainthisanecdotallydemonstratesthatwecanminimizeormaximizeMMItorecovertransformationsofrotationorscale.MIhastwopeaksinrotationbutbothpeaksarenotthepointwhererotationiszero.AlthoughMIachievesitsmaximumatthepointwherescaleiszero,itisverynoisycomparedwithorMMIanditcanassumenegativevalueswhicharehardtointerpret.HenceMIisnotagoodmeasureinmultimodalityregistrationofimageswhencomparedtoorMMI.ThedierencesandaccuracyinregistrationofandMMIwillbeshowninourexperiments.

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(a)PDimage (b)MRT2image (c)MRT1image (d)withrotation (e)MIwithrotation (f)modiedMIwithrotation (g)withscaling (h)MIwithscaling (i)modiedMIwithscaling Figure5{3.

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Theapproachin[ 34 ]usedminimumspanningtrees(MST)toestimatethe-entropyinimageregistration.TheMST-basedapproachdirectlyestimatesentropywithoutestimatingthehighdimensionalPMF.ButcomputinganMSTforagraphwithmanyedgesisveryexpensive[O(ElogE)]whereEisthenumberofvoxelsandfurthermore,themethodcannotcomputethenormalizedversionsoftheinformationmeasure.(AlsothemethodcomputestheRenyientropyinsteadoftheShannonentropy.)IndirectmethodscomputeentropybyrstestimatingthehighdimensionalPMF.WhilehistogrammingisapopularapproachforestimatingthePMF,ithasnotbeenusedforcomputingthehighdimensionalentropyinimageregistration,mainlybecausenaiveimplementationsareexponentialincomplexityinthedimensionalityofrandomvariables.Ourtechniqueforcomputinghighdimensionalhistograms(tobeexplainedbelow)overcomestheaforementioneddimensionalityproblem.ItscomputationalcomplexityisO(N)whereNisthenumberofsamplesdrawnfrom(corresponding)pixellocationsoverasetofimages.TheO(N)computationalcomplexityismuchsmallerthansomepopularhighdimensionalPMFestimationmethodssuchasParzenwindowsO(N2),GaussianmixturemodelsO(NK)whereKisthenumberofclusters,etc.AnapproximationtotheParzenwindowentropycanbecomputedinO(NM),M
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Wenowdescribethehighdimensionalhistogrammingapproach.AssumewehaveMimagesI(m);m2f1;:::;MgandthenumberofhistogrambinsforthemthimageI(m)isK(m),m2f1;:::;Mg.Thetotalnumberofbinsinthemulti-dimensionalhistogramofMimagesisQMm=1K(m),whichwillbeverylargeifMorK(m)islarge.ButinthespaceofthejointhistogramofMimages,mostofthebinsofthejointhistogramareempty.EmptybinsdonotcontributeanythingwhenwecomputethehighdimensionalShannonentropy(sinceplogp!0asp!0.)Hence,usingQMm=1K(m)binsinthespaceofthejointhistogramofMimagesisimpracticalandfurthermoreisunnecessarysinceweonlyneedknowthenon-emptybins. Assumeaboundedrange[I(m)min;I(m)max]forimageI(m):LetB(m)ibethebinnedintensityvalueofimageI(m)atlocationi,i2f1;:::;Ng: From( 5{12 ),weseethatthebinnedintensityvaluesofimageI(m)areintegersinf1;:::;K(m)g.LetL(m)betheminimumlengthofdigitalbitswhichcanrepresentK(m),m2f1;:::;Mg.ThenwegetanewcodeCi=B(1)iB(2)iB(M)iwithlengthPMm=1L(m),whichisaconcatenationofthebinnedintensityvaluesofallimagesatlocationi,i2f1;:::;Ng.ThenumberofdierentelementsofthesetfCi;i2f1;:::;Nggisthenumberofnon-emptybinsofthejointhistogramofMimages.HencewecanusefCi;i2f1;:::;NggtogeneratethejointhistogramofMimagesbycountingthenumberofidenticalCisinthecodeset.Thatthisisvalidisguaranteedbythefollowingtheorem.

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ThenumberofbinsK(m)istheonlyfreeparameterinourmethodbutitisalsoveryimportant.Below,following[ 68 ],weproposeacriterionforlimitingthemaximumnumberofbinsinthehistogram. whereA(u)isthesetinPthatcontainsuandIistheindicatorfunctionofaset.ThentheestimateisuniversallyconsistentinL1ifh!0andNhM!1asN!1,thatis,foranyftheL1erroroftheestimateRjfN(u)f(u)jduconvergestozeroinprobability,orequivalently,forany>0, limN!1PrZjfN(u)f(u)jdu=0:(5{14) Forourcase,thedomainofPMFisaboundedsubsetof0asN!1,whichsatisestheconditionofthetheorem.HenceweuseK=N1 FromTheorem1,weknowthattocomputethehighdimensionalhistogram,weonlyneedtocountthenumberofidenticalCiinthesetfCi;i2f1;:::;Ngg.FromTheorem2,weknowthatforanyCi;i2f1;:::;Ng,Ci2[1;N].Wecan

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countthenumberofidenticalCiinthesetfCi;i2f1;:::;NggbytraversingNsamplesonce.ThusthetimecomplexityofcomputinghighdimensionalhistogramsisO(N). 2(H(XjY)+H(XjZ))+1 2(H(YjX)+H(YjZ))+1 2(H(ZjX)+H(ZjY))=1 2((X;Y)+(Y;Z)+(X;Z)):(5{15) Inthereductionof( 5{15 ),wemainlyusethefollowingpropertyofentropy:H(XjY;Z)H(XjY). Let 2((X;Y)+(Y;Z)+(X;Z)):(5{16) Inmultimodalityimageregistration,wemayminimize( 5{16 )insteadofminimiz-ing( 5{8 ). Fromthedenitionofforthreerandomvariables,itcanbeseenthatwehavetoestimatethejointPMFp(X;Y;Z)ofthreerandomvariablesX,YandZ,whichiscomputationallymoreexpensivethantheestimationofthejointPMFoftworandomvariables.ButusinginsteadofinregistrationofthreeimagesdoesnotrequiretheestimationofthejointPMFofthreerandomvariables,whichwillslightlyalleviatethecomputationalburden.Thisisthemainbenetofusingtheupperbound.

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Finally,webrieydiscusstheeldofviewproblemwhichbesetsmuchofentropy-basedimageregistration.SincethejointPMFbetweentwoimagesisesti-matedbyconsideringtheoverlapregionofthetwoimages,thetrivialminimizationoftheinformationmetricandmaximizationofthemutualinformationoccurswhenthetwoimagesarespatiallyseparatedwithzerooverlap.Theinformationmetricisminimizedinthatcaseandthemutualinformationreachesitsmaximumvalueequaltothesumofthetwomarginalentropies.Asimple,butnon-uniquewayofxingthisproblemistousenormalizedversionofthemeasure.Therearetwowaysofnormalizing: 2H(X;Y;Z);(5{17) and 2(H(X)+H(Y)+H(Z));(5{18) whereitcanbeshownthat0(X;Y;Z)1.IfX=Y=Zthen(X;Y;Z)=0andifX,YandZareindependentofeachother,(X;Y;Z)=1.Thesealsoholdfor(X;Y;Z). InFigure 5{4 ,weplotthevaluesofthemeasureforaPDimage,arotatedMRT2andarotatedMRT1image,wherebothrotationanglesrangefrom-20degreesto20degreesandthevaluesofforaPDimage,scaledMRT2andscaledMRT1image,wherebothscalerangesarefrom-1to1.FromFigure 5{4 ,thenormalizedmeasureachievesitsminimumatthepointwhererotationorscaleiszero.Onceagainthisanecdotallydemonstratesthatwecanminimizetorecovertransformationsofrotationorscale.

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(a)PDimage (b)MRT2image (c)MRT1image (d)withrotation (e)withscaling Figure5{4.

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Inourpreviouswork[ 69 ],wehaveproposedanewinformationmetricasasimilaritymeasureandextendittomultimodalityimageregistration(mul-tipleimageregistration).Andin[ 70 ],wecomparedtensimilaritymeasuresofmultimodalityimagesandfoundthatthenormalizedmetric(??)hasthebestperformanceinanemultimodalityimageregistration.Inthissection,wewillusethenormalizedmetricandhighdimensionalhistogrammingtothenonrigidregistrationofmultimodalityimages.Forrecoveringlocaldeformation,wewilluseB-SplinestorepresentoweldsofpixelsbecauseB-SplineshavegoodlocalapproximationaslongasthegridsofB-Splinesareneenough. SupposewehavethreeimagesI(1),I(2)andI(3). Inthebiasedcase,assumeI(1)isthereferenceimage.WewishtoregisterI(2)andI(3)toI(1).Toachieveregistration,weneedtondoweldsu(2)forimageI(2)andoweldsu(3)forimageI(3)soastominimizethenormalizedmetricofthreeimagesin( 6{1 ). 46

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Forunbiasedcase,thereisnoreferenceimagehenceweneedtondeldsu(1)forimageI(1),eldsu(2)forimageI(2)andoweldsu(3)forimageI(3)soastominimizethenormalizedmetricofthreeimagesin( 6{2 ). In( 6{1 )and( 6{2 ),I(1)(u(1)),I(2)(u(2))andI(3)(u(3))aretransformedimagesofI(1),I(2)andI(3)usingoweldsu(1),u(2)andu(3). Butoptimizing( 6{1 )or( 6{2 )isverytimeconsumingandoweldswillnotbesmoothifwedirectlyoptimize( 6{1 )or( 6{2 )overoweldofeachpixel.Hence,researchersusesplinestocontroltheseoweldssoastobecomputa-tionallyecientandachievesmoothowelds.ApopularsplineistheB-Spline[ 71 ]. wherei=bxc1,j=byc1,s=xbxc,andt=ybyc.BkandBlareuniformcubicB-splinebasisfunctionsdenedasB0=(1t)3=6;B1=(3t36t2+4)=6;B2=(3t3+3t2+3t+1)=6;B3=t3=6:

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IfweuseB-splines( 6{3 )foroweldsu,wehave whereu(x;y)andijaretwodimensionalvectorsfor2Dimage. For3Dimages,wecangetsimilarform: whereu(x;y;z)andijkarethreedimensionalvectorsforthe3Dimage. AfterusingB-splinesonowelds,theunbiasedregistrationofthreeimagesin( 6{2 )becomes where(1),(2)and(3)arethevalueofcontrolpointsonthegridtocomputeoweldsu(1),u(2)andu(3)in( 6{4 ). Hencetheoptimizationisperformedinthespaceofinsteadofthespaceofoweldsu.Sincethecardinalityofismuchlessthanthatofu,theoptimiza-tionwillbemoreecient.AndbecauseoftheuseoftheB-spline,theoweldswillbesmooth. whereuarerepresentedby( 6{4 )for2Dimagesor( 6{5 )for3Dimages.Byminimizing 6{7 ,weachievethebestoweldutoregisterimageI(2)toI(1).In

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theregistrationprocess,iftheresolutionofthegridofB-Splinerepresentingtheoweldislow,thenumberofparameterswillbesmallsothattheoptimizationisveryecientbutsomesmalllocaldeformationwouldnotberecovered;butifweselectahighresolution,thesmalldeformationwillberecoveredbutthecomputationexpensewillbeveryhigh.Thusweuseamultiresolutionoptimizationalgorithm,showninAlgorithm 1 .ThebasicideaisthatusinglowresolutionofthegridofB-Splineandecientcomputationtorecoverlargedeformationatearlieriterationsofoptimizationthenusinghighresolutiontorecoversmalllocaldeformation.Atearlieriterationoftheoptimizationprocess,thecomputationwillbeecientbecausethenumberofparametersissmallandlargedeformationwillberecoveredbecausethegridiscoarsesothateachpointonthegridwillaectmorepixelsontheimage.Thenafterimprovingtheresolution,thesmalldeformationwillberecoveredifitisnotrecoveredinearlieriterations.Foreachresolution,thegradientdescentmethodisusedforminimizingtheenergyfunctionandtondthebestoweld.Andthenalowelduwillbetheaccumulationofthebestoweldfoundineachresolution.

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@; @; @islessthanasmallconstant; ThenweextendtheAlgorithm 1 tomultimodalityimageregistration.Supposewetrytounbiasedlyregisterthreeimagesandtheenergyfunctionis whereu(1);u(2)andu(3)arerepresentedby( 6{4 )for2Dimagesor( 6{5 )for3Dimages.Similartointermodalityregistrationbutwehavetond3setsofoweldsfor3images,whichminimizetheenergyfunction( 6{8 ).Theprocessofndingthe3setsofoweldsissimilartoAlgorithm 1 ,whichisshowninAlgorithm 2 .Ateachresolutionlevel,wendthebest3setsofoweldswhichminimizetheenergyfunction( 6{8 ).Eachbestoweldisfoundbygradientdescentmethodwithxingothertwoowelds.Thenthenal3setsofoweldsaretheaccumulationof3setsofthebestoweldsfoundineachresolutionlevel.

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@(m); @(m); @(m)islessthanasmallconstant;

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1. BayesianMAP:EMAP(u)=1 2. Mutualinformation:EEMI(u)=PK(1)a=1PK(2)b=1^Pr(a;bju)log^Pr(ajb;u)+kLuk2: Jointprobability:EEJP(u)=1 4. Jointentropy:EEJE(u)=PK(1)a=1PK(2)b=1^Pr(a;bju)log^Pr(a;bju)+kLuk2: u(n+1)=u(n)(n+1)E 52

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Figure7{1. Leftandmiddle:twosimpleshapeimages.Right:nalregistrationresult. Intheabove,Tisaniterationcap,isaconvergencethresholdandisastan-dardstep-sizeparameter.Weusenumericaldierentiation(with=1)forcomputingE 7{1 .Thecircleandsquareshapesareswappedandtheintensitiesofeachshapedierbetweenthetwoimages. TheBayesianMAPapproachwasusedtoregistertherightimagetotheleftimage.AsmallamountofisotropicGaussiansmoothingwasperformedpriortoregistration.Ateachiteration,wealsoobservethevaluesoftheempiricalmutualinformation(EMI),empiricaljointprobability(EJP)andempiricaljointentropy(EJE).FromFigure 7{2 ,weseethatthelikelihoodandmutualinformationplotsareverysimilarwhereasthejointprobabilityandnegativejointentropyactuallydecreasewhichiscounterintuitive.(Wealsoobservethatthelikelihooddoesnotincreasemonotonicallywhichisperhapsduetoa)bilinearinterpolationfactorsandb)thedeformationpenalty.)Thealgorithmwasabletoconvertthecircleandthesquaretoapproximatelyasquareandacircleinabout6iterations.

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Figure7{2. Thechangesini)log-likelihood,ii)mutualinformation,iii)jointprob-abilityandiv)negativejointentropywhenminimizingtheBayesianMAPobjectivefunction. Figure7{3. Leftmost:transverseT2image.Leftmiddle:transverseT1image.Middle:DeformedT1.Rightmiddle:Intensitydierencebetweenorig-inalT1anddeformedT1priortoregistration.Right:UnwarpednalT1image 72 ].The2DT1andT2axialimagesareshowninFigure 7{3 .Weuseda3%noiselevelforthesimulationwhichusestheICBMprotocol.TheadvantageofusingtheBrainwebsimulatoristhatthegroundtruthisknown.Anynon-rigiddeformationappliedtoaT1imagecanbesimultaneouslyappliedtoitsT2counterpart. Inourexperiments,weusedaGaussianradialbasisfunction(GRBF)splineasthenon-rigidparameterization.ThedeformedT1imageandtheintensitydierencebetweentheoriginalT1andthedeformedT1imageareshowninFigure 7{3 .TheregistrationalgorithmattemptstoregisterthedeformedT1imagetotheoriginalT2image.ThedeformedT1imageisgraduallyunwarpedduringregistration.DuringtheexecutionoftheBayesianMAPalgorithm,wealsoobservethevaluesoftheempiricalmutualinformation(EMI),empiricaljointprobability(EJP)andempiricaljointentropy(EJE).TheresultsareshowninFigure 7{4

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Figure7{4. Thechangesini)log-likelihood,ii)mutualinformation,iii)jointprob-abilityandiv)negativejointentropywhenminimizingtheBayesianMAPobjectivefunction. Figure7{5. DierenceimagesbetweenoriginalT1andunwarpedT1.Left:MAP.Leftmiddle:EMI.Rightmiddle:EJP.Right:EJE.TheSSDswere609beforeregistration,20.38(MAP),20.74(EMI),52.49(EJP)and52.47(EJE). Inthiscase,allfourcurvesmostlyshowanincreasewhichissomewhatdierentfromthebehaviorinFigure 7{2 .Onceagain,theMAPandEMIcurvesareinlockstepasareEJPandEJE.Asacomparisonbetweenthedierentalgorithms,weexecutedallfourapproachesonthesamedata.Thedierenceimages(betweenoriginalT1andunwarpedT1)showninFigure 7{5 clearlyindicatethattheMAPandEMIalgorithmsaresuperiortotheEJPandEJEalgorithms. WeperformedanotherexperimentonthepairofT1andT2simulated2DMRimages.Thistime,thedeformationontheoriginalT1imagewasmuchlarger.TheoriginalanddeformedT1imagesareshownontheleftinFigure 7{6 .TheresultsofexecutingtheBayesianMAPalgorithmonthedeformedT1andT2imagesareshownontherightinFigure 7{6 .Clearly,despiteerrorsnearhighgradientboundaries(whicharemostlycausedbyinterpolationartifacts),theMAPalgorithmisuptothetaskofrecoveringareasonablylargeglobaldeformation.

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Figure7{6. Leftmost:OriginalT1image,Leftmiddle:deformedT1image.Mid-dle:IntensitydierencebetweenoriginalT1anddeformedT1beforeregistration.Rightmiddle:IntensitydierencebetweenoriginalT1andunwarpedT1afterregistration.Right:UnwarpednalT1image.ThebeforeandafterSSDswere647and59respectively. 72 ].Thesimulationsarebasedonananatomicalmodelofthenormalbrainwiththemainadvantagebeingthatthegroundtruthisknownandcanbeusedforvalidation. 4{3 ).TheoriginalintensityrangeofthePDandT2imagesisin[01].WeadddierentlevelsofGaussiannoisewithmeanzeroandvaryingstandarddeviations(0.1,0.2and0.4)totheimages.Asasimpleexample,werotatetheT2imagewithinarangefrom-20degreesto20degreesandcomputetheNMIbetweenthesinglebestpairoffeatureimages.ThisiscomparedtotheNMIobtainedfromtheoriginalintensitypair.TheNMIplotsshownin

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Figure 7{7 demonstratethatthesinglebestfeaturefoundismorerobusttonoisethantheoriginalintensity. wheresandtarescaleandshearparameters,R()andR()aretworotationmatriceswithrotationangleand.Intheexperiments,therangeoftheshearandscaleparametersis[-11],therangeofrotationparametersare[-4545]degreesandtherangeoftranslationsis[-1010]pixels.Weused2Dslicesdrawnatsagittal,coronalandaxialorientations.ThebestlinearcombinationisrstestimatedbymaximizingtheNMIonthefeaturesetsofnoiselessregisteredPDandT2-weightedimages,whosenoisedandtransformedversionareusedinfollowingregistration.WethentransformtheT2-weightedimagewithananetransformationT.Theshearandscaleparametersare0.5andthetworotationparametersare10degrees,withthetranslationsalongthexandydirectionsbeing5pixels.HenceT=2666641:90950:513000:25650:45480551377775,s=0:5,t=0:5,=10,=10,e=5andf=5.Gaussiannoisewithmean0andstandarddeviation0.2isaddedtoPDandtransformedT2images.NMIissubsequentlyusedasthecriteriontoregisterthesetwoimages.Weusedacoarse-to-nesearchstrategytondthebestTin( 4{4 ).

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(a)intensityimage (b)featureimage Figure7{7. Left:Fromtoptobottom,NMIbetweentheoriginalintensitypairwithrotation.Right:Fromtoptobottom,NMIbetweenthebestfea-tureimagepairwithrotation.Therotationrangeisfrom-20degreesto20degrees.Fromtoptobottom:addedGaussiannoisewithmean0anddeviation0,0.1,0.2and0.4.

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(a)PD (b)T2 (c)recoveredT2 Figure7{8. Sagittal2Dslices Table7{1. Registrationresultsof2DsagittalPDandT2slicesusingintensityandbestfeaturepair groundtruth resultsfromintensity resultsfromfeature 0.45 0.5 0.45 0.5 12 10 11.5 10 5 5 4 5 NMIiscomputedonlyontheoverlapareaofthetwoimageswithnearestneighborinterpolationusedforthetransformationoftheimageinallexperiments. Figure 7{8 shows2DsagittalPD,transformedT2slicesandresultsrecoveredusingthebestfeatureimages.Table 7{1 showstheregistrationresultsusingintensityandthebestfeatures.Figure 7{9 shows2DcoronalPD,transformedT2slicesandresultsrecoveredusingthebestfeatureimages.Table 7{2 showstheregistrationresultsusingintensityandthebestfeatureimagepair.Figure 7{10 shows2DaxialPD,transformedT2slicesandresultsrecoveredusingthebest (a)PD (b)T2 (c)recoveredT2 Figure7{9. Coronal2Dslices

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Table7{2. Registrationresultsof2DcoronalPDandT2slicesusingintensityandbestfeaturepair groundtruth resultsfromintensity resultsfromfeature 0.45 0.48 0.45 0.52 11.5 10.6 11 9.4 5 5 5 5 (a)PD (b)T2 (c)recoveredT2 Figure7{10. Axial2Dslices Table7{3. Registrationresultsof2DaxialPDandT2slicesusingintensityandbestfeaturepair groundtruth resultsfromintensity resultsfromfeature 0.4 0.5 0.4 0.5 12 10 11 10 5 5 5 5

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Table7{4. Registrationresultsof2DsagittalPDandT2slicesbeforeandafterbootstrap groundtruth resultsbeforebootstrap resultsafterbootstrap 0.45 0.5 0.45 0.5 12 10.6 11.5 10.2 5 5 4 5 featureimages.Table 7{3 showstheregistrationresultsusingintensityandthebestfeatureimagepair. Fromtheregistrationresultsabove,weobservethatbetterresultsareachievedusingthefeatureimagepairthanusingtheoriginalintensitypair.Thefeatureimagesetswerecombinedusingprojectioncoecientsobtainedfromnoiseless,registered,trainingimages.However,itwouldbemuchmoreinterestingtoseeiftheaboveapproachextendstothecasewherewedonothaveregistered,trainingimages.Weturntothiscase,next.

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Table7{5. Registrationresultsof2DcoronalPDandT2slicesbeforeandafterbootstrap groundtruth resultsbeforebootstrap resultsafterbootstrap 0.45 0.5 0.45 0.52 11.5 9 11 11 5 5 5 5 Table7{6. Registrationresultsof2DaxialPDandT2slicesbeforeandafterboot-strap groundtruth resultsbeforebootstrap resultsafterbootstrap 0.4 0.52 0.4 0.52 12 9.4 11 9.6 5 5 5 5 ThesecondcolumnsofTable 7{4 7{5 and 7{6 areregistrationresultsobtainedbymaximizingNMIbetweentheoriginalimageintensitypairs.Theseareusedtoextractthebestprojectioncoecientsoffeatures.ThethirdcolumnsofTable 7{4 7{5 and 7{6 areregistrationresultsobtainedbymaximizingNMIbetweenthebestfeatureimagepairs.WeseethatmaximizingNMIbetweenthebestfeatureimagepairsisabletoimproveupontheregistrationresultobtainedbyusingNMIontheoriginalimageintensities.Despitethefactthatthebestfeatureimageswereobtainedfromimageswhichweresomewhatmis-registered,wewereabletoimproveupontheoriginalregistrationresultusingtheimperfectlyregisteredimagesasatrainingset.

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Table7{7. Resultsof2Dslicealongsagittaldirection TonMRT2 TonMRT1 groundtruth results groundtruth results 0.1 0.2 0.18 0.1 0.2 0.18 5 10 9.4 5 10 9.8 3 5 5 3 5 5 7.3.1AneRegistrationofPD,T2andT1MR2DImages 72 ].Thesimulatorisbasedonananatom-icalmodelofanormalbrain.ThemainadvantageofusingsimulatedMRdataisthatthegroundtruthisknown. Wedecomposeananetransformationmatrixintoaproductofshear,scaleandrotations.LetT=266664ab0cd0ef1377775beananetransformation.264abcd375=2642s002s375R()2642t002t375R() wheresandtarescaleandshearparameters,andR()=264cos()sin()sin()cos()375,R()=264cos()sin()sin()cos()375aretworotationmatrices.Inourexperiments,therangeofshearandscaleparametersis[-11],therangeofrotationparametersare[-4545]andtherangeoftranslationsis[-1010].

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(a)PD (b)T2 (c)T1 (e)recoveredT2 (f)recoveredT1 Figure7{11. Sagittal2Dslice Intheexperimentsweuse3tripletsof2Dslicesof3DPD,T2andT1MRbrainvolumeimages.Theslicesarechoseninsagittal,coronalandaxialdirections.WethentransformtheT2imagewithananetransformation^T1.Thescaleandshearparametersare0.1and0.1respectively,andthetworotationparametersare5and5degreesrespectively,withthetwotranslationsalongthexandydirectionbeing3and3pixelsrespectively.Hence^T1=2666641:13240:186600:18660:98370331377775,withs1=0:1,t1=0:1,1=5,1=5,e1=3andf1=3.WethentransformtheT1MRimagewithananetransformation^T2.Thescaleandshearparametersare0.3and-0.1respectivelyandthetworotationparametersare10and-5degreesrespectively,withthetranslationsalongthexandydirectionsbeing5and-3pixelsrespectively.Hence^T2=2666641:24960:396700:39670:93010551377775,withs2=0:2,t2=0:2,2=10,2=10,e2=5andf2=5.WeaddGaussiannoisewithzeromeanandstandarddeviation0.1tothePD,transformedT2andtransformedT1MRimagesandregisterthethreeimagessimultaneously.(Theoriginalintensityrangeofall

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(a)PD (b)T2 (c)T1 (e)recoveredT2 (f)recoveredT1 Figure7{12. Coronal2Dslice Table7{8. Resultsof2Dslicealongcoronaldirection TonMRT2 TonMRT1 groundtruth results groundtruth results 0.1 0.2 0.16 0.1 0.2 0.22 5.4 10 10.6 5.4 10 10.4 3 5 5 3 5 5 imagesisnormalizedtothe[01]interval).Weuseacoarse-to-nesearchstrategytondtheoptimalT1andT2.Theregistrationmeasureiscomputedonlyintheoverlapareaofthethreeimageswithnearestneighborinterpolationusedfortransformingtheimageintensities. Inallresultsshownhere,thenormalizedmeasurewasused.Figure 7{11 shows2DPD,transformedT2andtransformedT1slicesalongthesagittaldirectionandtheregistrationresults.Table 7{7 showstheregistrationresultsofthesesagittalslices.Figure 7{12 shows2DPD,transformedT2andtransformedT1slicesalongcoronaldirectionandregistrationresults.Table 7{8 showstheregistrationresultsofthesecoronalslices.Figure 7{13 shows2DPD,transformed

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(a)PD (b)T2 (c)T1 (e)recoveredT2 (f)recoveredT1 Figure7{13. Axial2Dslice Table7{9. Resultsof2Dslicealongaxialdirection TonMRT2 TonMRT1 groundtruth results groundtruth results 0.12 0.2 0.18 0.1 0.2 0.2 5 10 9.4 5.4 10 10.2 3 5 5 3 5 5 T2andtransformedT1slicesalongaxialdirectionandregistrationresults.Table 7{9 showstheregistrationresultsoftheseaxialslices. TheseexperimentsabovedemonstrateaproofofconceptofourapproachtomultimodalityimageregistrationsinceT1andT2arebeingsimultaneouslydetermined.Futureworkwillfocusonvalidationstudiesfromwhichwehopetoelicitcapturerangeandtolerancetonoise,etc. 73 ].Wesimultaneouslyregisterthreefaceimageswithdierentilluminations.Essentially,eitheronesideofthefaceortheotherornoneareexposedtoa

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(a)leftlighton (b)rightlighton (c)nolighton (e)recoveredrightlighton (f)recoverednolighton Figure7{14. Imagesunderdierentlightingconditions(leftlighton,rightlighton,andnolighton)andwearingsunglasses Table7{10. Resultsunderdierentlightingconditions(leftlighton,rightlighton,andnolighton)andwearingsunglasses Tonrightlighton Tonnolighton groundtruth results groundtruth results -0.22 0.2 0.14 -0.2 0.2 0.14 -9.6 10 9.6 -10 10 10.6 -5 5 5 -5 5 5 lightsource.Weuseanetransformations^T1=2666640:70490:300600:30060:97400551377775and^T2=2666641:24960:396700:39670:93010551377775totransformtwoofthefaceimages.Registrationisperformedagainsttheoneuntransformedimage.Thetrueanetransformationparametersares1=0:2,t1=0:2,1=10,1=10,e1=5,f1=5,s2=0:2,t2=0:2,2=10,2=10,e2=5andf2=5. Inallsubsequentresults,thenormalizedmeasurewasused.Figure 7{14 showsleft-light-on,transformedright-light-onandno-light-onfaceimages

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(a)leftlighton (b)rightlighton (c)nolighton (e)recoveredrightlighton (f)recoverednolighton Figure7{15. Imagesunderdierentlightingconditions(leftlighton,rightlighton,andnolighton)andwearingascarf Table7{11. Resultsunderdierentlightingconditions(leftlighton,rightlighton,andnolighton)andwearingascarf Tonrightlighton Tonnolighton groundtruth results groundtruth results -0.20 0.2 0.16 -0.22 0.2 0.2 -10.6 10 10.2 -9.6 10 10.2 -5 5 5 -5 5 5 wearingsunglassesandthecorrespondingregistrationresultsrecoveredusingthenormalizedmeasure.Table 7{10 showstheregistrationresultsofthesefaceimageswearingsunglassesunderdierentlightconditions.Figure 7{15 showsleft-light-on,transformedright-light-onandno-light-onfaceimageswearingascarfandtheregistrationresults.Table 7{12 showstheregistrationresultsofthesefaceimageswearingascarfunderdierentlightconditions.Figure 7{16 showsleft-light-on,transformedright-light-onandno-light-onfaceimageswearingsunglassesorascarfandresultsrecoveredusingthenormalizedmeasure.Table 7{12 showstheregistrationresultsofthesefaceimageswearingsunglassesorascarfunderdierentlightconditions.

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(a)leftlighton (b)rightlighton (c)nolighton (e)recoveredrightlighton (f)recoverednolighton Figure7{16. Imagesunderdierentlightingconditionsandwearingsunglassesorscarf Table7{12. Resultsunderdierentlightingconditions(leftlighton,rightlighton,andnolighton)andwearingsunglassesorascarf Tonrightlighton Tonnolighton groundtruth results groundtruth results -0.24 0.2 0.14 -0.2 0.2 0.14 -9.4 10 9.6 -9.6 10 10.6 -5 5 5 -5 5 5 Onceagain,thesethreeexperimentsdemonstrateaproofofconceptwithmorevalidationexperimentsrequiredtobetterunderstandtheperformanceunderdierentilluminations. 7.4.1Multimodalityvs.Intermodality:SimultaneousRegistrationof3ImagesandPair-wiseRegistrationonSyntheticPD,T2andT1MRImages 72 ].Themainadvantageofusing

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simulatedMRdataisthatthegroundtruthisknown.Thesizeofeachimageis256mm256mm. Wedecomposeananetransformationmatrixintoaproductofshear,scaleandrotations.LetT=266664ab0cd0ef1377775beananetransformation.264abcd375=2642s002s375R()2642t002t375R(),wheresandtarescaleandshearparameters,andR()=264cos()sin()sin()cos()375,R()=264cos()sin()sin()cos()375aretworotationmatrices.Inourexperiments,therangeofshearandscaleparametersis[-11],therangeofrotationparametersare[-4545]degreesandtherangeoftranslationsis[-1010]mm.Inthisdecompositionofananetransformation,reectionsarenotallowed. Intheexperiments,weusethefollowingtenmeasurestoregister3tripletsof2Dslicesof3DPD,T2andT1MRbrainvolumeimages. 1. 2. 3. modiedmutualinformation:mMI(X;Y;Z)=H(X)+H(Y)+H(Y)H(X;Y;Z) 8. sumofpair-wisemutualinformation:pMI(X;Y;Z)=MI(X;Y)+MI(Y;Z)+MI(Z;X) 9. modiednormalizedinformation:mNMI(X;Y;Z)=H(X)+H(Y)+H(Y)

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10. sumofpair-wisenormalizedmutualinformation:pNMI(X;Y;Z)=NMI(X;Y)+NMI(Y;Z)+NMI(Z;X) Theslicesarechosenintheaxialdirection.WethentransformtheMRT2imagewithananetransformation^T1=2666641:24960:3966600:396660:930060441377775,withs1=0:2,t1=0:2,1=10,1=10,e1=4andf1=4.WealsotransformtheMRT1imagewithananetransformation^T2=2666641:42050:8809700:880970:679350881377775,withs2=0:4,t2=0:4,2=20,2=20,e2=8andf2=8.Wehavedonetwoexperimentswiththesedata.Eachexperimentisrepeated30timeswithdierentGaussiannoise.WeaddGaussiannoisewithzeromeanandstandarddeviation0.1intherstexperimentandzeromeanandstandarddeviation0.2inthesecondexperiment.(Theintensityrangeofallimagesisnormalizedtothe[0,1]interval.)Weuseacoarse-to-nebruteforcesearchstrategytondtheoptimalT1andT2.Thenestsearchresolutionofscaleandshearis0.05.Thenestsearchresolutionofrotationis0.5degreesintherstexperimentand1degreeinthesecondexperiment.Thenestsearchresolutionoftranslationis1mm.Theregistrationmeasuresarecomputedonlyintheoverlapareaofthethreeimageswithbilinearinterpolationusedfortransformingtheimageintensities. Tocompareeachmeasureandvalidatetheregistrationresults,wecomputethemeanerrorofeachparameteroftwoanetransformationsrecoveredbytenmeasuresandthesumof^T1T1+^T2T2of30experimentsineachexperiment. Table 7{13 ismeanerrorofeachparameteroftwoanetransformationsrecoveredwithtenmeasuresof30experimentsintherstexperiment.Figure 7{17 depictsthesumof^T1T1+^T2T2of30noisetrialsintherstsetof

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Table7{13. Meanerrorsondierentaneparametersintherstexperimentwithnoise0.1 erroroftransformationonMRT1 measures t e f s t e f 0 0.83 0.77 1.8 0.17 0 0 1.22 0.62 1.57 0.87 0 0.75 0.77 1.87 0.17 0 0 1.35 0.97 1.1 0.93 0 0.83 0.77 1.9 0.17 0 0 1.08 0.47 1.63 0.7 0 0.62 0.63 1.67 0.17 0 0 1.02 0.55 1.53 0.8 0 0.67 0.68 1.9 0.2 0 0 1.38 0.63 1.47 0.83 0 0.67 0.68 1.9 0.2 0 0 1.38 0.63 1.47 0.83 mMI 0 0 0.68 0.63 1.87 0.2 0 0 1.31 0.62 1.4 0.87 pMI 0 0 0.7 0.78 1.9 0.17 0.0083 0.0017 2.93 0.62 1.4 0.73 mNMI 0 0 0.67 0.68 1.9 0.2 0 0 1.38 0.63 1.47 0.83 pNMI 0 0 0.73 0.8 1.9 0.17 0.0083 0.0017 2.87 0.63 1.47 0.77 Plotsofsumof^T1T1+^T2T2of30trialsrecoveredbytenmeasuresintherstexperimentwithnoisestd.0.1.Numbers1to10represent,,,,,,mMI,pMI,mNMIandpNMI|thetenregistra-tionmeasures.

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Table7{14. MeanerrorsofdierentaneparametersinthesecondexperimentwithGaussiannoisewithmean0andstd.0.2 erroroftransformationonMRT1 measures t e f s t e f 0.01 2.53 1.53 2.53 0.7 0.11 0.02 3.77 2.4 1.73 1.2 0.06 10.57 3.03 5.93 1.57 0.42 0.08 4.87 3.53 2.97 2.03 0 1.1 1.33 1.93 0.43 0.0033 0.0083 3.83 1.67 1.833 0.97 0 0.97 1.33 1.93 0.33 0.0017 0.0083 2.8 1.23 1.77 0.93 0 1.03 1.2 2.07 0.37 0.005 0.0117 3.53 1.43 2.13 0.7 0 1.03 1.2 2.07 0.37 0.005 0.0117 3.53 1.43 2.13 0.7 mMI 0 0 1.1 1.2 2.03 0.37 0.005 0.0117 3.93 1.4 2 0.9 pMI 0 0 1.2 1.37 2.17 0.3 0.005 0.013 7.43 1.8 2 0.67 mNMI 0 0 1.03 1.2 2.07 0.37 0.005 0.0117 3.53 1.43 2.13 0.7 pNMI 0 0 1.16 1.37 2.17 0.3 0.005 0.0133 7.4 1.8 2.23 0.77 Plotsofsumof^T1T1+^T2T2of30trialsrecoveredbytenmeasuresinthesecondexperimentwithnoise0.2.Numbers1to10represent,,,,,,mMI,pMI,mNMIandpNMI|thetenregistra-tionmeasures.

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experiments.Fromtheresults,weseethatmultimodalityregistrationismoreaccuratethanrepeatedpair-wise(intermodality)registration.Andthenormalizedmetrichasbestperformance.Table 7{14 showsthemeanerrorofeachparameteroftwoanetransformationsrecoveredwiththetenmeasuresof30noisetrialsinthesecondexperiment.Figure 7{18 showsthesumof^T1T1+^T2T2of30noisetrialsinthesecondexperiment.Fromtheresults,weseethatthetwonon-normalizedmetricsandfailedinrecoveringscalebecauseofhighnoise.Butthenormalizedmetric(whichisbasedon)stillhasbestperformance.Andmultimodalityregistrationismoreaccuratethanrepeatedpair-wiseregistration. WiththeseexperimentsonsyntheticPD,T2andT1MR2Dimages,weseethatthesetenmeasureshavesimilarperformanceinlownoiseexperiments.Generally,theycancorrectlyrecoverscaleandshearparametersbuthaveerrorinrecoveringrotationandtranslation.Andweseethatmultimodalityregistrationismoreaccuratethanrepeatedpair-wiseregistration.Inthehighnoisecase,thetwonon-normalizedmetricsfailedtorecoverscalebecausetheyprefersmalloverlapsofimages.Thenormalizedmetricstillhasbestperformance.Andtheseexperimentalresultsalsoshowthatminimizingthenormalizedmetricorisequivalenttomaximizingthemodiednormalizedmutualinformation. Inourfollowingexperiments,wewillonlyusethenormalizedmeasure.

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ananetransformationandweminimizethenormalizedmetriconveanetransformations: 1. sequentiallysearchtentranslationswhichminimizecorrespondingto5images; 2. sequentiallysearchtenscalingandshearparameterswhichminimizefor5images; 3. sequentiallysearchtenrotationswhichminimizefor5images; 4. ifdecreasesinthisiterationthengoto1;elseend. whereT=fT1;T2;T3;T4;T5gandT1,T2,T3,T4andT5areveanetransforma-tions.I(m)(Tm)isthetransformedimageofimageI(m)usinganetransformationTm;m2f1;:::;5g.Sincethetimecomplexityofsearchingfor30parametersof5anetransformationsishigh,weusediteratedsequentialsearchusingalgorithm 3 foreachparameteruntilthenormalizedmeasureachievestheminimum.Thecolorimagesoftheanatomicalsliceareconvertedtograyimagesandtheintensityofimagesisnormalizedtotheinterval[0;1]priortoregistration.Thenormalizedmeasureiscomputedonlyintheoverlapareaofthethreeimageswithbilinearinterpolationusedfortransformingtheimageintensities.Theimagesizeis256by256.(Thepixelsizeis0.32mmsquareforaphotographofanatomicalsliceand1mmforMRandCTimages.)Thehistogramofeachimageused8bins.Highdimensionalhistogramsarecomputedusingthetechniquein 5.3 Ingures 7{19 7{21 and 7{23 ,weshowtheimagesbeforeandafterregis-tration.Inorderforhumanperceptiontogaugetheresultsofregistration,we

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(a)anatomical (b)CT (c)MRPD (d)MRT1 (e)MRT2 (f)overlap Figure7{19. Therstrowisthesetofimagesbeforeregistration;thesecondrowisthesetafterregistration.[Datasetindex:VHD#1080.] Table7{15. Resultsofunbiasedregistrationofanatomicalslice,CT,MRPD,T1andT2images.[Datasetindex:VHD#1080.] Anatomic CT MRPD MRT1 MRT2 0.1 0 0 0 0 0 -0.1 0.04 -4 0 0 2 6 1 -18 20 -1 0 -1 0 6 0 0 0 (a)anatomical (b)CT (c)MRPD (d)MRT1 (e)MRT2 (f)overlap Figure7{20. Segmentedimagesbefore(1strow)andafter(2ndrow)registration.[Datasetindex:VHD#1080.]

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Table7{16. Numberofpixelsinnonoverlapregionofsegmentedimagesbeforeandafterregistration.Uppertriangleisbeforeregistrationandlowertriangleisafterregistration.[Datasetindex:VHD#1080.] nonoverlap Anatomic CT MRPD MRT1 MRT2 Anatomic 0 7330 5054 8196 7635 CT 1730 0 3762 6214 5595 MRPD 1910 776 0 6258 6219 MRT1 2023 833 571 0 8543 MRT2 3385 2221 1889 2182 0 (a)anatomical (b)CT (c)MRPD (d)MRT1 (e)MRT2 (f)overlap Figure7{21. Therstrowisthesetofimagespriortoregistration;thesecondrowisthesetafterregistration.[Datasetindex:VHD#1110.] Table7{17. Resultsofunbiasedregistrationofanatomicalslice,CT,MRPD,T1andT2images.[Datasetindex:VHD#1110.] Anatomy CT MRPD MRT1 MRT2 0.07 0.01 0.01 0.01 0 0 0.01 0.05 0 0 0 0 -19 0 20 0 -1 0 0 0 6 0 0 0

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(a)anatomical (b)CT (c)MRPD (d)MRT1 (e)MRT2 (f)overlap Figure7{22. Segmentedimagesbefore(1strow)andafter(2ndrow)registration.[Datasetindex:VHD#1110.] Table7{18. Numberofpixelsinnonoverlapregionofsegmentedimagesbeforeandafterregistration.Uppertriangleisbeforeregistrationandlowertriangleisafterregistration.[Datasetindex:VHD#1110.] nonoverlap Anatomic CT MRPD MRT1 MRT2 Anatomic 0 9325 6992 8129 8432 CT 2844 0 4299 5580 4689 MRPD 3442 1320 0 4413 2593 MRT1 3445 1281 699 0 5481 MRT2 4590 2524 1464 1615 0 (a)anatomical (b)CT (c)MRPD (d)MRT1 (e)MRT2 (f)overlap Figure7{23. Therstrowisthesetofimagesbeforeregistration;thesecondrowisthesetafterregistration.[Datasetindex:VHD#1165.]

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Table7{19. Resultsofunbiasedregistrationofanatomicalslice,CT,MRPD,T1andT2images.[Datasetindex:VHD#1165.] Anatomy CT MRPD MRT1 MRT2 0.01 0.02 -0.03 0.07 0.09 -0.01 0.08 -0.02 3 20 0 0 -2 0 0 0 2 -1 0 0 1 0 0 0 (a)anatomical (b)CT (c)MRPD (d)MRT1 (e)MRT2 (f)overlap Figure7{24. Segmentedimagesbefore(1strow)andafter(2ndrow)registration.[Datasetindex:VHD#1165.] Table7{20. Numberofpixelsinnonoverlapregionofsegmentedimagesbeforeandafterregistration.Uppertriangleisbeforeregistrationandlowertriangleisafterregistration.[Datasetindex:VHD#1165.] nonoverlap Anatomic CT MRPD MRT1 MRT2 Anatomic 0 8250 8721 7719 9449 CT 2372 0 4173 1915 3853 MRPD 2984 1530 0 4446 3632 MRT1 2980 1234 1118 0 4292 MRT2 3390 1700 1434 800 0

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addagridtotheimages.Acarefulexaminationoftheimagesbeforeandafterregistrationrevealsthattheimagesareindeedbetteraligned.Foraquantita-tiveevaluationoftheregistration,wecoarselysegmenttheseimagesbybasicallysegmentingtheobjectfromthebackgroundintheimages.Thenwerepresentthesesegmentedimagesasbinaryimagesasshowningures 7{20 7{22 and 7{24 .(Objectiswithintensityvalue1andbackgroundiswithintensityvalue0.)Weevaluatethequalityoftheregistrationbycomparingthenumberofpixelsinthenonoverlapregionofpairwisesegmentedimagesbeforeandafterregistration.Fromtheseresultsintables 7{16 7{18 and 7{20 ,weseethatthenumberofpixelsinthenonoverlapregionofsegmentedpairwiseimagesafterregistrationismuchlesspriortoregistration.Providedthatthesegmentationerrorsarenotsignicantandthesecanalsobegaugedbyhumanperception,weseetheimagesarebetteralignedafterregistration.Also,fromthesegmentedimagesingures 7{20 7{22 and 7{24 ,weseethattheseimagesarebetteralignedafterregistration. Fromtheanetransformationsachievedintheregistrationasshownintables 7{15 7{17 and 7{19 ,weseethattheanetransformationsofallthreeimagesincludeacertainamountofshear.Thisservesasaverypreliminaryjusticationforusingananemapping. Fromtheseevaluationresultswhichareadmittedlyanecdotal,weseethatminimizingthenormalizedmeasureandcomputinghighdimensionalhistogramsworkswellforthesimultaneous(andunbiased)registrationofmultimodalityimages.

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Figure7{25. Therstrowaretheimagesbeforeregistrationand2ndrowistheimagesafterregistration. Figure7{26. CorrespondingMRPDimagesbeforeandafterregistration. totesttheabilityofourmulti-dimensionalhistogramcomputingtechniquetocomputeahighdimensionalhistogram.Thisisnotanarbitraryexercise.Whenweseektoestimateanatlasfromasetofmultimodalityimages,therststepistoregisterallimages.Thisexperimentisdesignedforthispracticalpurpose.Intheexperiment,wegiveeachimageananetransformationandminimizethenormalizedmeasuredenedon9imagesfor9anetransforms.Despitetheconsiderablecomputationalexpenseofthisapproach,westillusetheiteratedsequentialsearchalgorithminsectionIIbecausewedonotwanttobeaectedbythevagariesofaparticularsuboptimalsearchtechnique.Theimagesbeforeandafterregistrationareshowningure 7{25 Forthevalidationoftheregistration,wetransformthecorrespondingMRPDimagesofMRT2andMRT1usedinregistrationwiththeseanetransformationsobtainedintheregistrationshowningure 7{26 .ThenwecomputetheSSDsoftheintensityofpairwiseMRPDimagesbeforeandafterregistrationasshownintable 7{21 .Fromtheseresults,weseethemaximumdecreasingrateofthetheseSSDsis94.31%,theminimumdecreasingrateis43.54%andthemeandecreasingrateis67.53%.Hencetheseimagesaregotbetteralignmentafterregistration.

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Table7{21. SSDsofintensityofpairwiseMRPDimagesbeforeandafterregis-tration.uppertriangleisbeforeregistrationandlowertriangleisafterregistration SSDbeforeandafterRegistration 1 2 3 3 5 6 7 8 9 1 0 1519.3 2140.7 2677.4 2820.8 2934 2688.1 3172.9 3566.8 2 482.14 0 812.28 2846.7 2692 2737.9 3156.7 2684.6 2866 3 923.06 411.65 0 2932.8 2747.3 2680.5 3540.4 2842.7 2732.7 4 316.93 413.95 878.21 0 885.33 1259.1 4329.4 4439.1 4517 5 160.56 503.67 917.61 291.24 0 609.84 4445.3 4322.6 4329.2 6 258.91 534.18 1007.6 506.27 344.33 0 4515.2 4338 4259.1 7 983.29 522.9 496.31 1004.6 1033.1 949.24 0 2370.4 3275.8 8 937.78 448.48 364.34 948.83 976.48 933.76 205.73 0 1279.4 9 900.75 451.6 228.26 906.27 890.14 982.63 544.96 414.66 0 7.5.1ValidityofMultiresolutionOptimizationAlgorithmsoverB-Spline 1 forintermodalityregistrationandAlgorithm 2 formultimodalityregistration.Forintermodalityimageregistration,weuseBrainwebsynthetic3DMRdataandformultimodalityimageregistration,weuseVisibleHumanDataincluding2Danatomicalphoto,CTandMRdata. 6{7 )andusingAlgorithm 1 .TheresolutionsusedinAlgorithm 1 are16mmand8mm.

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Table7{22. DDF,ADFandSSDofintermodalityregistrationofsynthetic3DMRPDandT2imagesbeforeandafterregistration. image MRT2 MeasureofError DDF(mm) ADF(degree) SSD BeforeRegistration 2.91 10004 IntermodalityRegistration 0.92 13.9 949 Inordertovalidatetheregistrationresultfromintermodalityregistration,weusethreeerrormeasure:dierenceofdisplacementeld(DDF),anglebetweendisplacementelds(ADF)andsumofsquaredierenceofintensity(SSD). Intable 7{22 ,weshowDDFandSSDbeforeregistrationandafterintermodal-ityregistration.WecanseeDDFandSSDafterintermodalityregistrationaremuchlessthanthosebeforeregistration.Andacarefulexaminationoftheimagesbefore(gure 7{27 )andafterregistration(gure 7{28 )revealsthattheimagesareindeedbetteraligned.HencethemultiresolutionoptimizationalgorithmfornonrigidintermodalityimageregistrationorAlgorithm 1 isvalid. k^vxkkuxk.LetIbeoriginalim-ageand^Iberecoveredimage,thenSSD=Px^IxIx2,whereNisthenumberofimagepixelsandxrepresentsapixelintheimage.

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(a)MRPDslices (b)MRT2slicesbeforeregistration Figure7{27. Someslicesof3DMRPDandT2imagesbeforeregistration. (c)deformedgridusingdisplacementeld (d)MRT2slicesafterregistration Figure7{28. Someslicesof3DMRPDandT2imagesafterregistration.

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Figure7{29. Anatomicalphotoandoverlapof3imagesbeforeandafterregistra-tion. 6{1 )andAlgorithm 2 .TheresolutionsusedinAlgorithm 2 are32mm,24mmand16mm. (a)ingure 7{29 istheanatomicalphoto,whichistargetinregistration.(d)ingure 7{30 and(g)ingure 7{31 areCTandMRPDimages,whicharethesourceimagesintheregistration.(b)ingure 7{29 istheoverlapofanatomical

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Figure7{30. CTimagebeforeandafterregistrationanddeformedgridwithdis-placementeld. Figure7{31. PDimagebeforeandafterregistrationanddeformedgridwithdis-placementeld. Table7{23. Crosscorrelationoftheimagesbeforeandafterregistration.Uppertriangleisbeforeregistrationandlowertriangleisafterregistration.[Datasetindex:VHD#1080.] crosscorrelation Anatomic CT MRPD Anatomic 1 0.7540 0.7707 CT 0.7898 1 0.7779 MRPD 0.8433 0.8367 1

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(a)Anatomical(target) (b)CT (c)MRPD (d)Overlap Figure7{32. Segmentedimagesbeforeregistration. (a)Anatomical(target) (b)CT (c)MRPD (d)Overlap Figure7{33. Segmentedimagesafterregistration. Table7{24. Numberofpixelsinnonoverlapregionofsegmentedimagesbeforeandafterregistration.Uppertriangleisbeforeregistrationandlowertriangleisafterregistration.[Datasetindex:VHD#1080.] nonoverlap Anatomic CT MRPD Anatomic 0 6832 5519 CT 1833 0 3637 MRPD 1706 595 0

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,CTandMRPDimagesbeforeregistration.(e)ingure 7{30 and(h)ingure 7{31 aretheCTandMRPDimagesafterregistration.(c)ingure 7{29 istheoverlapofanatomical,CTandMRPDimagesafterregistration.(f)ingure 7{30 and(i)ingure 7{31 arethedeformedgridwithdisplacementeldsofregistrationofCTandMRPDimages.Acarefulexaminationoftheimagesbeforeandafterregistrationrevealsthattheimagesareindeedbetteraligned.Ourrstquantitativevalidationofthismultimodalityregistrationexperimentisbycomputingthecrosscorrelation 7{23 ,fromwhichweseethepairwisecrosscorrelationsbecomebiggeraftertheregistration,whichmeanstheimagesaremorecorrelatedorbetteralignedaftertheregistration.Foranotherquantitativeevaluationoftheregistration,wecoarselysegmenttheseimagesbybasicallysegmentingtheobjectfromthebackgroundintheimages.Thenwerepresentthesesegmentedimagesasbinaryimagesasshowningures 7{32 and 7{33 .(Objectiswithintensityvalue1andbackgroundiswithintensityvalue0.)Inorderforhumanperceptiontogaugetheresultsofregistration,weaddagridtotheimages.Weevaluatethequalityoftheregistrationbycomparingthenumberofpixelsinthenonoverlapregionofpairwisesegmentedimagesbeforeandafterregistration.Fromtheseresultsintables 7{24 ,weseethatthenumberofpixelsinthenonoverlapregionofsegmentedpairwiseimagesafterregistrationismuchlesspriortoregistration.Providedthatthesegmentationerrorsarenotsignicantandthesecanalsobegaugedbyhuman Px(I(1)xI(1))2q P(I(2)xI(2))2

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perception,weseetheimagesarebetteralignedafterregistration.Also,fromthesegmentedimagesingures 7{32 and 7{33 ,weseethattheseimagesarebetteralignedafterregistration.HencethemultiresolutionoptimizationalgorithmfornonrigidmultimodalityimageregistrationorAlgorithm 2 isvalid. WewillusesyntheticMRPD,T2andT13Dimageinthisexperiment.Theimagesize10111993andthepixelsizeis1mm.Theintensityofallimagesarenormalizedtorange[01].Atthebeginning,allimagesareregisteredthenweusearticialdisplacementeldu(1)todeformT1imageanduseu(2)todeformPDimage.WewillregisterthedeformedT1anddeformedPDimagestotheT2image.Inintermodalityregistration,wendthedisplacementelduinter(1),whichregisterthedeformedT1imagetoT2image,anduinter(2),whichregisterthedeformedPDimagetoT2image,byminimizingenergyfunction( 6{7 )andAlgorithm 1 .Inmultimodalityregistration,wendthedisplacementeldumulti(1),whichregisterthedeformedT1imagetoT2image,andumulti(2),whichregisterthedeformedPDimagetoT2image,byminimizingenergyfunction( 6{1 )andAlgorithm 2 .TheresolutionsusedinAlgorithm 1 are16mmand8mmandtheresolutionsusedinAlgorithm 2 is8mmbecauseweusetheresultsfromintermodalityregistrationasinitialvalueofmultimodalityregistration.Inordertocomparetheresultsfromintermodalityregistrationandmultimodalityregistration,weusethreeerror

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Table7{25. DDFsandSSDsofSimultaneousregistrationof3imagesvs.pair-wiseregistrationonsyntheticPD,T2andT13DMRimagesbeforeandafterregistration.Therstrowistheerrorsbeforeregistration,thesecondrowistheerrorsafterintermodalityregistrationandthethirdrowistheerrorsaftermultimodalityregistration. MRT1 MRPD MeasureofError DDF(mm) ADF(degree) SSD DDF(mm) ADF(degree) SSD Before 9.7 43337 9.7 92879 Inter. 3.5 8.0 4378 3.4 7.6 10312 Multi. 3.4 7.3 4277 3.3 7.4 10120 7{25 ,weshowDDF,ADFandSSDbeforeregistration,afterinter-modalityregistrationandmultimodalityregistration.Fromtheseresults,wecanseeDDF,ADFandSSDafterintermodalityormultimodalityregistrationaremuchlessthanthosebeforeregistrationandtheresultsofmultimodalityregistrationisbetterthanthoseofintermodalityregistration,whichhavebeenseeninpreviousaneregistration.Hencethemultimodalityregistrationismoreaccuratethan

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(a)MRT2slices(target) Figure7{34. Someslicesof3DMRT2images(targetintheregistration). (b)MRT1slicesbeforeregistration (c)MRPDslicesbeforeregistration Figure7{35. Someslicesof3DMRT1andPDimagesbeforeregistration.

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(d)MRT1slicesafterregistration (e)MRPDslicesafterregistration Figure7{36. Someslicesof3DMRT1andPDimagesafterregistration. (f)deformedgridofMRT1 (g)deformedgridofMRPD Figure7{37. Deformedgridwithdisplacementeldsof3DMRT1andPDimagesinregistration.

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Table7{26. SSDsbeforeregistrationandafterunbiasedmultimodalityregistrationof3MR3Dimages.Uppertriangleisbeforeregistrationandlowertriangleisafterregistration. SSDs 1 2 3 1 0 26767 17880 2 10284 0 21519 3 7570 6378 0 intermodalityregistrationinnonrigidregistration,too.Figure 7{34 is36slicesof3DMRT2imagesbeforeregistration,whichisthetargetimageofregistration.Figure 7{35 andgure 7{36 areMRT1andMRT2imagesbeforeregistrationandaftermultimodalityimageregistration.Acarefulexaminationoftheimagesbeforeandafterregistrationrevealsthattheimagesareindeedbetteraligned.Figure 7{37 showsthethedeformedgridsofdisplacementeldsinregistrationofMRT1andPDimages.Sincetwoimageshavesamedeformation,therecovereddisplacementeldsalsoalmostlookssame. 6{2 )andAlgorithm 2 .TheresolutionsusedinAlgorithm 2 are32mm,24mmand16mm.Inordertovalidatetheresultsoftheunbiasedmultimodalityregistration,wecomputetheerrormeasure:SSD.TheSSDbeforeregistrationistheintensitydierencebetweeneachtwoimagesandtheSSDafterunbiasedmultimodalityregistrationistheintensitydierencebetweeneachtworegisteredimageswithdisplacementeldumulti(m),m=1;2;3.

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Figure7{38. SomeslicesofthreeMR3Dimagesbeforeregistration. Figure7{39. SomeslicesofthreeMR3Dimagesafterregistration. Figure7{40. Gridsdeformedwithdisplacementeldsinunbiasedmultimodalityimageregistration

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Intable 7{26 ,weshowSSDsbeforeregistrationandafterunbiasedmul-timodalityregistrationof3MR3Dimages.WecanseeSSDsafterunbiasedmultimodalityregistrationaremuchlessthanthosebeforeregistration.Figure 7{38 andgure 7{39 are25slicesof3DMRimagesbeforeregistrationandafterunbi-asedmultimodalityimageregistration.Acarefulexaminationoftheimagesbeforeandafterregistrationrevealsthattheimagesareindeedbetteraligned.Figure 7{40 showsthethedeformedgridsofdisplacementeldsinunbiasedmultimodalityimageregistrationof3MR3Dimages. Fromtheexperimentalresults,theunbiasedmultimodalityimageregistrationisvalidandthemethodscanbeusedtobuildanatlasofmultipleimages.

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Inthedissertation,rstlyweproposeaBayesianmultimodalitynon-rigidimageregistrationmethodandweprovethatthedisplacementeldwhichmin-imizestheBayesianmaximumaposteriori(MAP)objectivealsomaximizesthetruemutualinformation(withasmalldeformationpenalty)asthenumberofpixelstendstoinnity.Thecriterionimposesanupperboundonthenumberofpermissiblecongurationsofthedisplacementeld.Wethinkthisisthersttimethatsuchaquantitativecriterionhasbeenderivedtohelpassessthevalidityofnon-parametricdensityestimationapproachestomultimodalitynon-rigidregistra-tion.Thecriterion|asucientcondition|requiresthatthenumberofallowedcongurationsofthedisplacementeldgrowmoreslowlythanthenumberofimagepixelsdoes.Thecriterioniseasilysatisedinthecaseofquantized,aneparam-etercongurationsbutisnotsatisedinthegeneralnon-rigidsetting.Andunderthiscondition,themaximizerofBayesianMAPalsomaximizesthetruemutualinformation. Secondly,wendabetterfeaturethanimageintensityforNMI-basedinter-modalityimageregistration.WehavedemonstratedaproofofconceptofthebasicideathatfeatureimagescanimproveupontheoriginalintensitieswhenusingNMIasaregistrationmeasure.Thebestfeaturecombinationofimagesineachmodalityisobtainedbyprojectingthesetoffeatureimagesontothesinglebestdimension,withNMIbeingthecriteriononceagain. Thirdly,Wehavepresentedaninformationmetricforintermodalityimageregistration,whichcanbeeasilyextendedtothemultimodalitycaseasopposedtomutualinformationwhichisnotsoeasilyextended.Theinformationmetricis 96

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alinearcombinationofconditionalentropiesandhasthepropertiesofsymmetry,non-negativityandtriangleinequality.Normalizedversionsofthisextensiblein-formationmetricarealsoproposedandusedformultimodalityimageregistration.Wederiveanduseanewecienttechniqueforcomputinghighdimensionalhis-togramssoastoecientlycomputethejointentropyofmultipleimages.Wethendemonstratehowthehighdimensionalhistogrammingtechniquecanbeusedtosimultaneouslyregistermanyimageswithoutbeingbiasedtoareferenceimage. Thereareafewpossiblefuturework,whichcanfollowthedissertation.Firstly,forBayesianmultimodalityimageregistrationmethod,apossibledirectionistoextendthetheorytocontinuouscase,whichmeanstondaquantitativecriterionorasucientcondition,underwhichthemaximizerofBayesianMAPalsomaximizesthetruemutualinformationwhencongurationsofthedisplacementeldarecontinuous.Secondly,fortheuniedfeature-basedmultimodalityimagesregistrationmethod,thebasicideahowtoget\bestfeature"forNMI-basedregistrationmethodcanbeusedtootherintensitysimilaritymeasuresandthefeaturesetscanalsobeaddedmorefeaturessuchasthefeaturesfrommultipledirectionGaborlters,fromindependentcomponentanalysisandetc.Thirdly,fortheextensiblemetricandhighdimensionalhistogramusedtomultimodalityimageregistration,agooddirectionistondananalyticanddierentiableformforenergyfunctionsothatthegradientcanbecomputedanalyticallytoacceleratethemultiresolutionoptimizationalgorithm.Withtheacceleratedalgorithm,moreimagescanberegisteredsimultaneouslysothatanatlasofmanyimagescanalsobegeneratedthroughunbiasedregistration.

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Proofsofthetriangleinequalityofthemetric(X;Y)=H(XjY)+H(YjX)andthenormalizedmetric(X;Y)=H(XjY)+H(YjX) Prove(X;Y)+(Y;Z)(X;Z) orH(XjY)+H(YjX)+H(YjZ)+H(ZjY)H(XjZ)+H(ZjX): Usingthepropertiesofentropy:H(XjY)H(XjY;Z)andH(X;Y;Z)H(X;Z),wehaveH(XjY)+H(YjZ)H(XjY;Z)+H(YjZ)=H(X;Y;Z)H(Y;Z)+H(Y;Z)H(Z)H(X;Z)H(Z)=H(XjZ) Insameway,wehaveH(ZjY)+H(YjX)H(ZjX):Hencethethetriangleinequalityofthemetric(X;Y)=H(XjY)+H(YjX)isproved. Prove(X;Y)+(Y;Z)(X;Z) 98

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orH(XjY)+H(YjX) Usingthepropertiesofentropy:H(XjY)H(XjY;Z)andH(X;Y;Z)H(X;Z),wehaveH(XjY)+H(YjX) AndH(YjZ)H(YjX;Z)+H(XjY;Z)=H(Y;Z)H(Z)H(X;Y;Z)+H(X;Z)+H(X;Y;Z)H(Y;Z)=H(X;Z)H(Z)=H(XjZ) andH(YjX)H(YjX;Z)+H(ZjX;Y)=H(X;Y)H(X)H(X;Y;Z)+H(X;Z)+H(X;Y;Z)H(X;Y)=H(X;Z)H(X)=H(ZjX)

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Thus()=H(XjZ)+H(ZjX)+H(XjY)H(XjY;Z)+2H(YjX;Z)+H(ZjY)H(ZjX;Y) Hencethetriangleinequalityofthenormalizedmetric(X;Y)=H(XjY)+H(YjX) Acounterexampleforthat(X;Y)=(X;Y) LetH(X)=9 2,H(Y)=15 2,H(Z)=9 2,H(X;Y)=8,H(Y;Z)=8andH(X;Z)=8. Then(X;Y)=4,(Y;Z)=4and(X;Z)=7;(X;Y)=1 2,(Y;Z)=1 2and(X;Y)=7 8;(X;Y)=1 3,(Y;Z)=1 3and(X;Z)=7 9.Thuswehave(X;Y)+(Y;Z)(X;Z)(X;Y)+(Y;Z)(X;Z) but(X;Y)+(Y;Z)<(X;Z):Hence(X;Y)=(X;Y)

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[1] D.Hill,P.Batchlor,M.Holden,andD.Hawkes,\Medicalimageregistration,"Phys.Med.Biol.,vol.46,no.3,pp.R1{R45,2001. [2] J.B.A.MaintzandM.A.Viergever,\Asurveyofmedicalimageregistra-tion,"MedicalImageAnalysis,vol.2,pp.1{36,1998. [3] P.vandenElsen,E.-J.D.Pol,andM.Viergerver,\Medicalimagematching:areviewwithclassication,"IEEEEng.Med.Biol.,vol.12,pp.26{39,1993. [4] K.Rohr,Landmark-basedimageanalysis:usinggeometricandintensitymodels.Norwell,MA:KluwerAcademicPublishers,2001. [5] M.Alker,S.Frantz,K.Rohr,andH.S.StiehlAlker,\Improvingthero-bustnessinextracting3Dpointlandmarksfrom3Dmedicalimagesusingparametricdeformablemodels,"inMICCAI2002,pp.582{590,NewYork,NY:Springer,2002. [6] S.WorzandK.Rohr,\Localizationofanatomicalpointslandmarksin3Dmedicalimagesbytting3Dparametricintensitymodels,"inIPMI2003,pp.76{88,NewYork,NY:Springer,2003. [7] C.Small,Thestatisticaltheoryofshape.NewYork,NY:Springer-Verlag,1996. [8] I.DrydenandK.Mardia,Statisticalshapeanalysis.NewYork,NY:JohnWileyandSon,1998. [9] G.GolubandC.VanLoan,Matrixcomputations.Baltimore,MD:JohnsHopkinsUniversityPress,2nded.,1989. [10] H.ChuiandA.Rangarajan,\Anewalgorithmfornon-rigidpointmatching,"inProceedingsofIEEEConf.onComputerVisionandPatternRecognition{CVPR2000,vol.2,pp.44{51,Piscataway,NJ:IEEEPress,2000. [11] S.Belongie,J.Malik,andJ.Puzicha,\Shapematchingandobjectrecognitionusingshapecontext,"IEEEtrans.PatternAnal.Mach.Intell.,vol.24,no.24,pp.509{522,2002. [12] S.JoshiandM.Miller,\Landmarkmatchingvialargedeformationdieomor-phisms,"IEEETrans.ImageProcessing,vol.9,pp.1357{1370,2000. 101

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[13] C.PapadimitriouandK.Steiglitz,Combinatorialoptimization.EnglewoodClis,NJ:Prentice-Hall,Inc.,1982. [14] R.JonkerandA.Volgenant,\Ashortestaugmentingpathalgorithmfordenceandsparselinearassignmentproblems,"Computing,vol.38,pp.325{340,1987. [15] P.J.BeslandN.D.McKay,\Amethodforregistrationof3-Dshapes,"IEEETrans.Patt.Anal.Mach.Intell.,vol.14,pp.239{256,Feb.1992. [16] E.Cuchet,J.Knoplioch,D.Dormont,andC.Marsault,\Registrationinneurosurgeryandneuroradiotherapyapplications,"J.ImageGuidedSurg.,vol.1,pp.198{207,1995. [17] J.Declerck,J.Feldmar,M.Goris,andF.Betting,\Automaticregistrationandalignmentonatemplateofcardiacstressandrestreorientedspectimages,"IEEETrans.Med.Imaging,vol.16,pp.727{737,1997. [18] C.J.Maurer,R.Maciunas,andJ.Fitzpatrick,\RegistrationofheadCTimagestophysicalspaceusingaweightedcombinationofpointsandsurfaces,"IEEETrans.onMed.Imaging,vol.17,pp.753{761,1998. [19] J.FeldmarandN.Ayache,\Rigid,aneandlocallyaneregistrationoffree-formsurfaces,"Intl.J.ComputerVision,vol.18,pp.99{119,May1996. [20] H.Chui,J.Rambo,J.Duncan,R.Schultz,andA.Rangarajan,\Registrationofcorticalanatomicalstructuresviarobust3Dpointmatching,"inProceedingsofInformationProcessinginMedicalImaging{IPMI99,pp.168{181,NewYork,NY:Springer-Verlag,1999. [21] C.A.Pelizzari,G.T.Y.Chen,D.R.Spelbring,R.R.Weichselbaum,andC.-T.Chen,\Accuratethree-dimensionalregistrationofCT,PET,and/orMRimagesofthebrain,"J.ComputerAssistedTomography,vol.13,pp.20{26,1989. [22] D.N.Levin,C.A.Pelizzari,C.T.Chen,andM.D.Cooper,\RetrospectivegeometriccorrelationofMR,CT,andPETimages,"Radiology,vol.169,pp.817{823,1988. [23] H.Jiang,K.Holton,andR.Robb,\Imageregistrationofmultimodality3Dmedicalimagesbychamfermatching,"inProc.SPIEBiomedicalImageProcessingandThree{DimensionalMicroscopy,vol.1660,pp.356{366,Bellingham,WA:SPIEPress,1992. [24] P.VandenElsen,Multimodalitymatchingofbrainimages.PhDthesis,UtrechtUniversity,Utrecht,Netherlands,1993.

PAGE 118

[25] G.Borgefors,\Hierarchicalchamfermatching:aparametricedgematchingalgorithm,"IEEETrans.Patt.Anal.Mach.Intell.,vol.10,no.6,pp.849{865,1988. [26] C.HuangandO.Mitchell,\Aeuclideandistancetransformusinggrayscalemorphologydecomposition,"IEEETransactiononPatternAnalysisandMachineIntelligence,vol.16,pp.443{448,1994. [27] X.Gu,Y.Wang,andS.-T.Yau,\Multiresolutioncomputationofconformalstructuresofsurfaces,"JournalofSystemics,vol.1,no.6,pp.1{6,2004. [28] X.Gu,Y.Wang,T.F.Chan,P.M.Thompson,andS.-T.Yau,\Genuszerosurfaceconformalmappinganditsapplicationtobrainsurfacemapping,"IEEETransactiononMedicalImaging,vol.23,no.7,pp.1{8,2004. [29] H.Li,B.Manjunath,andS.Mitra,\Acontour-basedaproachtomultisensorimageregistration,"IEEETrans.onImageProcessing,vol.4,no.3,pp.239{254,1995. [30] E.Klassen,A.Srivastava,W.Mio,andS.Joshi,\Analysisofplanarshapesusinggeodesicpathsonshapespaces,"IEEETransactiononPatternAnalysisandMachineIntelligence,vol.26,no.3,pp.372{383,2004. [31] J.Maintz,P.A.vandenElsen,andM.A.Viergerver,\Comparisonofedge-basedandridge-basedregistrationofCTandMRbrainimages,"Med.ImageAnal.,vol.1,no.2,pp.151{161,1996. [32] J.Liu,B.Vemuri,andJ.Marroquin,\Localfrequencyrepresentationsforrobustmultimodalimageregistration,"IEEETransactiononMedicalImaging,vol.21,no.5,pp.462{469,2002. [33] A.O.Hero,B.Ma,O.Michel,andJ.Gorman,\Applicationsofentropicspanninggraphs,"IEEESignalProc.Magazine(SpecialIssueonMathematicsinImaging),vol.19,no.5,pp.85{95,2002. [34] H.Neemuchwala,A.Hero,P.Carson,andC.Meyer,\Localfeaturematchingusingentropicgraphs,"inIEEEInternationalSymposiumonBiomedicalImaging,pp.704{707,Arlington,VA:MiraDigitalPublishing,2004. [35] P.ViolaandW.M.WellsIII,\Alignmentbymaximizationofmutualinfor-mation,"inFifthIntl.Conf.ComputerVision(ICCV),pp.16{23,Piscataway,NJ:IEEEPress,1995. [36] A.Collignon,D.Vandermeulen,P.Suetens,andG.Marchal,\3Dmulti{modalitymedicalimageregistrationusingfeaturespaceclustering,"inComputerVision,VirtualRealityandRoboticsinMedicine(N.Ayache,ed.),vol.905ofLectureNotesinComputerScience,NewYork,NY:Springer{Verlag,1995.

PAGE 119

[37] J.P.W.Pluim,J.B.A.Maintz,andM.A.Viergever,\Mutual-information-basedregistrationofmedicalimages:Asurvey,"IEEETrans.onMedicalImaging,vol.22,no.8,pp.986{1004,2003. [38] C.Studholme,D.L.G.Hill,andD.J.Hawkes,\Anoverlapinvariantentropymeasureof3Dmedicalimagealignment,"PatternRecognition,vol.32,no.1,pp.71{86,1999. [39] B.Kim,J.L.Boes,K.A.Frey,andC.R.Meyer,\Mutualinformationforautomatedunwarpingofratbrainautoradiographs,"NeuroImage,vol.5,pp.31{40,1997. [40] J.B.A.Maintz,H.W.Meijering,andM.A.Viergever,\Generalmultimodalelasticregistrationbasedonmutualinformation,"inMedicalImaging|ImageProcessing(SPIE3338),vol.3338,pp.144{154,Bellingham,WA:SPIEPress,1998. [41] N.Hata,T.Dohi,S.Wareld,W.Wells,R.Kikinis,andF.A.Jolesz,\Mul-timodalitydeformableregistrationofpre-andintraoperativeimagesforMRI-guidedbrainsurgery,"inMedicalImageComputingandComputer-AssistedIntervention(MICCAI)(W.Wells,A.Colchester,andS.Delp,eds.),pp.1067{1074,NewYork,NY:Springer,1998. [42] D.Rueckert,L.I.Sonoda,C.Hayes,D.L.G.Hill,M.O.Leach,andD.J.Hawkes,\Non-rigidregistrationusingfree-formdeformations:ApplicationtobreastMRimages,"IEEETrans.Med.Imag.,vol.18,no.8,pp.712{721,1999. [43] T.Rohlng,R.Brandt,C.R.Maurer,andR.Menzel,\Beebrains,B-splinesandcomputationaldemocracy:Generatinganaverageshapeatlas,"inIEEEWorkshoponMathematicalMethodsinBiomedicalImageAnalysis(MMBIA),pp.187{194,Piscataway,NJ:IEEEPress,2001. [44] T.Gaens,F.Maes,D.Vandermeulen,andP.Suetens,\Non-rigidmultimodalimageregistrationusingmutualinformation,"inMedicalImageComputingandComputer-AssistedIntervention(MICCAI)(W.Wells,A.Colchester,andS.Delp,eds.),pp.1099{1106,NewYork,NY:Springer,1998. [45] L.Lemieux,R.Jagoe,D.Fish,N.Kitchen,andD.Thomas,\Apatient-to-computed-tomographyimageregistrationmethodbasedondigitallyreconstructedradiographs,"Med.Phys.,vol.21,no.11,pp.1749{1760,1994. [46] L.Lemieux,U.Wieshmann,N.Moran,D.Fish,andS.Shorvon,\Thedetectionandsignicanceofsubtlechangesinmixed-signalbrainlesionbyserialMRIscanmatchingspaticalnormalization,"Med.ImageAnal.,vol.21,pp.227{242,1998.

PAGE 120

[47] T.M.Buzug,J.Weese,C.Fassnacht,andC.Lorenz,\UsinganentropysimilaritymeasuretoenhancethequalityofDSAimageswithanalgorithmbasedontemplatematching,"inVisualizationinBiomedicalComputing(K.H.HohneandR.Kikinis,eds.),vol.1131ofLecturenotesinComputerScience,pp.235{240,NewYork,NY:Springer-Verlag,1996. [48] U.Weese,T.M.Buzug,C.Lorenz,andC.FassnachtAlker,\Anapproachto2D/3Dregistrationofavertebrain2DX-rayuoroscopieswith3DCTimages,"inProceedingsoftheFirstJointConferenceonComputerVision,VirtualRealityandRoboticsinMedicineandMedialRoboticsandComputer-AssistedSurgery,pp.119{128,NewYork,NY:Springer,1997. [49] C.Studholme,D.Hill,andD.Hawkes,\MultiresolutionvoxelsimilaritymeasuresforMR-PETregistration,"inInformationProcessinginMedicalImaging,pp.287{298,NewYork,NY:Springer,1995. [50] A.Collignon,F.Maes,D.Delaere,D.Vandermeulen,P.Suetens,andG.Mar-chal,\Automatedmulti-modalityimageregistrationbasedoninformationtheory,"inInformationProcessinginMedicalImaging,pp.263{274,NewYork,NY:Springer,1995. [51] M.E.LeventonandW.E.L.Grimson,\Multi-modalvolumeregistra-tionusingjointintensitydistributions,"inMedicalImageComputingandComputer-AssistedIntervention(MICCAI)(W.Wells,A.Colchester,andS.Delp,eds.),pp.1057{1066,NewYork,NY:Springer,1998. [52] F.Wang,B.Vemuri,M.Rao,andY.Chen,\Anewandrobustinformationtheoreticmeasureanditsapplicationtoimagealignment,"inInformationProcessinginMedicalImaging,pp.388{400,NewYork,NY:Springer,2003. [53] G.Penney,J.Weese,J.Little,P.Desmedt,D.Hill,andD.Hawkes,\Acom-parisonofsimilaritymeasureforusein2-D-3-Dmedicalimageregistration,"IEEETransactiononMedicalImaging,vol.17,no.4,pp.586{595,1998. [54] T.CoverandJ.Thomas,Elementsofinformationtheory.NewYork,NY:JohnWileyandSons,1991. [55] C.Studholme,D.L.G.Hill,andD.J.Hawkes,\Incorporatingconnectedregionlabellingintoautomatedimageregistrationusingmutualinformation,"inMathematicalmethodsinbiomedicalimageanalysis(MMBIA)(A.A.Amini,F.L.Bookstein,andD.C.Wilson,eds.),pp.23{31,SanFrancsico,CA:IEEEComputerSoc.Press,1996. [56] J.L.BoesandC.R.Meyer,\Multi-variatemutualinformationforregis-tration,"inMedicalimagecomputingandcomputer-assistedintervention(MICCAI)(C.TaylorandA.Colchester,eds.),vol.1679ofLecturenotesinComputerScience,pp.606{612,NewYork,NY:Springer-Verlag,1999.

PAGE 121

[57] J.A.Lynch,C.G.Peterfy,D.L.White,R.A.Hawkins,andH.K.Genant,\MRI-SPECTimageregistrationusingmultipleMRpulsesequencestoexamineosteoarthritisoftheknee,"inMedicalImaging:ImageProcessing(K.M.Hanson,ed.),vol.3661ofProc.SPIE,pp.68{77,SanDiego,CA:SPIE,1999. [58] V.PoosalaandY.Ioannidis,\Selectivityestimationwithouttheattributevalueindependenceassumption,"in23rdVLDBConference,pp.486{495,SanFrancisco,CA:MorganKaufmannPublishersInc.,1997. [59] R.ZhaoandG.G.Belford,\Anextendableregistrationsimilaritymetricforanatomicalimagesequencealignment,"inIEEEInternationalSymposiumonBiomedicalImaging,pp.736{739,Arlington,VA:MiraDigitalPublishing,2004. [60] A.RangarajanandR.Chellappa,\Markovrandomeldmodelsinimageprocessing,"inHandbookofBraintheoryandNeuralNetworks,pp.564{567,Cambridge,MA:MITPress,1995. [61] S.C.Zhu,Y.N.Wu,andD.B.Mumford,\Minimaxentropyprincipleanditsapplicationstotexturemodeling,"NeuralComputation,vol.9,no.8,pp.1627{1660,1997. [62] F.Maes,A.Collignon,D.Vandermeulen,G.Marchal,andP.Suetens,\Multi-modalityimageregistrationbymaximizationofmutualinformation,"IEEETrans.Med.Imag.,vol.16,no.2,pp.187{198,1997. [63] W.WellsIII,P.Viola,H.Atsumi,S.Nakajima,andR.Kikinis,\Multi-modalvolumeregistrationbymaximizationofmutualinformation,"MedicalImageAnalysis,vol.1(1),pp.35{52,1996. [64] G.Wahba,Splinemodelsforobservationaldata.Philadelphia,PA:SIAM,1990. [65] V.N.Vapnik,Statisticallearningtheory.NewYork:JohnWiley,1998. [66] C.Rajski,\Ametricspaceofdiscreteprobabilitydistributions,"InformationandControl,vol.4,pp.371{377,1961. [67] C.Yang,R.Duraiswami,N.Gumerov,andL.Davis,\ImprovedfastGausstransformandecientkerneldensityestimation,"inNinthIEEEInternationalConferenceonComputerVision(ICCV),vol.1,pp.464{471,Washington,DC:IEEEComputerSociety,2003. [68] L.Devroye,L.Gyor,andG.Lugosi,Aprobabilistictheoryofpatternrecogni-tion.NewYork,NY:Springer-Verlag,1997.

PAGE 122

[69] J.ZhangandA.Rangarajan,\Aneimageregistrationusinganewinfor-mationmetric,"inIEEEComputerVisionandPatternRecognition(CVPR),vol.1,pp.848{855,Washington,DC:IEEEComputerSociety,2004. [70] J.ZhangandA.Rangarajan,\Multimodalityimageregistrationusinganextensibleinformationmetricandhighdimensionalhistogramming,"inInformationProcessinginMedicalImaging|IPMI2005,pp.725{737,NewYork,NY:Springer,2005. [71] S.Lee,G.Wolberg,andS.Y.Shin,\ScattereddatainterpolationwithmultilevelB-spline,"IEEETrans.VisualizationandComputerGraphics,vol.3,pp.228{244,July1997. [72] D.L.Collins,A.P.Zijdenbos,V.Kollokian,J.G.Sled,N.J.Kabani,C.J.Holmes,andA.C.Evans,\Designandconstructionofarealisticdigitalbrainphantom,"IEEETrans.Med.Imag.,vol.17,no.3,pp.463{468,1998. [73] A.M.MartinezandR.Benavente,\TheARfacedatabase,"Tech.Rep.24,ComputerVisionCenter,theUniversityAutnomadeBarcelona,Barcelona,Spain,1998.

PAGE 123

JieZhangwasborninXiningofChina.HereceivedhisBSincomputationalmathematicsfromCentralUniversityforNationinBeijing,hisMSinappliedmathematicsfromBeijingNormalUniversityinBeijingandhisPhDincomputerengineeringfromtheUniversityofFloridainFlorida.Hisresearchinterestsincludebiomedicalimageanalysis,computervision,patternrecognition,machinelearninganddatamining. 108


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NEW INFORMATION THEORETIC DISTANCE MEASURES
AND ALGORITHMS FOR MULTIMODALITY IMAGE REGISTRATION
















By

JIE ZHANG


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2005

































Copyright 2005

by

Jie Zhang



































I dedicate this work to my family.















ACKNOWLEDGMENTS

Firstly I extend my thanks to my advisor Dr. Anand Rangarajan for his

excellent academic guidance and open-minded research support. It was pleasure

but tough to pursue my PhD degree under his advising and pressing. Working with

him for 5 years was worthy and fruitful, from which my future will benefit. I also

express my thanks to Dr. Arunava Banerjee, Dr. Yunmei C'!, i, Dr. Jorg Peters

and Dr. Baba C. Vemuri for their willingness to serve on my committee and their

valuable comments to the dissertation.

I also thank my fellow students Hongyu Guo, Fei Wang, Bin Jian, Eric

Spellman, Santhosh Kodipaka and Ajit Rajwade for their help and support in

studying and research. And I also extend my thanks to my friends: Xiaohui

Gao, Weihong Guo, Qingguo Zeng, Hongchao Zhang and others, who helped and

supported me in my life and studying at UF.

Finally I would express my appreciations to my parents and sister for their

understanding and encouragement in my life.















TABLE OF CONTENTS
page

ACKNOWLEDGMENTS ................... ...... iv

LIST OF TABLES ................... .......... viii

LIST OF FIGURES ................................ x

ABSTRACT ................... .............. xiv

CHAPTER

1 INTRODUCTION ........................... 1

1.1 W hat is Registration? ......................... 2
1.2 Contributions of the Dissertation Work ......... .... .... 4
1.2.1 A B ,i- i i, Multimodality Nonrigid Image Registration
Method ............ .. ............. 4
1.2.2 A Unified Feature-based Registration Method for Multi-
modality Images ....... . . . 5
1.2.3 Multimodality Image Registration Using an Extensible In-
formation Metric and High Dimensional Histogramming 5
1.3 Outlines of the Dissertation ..... ........... ... 6

2 RELATED PREVIOUS WORK .................. ...... 9

2.1 Feature-based Methods .................. ..... 9
2.1.1 Point-based Registration ................. 9
2.1.2 Surface-based Registration .............. .. .. 10
2.1.3 Edge-based Registration .................. .. 12
2.1.4 Other Feature-based Registration . . ..... 12
2.2 Intensity-based Registration ..... ........... .... 12
2.2.1 Mutual Information .................. .... 13
2.2.2 Normalized Cross Correlation. .. . . ..... 14
2.2.3 Entropy of Difference Image and Pattern Intensity ..... 14
2.2.4 Joint Entropy and Joint Probability . . 15
2.2.5 Other Measures .................. ... .. 16
2.3 Multimodality Image Registration ......... .16
2.3.1 Mutual Information .................. .... 16
2.3.2 Jensen Divergence ........ . . .... 18
2.3.3 Minimum Entropy of Bad Prediction (ll: IP) ..... ..19









3 BAYESIAN MULTIMODALITY NON-RIGID IMAGE REGISTRA-
TION VIA CONDITIONAL DENSITY ESTIMATION .......... 20

3.1 Conditional Density Estimation ........ ........... 20
3.2 B li, -i ,i Non-rigid Registration .... .............. 21
3.3 Convergence of the B li, -i ,i MAP Minimizer in the General Set-
ting ................... .............. 23

4 A UNIFIED FEATURE-BASED REGISTRATION METHOD FOR MUL-
TIMODALITY IMAGES ................... ....... 29

4.1 Feature Combination .......... ...... ......... 30
4.2 Affine Image Registration with the "B, -1 Feature Images .... 31

5 SIMULTANEOUS MULTIMODALITY IMAGE REGISTRATION US-
ING AN EXTENSIBLE INFORMATION METRIC AND HIGH DI-
MENSIONAL HISTOGRAMMING .......... ....... .... 32

5.1 Multimodality Registration Using the Extensible Metric ...... 33
5.1.1 Metric Definition ................. ..... .. 33
5.1.2 Relationship between the Information Metric and Mutual
Information ................... ... 34
5.1.3 Affine Registration by Minimizing the Metric ....... 35
5.1.4 Normalized Versions of our Metric . . ..... 36
5.2 Extension to the Multimodality Case . . ..... 37
5.3 Computing the Entropy of Multiple Random Variables . 40
5.4 Another Measure for Multimodality Image Registration . 43

6 NONRIGID MULTIMODALITY IMAGE REGISTRATION ....... 46

6.1 Nonrigid Multimodality Image Registration . . 46
6.2 B-Splines for Flow Field Representation . . ...... 47
6.3 Multiresolution Optimization over B-Spline . . 48

7 EXPERIMENTAL RESULTS .................. .... .. 52

7.1 Experimental Results on the B li, -i ,i Multimodality Nonrigid
Image Registration ....... . . . 52
7.1.1 Experiments on Simple Multimodality Shape Images . 53
7.1.2 Experiments on Simulated T1 and T2 2D MR Images .. 54
7.2 Experimental Results on the Unified Feature-based Registration
Method for Multimodality Images ................. .. 56
7.2.1 Robustness of Feature Images to Noise .......... ..56
7.2.2 Affine Registration of PD and T2 2D Image Slices . 57
7.2.3 Bootstrapping the Feature Combination With Imperfect
Registration .................. ..... .. 61
7.3 Experimental Results on the Affine Image Registration Using the
Upper Bound of the Information Metric ... . . 63









7.3.1 Affine Registration of PD, T2 and T1 MR 2D Images .
7.3.2 Matching Face Images Obtained under Different Illumina-
tio n s . . . . . . . .
7.4 Experimental Results on the Affine Multimodality Image Regis-
tration using the Information Metric and High Dimensional His-
togram m ing . . . . . . . .
7.4.1 Multimodality vs. Intermodality: Simultaneous Registra-
tion of 3 Images and Pair-wise Registration on Synthetic
PD, T2 and T1 MR Images .. ...............
7.4.2 Unbiased Multimodality Image Registration of Visible Hu-
m an D ata . . . . . . .
7.4.3 Multimodality Image Registration on Synthetic MR Data
7.5 Experimental Results on the Nonrigid Multimodality Image Reg-
istration Using the Information Metric and High Dimensional His-
togram m ing . . . . . . . .
7.5.1 Validity of Multiresolution Optimization Algorithms over
B -Spline . . . . . . .
7.5.1.1 Validity of intermodality registration with syn-
thetic PD and T2 3D MR images .. .......
7.5.1.2 Validity of multimodality registration with Visi-
ble Human Data including 2D anatomical photo,
CT and MRPD .. ...............
7.5.2 Intermodality vs. Multimodality: Comparison of Simul-
taneous Multimodality Registration and Pair-wise Inter-
modality Registration of 3D Images .. ...........
7.5.3 Unbiased Nonrigid Registration on 3D MR Images .....

8 CONCLUSIONS AND FUTURE WORK .. ...............

APPENDIX: PROOFS OF THE TRIANGLE INEQUALITY OF THE MET-
R IC . . . . . . . . . . .

REFEREN CES . . . . . . . . .

BIOGRAPHICAL SKETCH .. .......................















LIST OF TABLES


7-1 Registration results of 2D
and best feature pair .

7-2 Registration results of 2D
and best feature pair .

7-3 Registration results of 2D
best feature pair .....

7-4 Registration results of 2D
bootstrap .. .......

7-5 Registration results of 2D
bootstrap .. .......

7-6 Registration results of 2D
strap . . .


sagittal PD and T2 slices using intensity


coronal PD and T2 slices using intensity


axial PD and T2 slices using intensity and


sagittal PD and T2 slices before and after


coronal PD and T2 slices before and after


axial PD and T2 slices before and after boot-


7-7 Results of 2D slice along sagittal direction .. .............

7-8 Results of 2D slice along coronal direction .. .............

7-9 Results of 2D slice along axial direction .. ..............

7-10 Results under different lighting conditions (left light on, right light
on, and no light on) and wearing sun glasses ......

7-11 Results under different lighting conditions (left light on, right light
on, and no light on) and wearing a scarf .......

7-12 Results under different lighting conditions (left light on, right light
on, and no light on) and wearing sun glasses or a scarf ...

7-13 Mean errors on different affine parameters in the first experiment with
n oise 0 .1 . . . . . . . . .

7-14 Mean errors of different affine parameters in the second experiment
with Gaussian noise with mean 0 and std. 0.2 .. ............

7-15 Results of unbiased registration of anatomical slice, CT, MR PD, T1
and T2 images. [Dataset index: VHD #1080.] ......


Table


page









7-16 Number of pixels in nonoverlap region of segmented images before and
after registration. Upper triangle is before registration and lower tri-
angle is after registration. [Dataset index: VHD #1080.] . ... 77

7-17 Results of unbiased registration of anatomical slice, CT MR PD, T1
and T2 images. [Dataset index: VHD #1110.] ............ .. 77

7-18 Number of pixels in nonoverlap region of segmented images before and
after registration. Upper triangle is before registration and lower tri-
angle is after registration. [Dataset index: VHD #1110.] ...... .. 78

7-19 Results of unbiased registration of anatomical slice, CT, MR PD, T1
and T2 images.[Dataset index: VHD #1165.] . ...... 79

7-20 Number of pixels in nonoverlap region of segmented images before and
after registration. Upper triangle is before registration and lower tri-
angle is after registration. [Dataset index: VHD #1165.] ...... .. 79

7-21 SSDs of intensity of pairwise MR PD images before and after registra-
tion. upper triangle is before registration and lower triangle is after
registration .. .. ... .. .. .. .. .. .. .. .. ....... 82

7-22 DDF, ADF and SSD of intermodality registration of synthetic 3D MR
PD and T2 images before and after registration. . . 83

7-23 Cross correlation of the images before and after registration. Upper
triangle is before registration and lower triangle is after registration.
[Dataset index: VHD #1080.] .................. .. 86

7-24 Number of pixels in nonoverlap region of segmented images before and
after registration. Upper triangle is before registration and lower tri-
angle is after registration. [Dataset index: VHD #1080.] . . 87

7-25 DDFs and SSDs of Simultaneous registration of 3 images vs. pair-
wise registration on synthetic PD, T2 and T1 3D MR images before
and after registration. The first row is the errors before registration,
the second row is the errors after intermodality registration and the
third row is the errors after multimodality registration. . ... 90

7-26 SSDs before registration and after unbiased multimodality registra-
tion of 3 MR 3D images. Upper triangle is before registration and lower
triangle is after registration. .................. .... 93















LIST OF FIGURES
Figure page

1-1 Examples of multimodality brain images: the photographs in the first
row from left to right are MR T2, SPECT and PET brain images,
which come from The Whole Brain Atlas (http://www.med.harvard.
edu/AANLIB/home.html); the second row from left to right are
anatomical photograph, CT and MR PD Brain images, which are from
Atlas of the Visible Human Male. .................. 1

1-2 Multimodality image registration .................. 2

2-1 Definitions of mutual information and modified MI of three images
(shaded areas) .................. ............ .. 17

5-1 Venn diagram for two random variables ................ .. 34

5-2 The metric p and mutual information between PD and rotated and
scaled T2 images .................. .......... .. 35

5-3 p MI and MMI with rotation (2nd row) and scaling (3rd row) of
MR PD, MR T2 and MR T1 images ................. .. 39

5-4 a with rotation and scaling of PD, rotated T2 and rotated T1 images 45

7-1 Left and middle: two simple shape images. Right: final registration
result ............... ............ 53

7-2 The changes in i) log-likelihood, ii) mutual information, iii) joint prob-
ability and iv) negative joint entropy when minimizing the B li, -i il
MAP objective function. ................ .. .... 54

7-3 Leftmost: transverse T2 image. Left middle: transverse T1 image.
Middle: Deformed T1. Right middle: Intensity difference between
original T1 and deformed T1 prior to registration. Right: Unwarped
final T1 image ............... ........... .. 54

7-4 The changes in i) log-likelihood, ii) mutual information, iii) joint prob-
ability and iv) negative joint entropy when minimizing the B li, -i iI
MAP objective function. ................ .. .... 55









7-5 Difference images between original T1 and unwarped T1. Left: MAP.
Left middle: EMI. Right middle: EJP. Right: EJE. The SSDs were
609 before registration, 20.38 (\!MAP), 20.74 (EMI), 52.49 (EJP) and
52.47 (EJE). .. .. ... .. .. .. .. ... .. .... .. .. .. .. 55

7-6 Leftmost: Original T1 image, Left middle: deformed T1 image. Mid-
dle: Intensity difference between original T1 and deformed T1 before
registration. Right middle: Intensity difference between original T1
and unwarped T1 after registration. Right: Unwarped final T1 im-
age. The before and after SSDs were 647 and 59 respectively. . 56

7-7 Left: From top to bottom, NMI between the original intensity pair
with rotation. Right: From top to bottom, NMI between the best
feature image pair with rotation. The rotation range is from -20 de-
grees to 20 degrees. From top to bottom: added Gaussian noise with
mean 0 and deviation 0, 0.1, 0.2 and 0.4. .............. 58

7-8 Sagittal 2D slices .................. ........ .. .. 59

7-9 Coronal 2D slices .................. ........ .. .. 59

7-10 Axial 2D slices .................. ............ .. 60

7-11 Sagittal 2D slice .................. ........... .. 64

7-12 Coronal 2D slice .................. .......... .. 65

7-13 Axial 2D slice .................. ............ .. 66

7-14 Images under different lighting conditions (left light on, right light
on, and no light on) and wearing sun glasses . . ...... 67

7-15 Images under different lighting conditions (left light on, right light
on, and no light on) and wearing a scarf ............... .. 68

7-16 Images under different lighting conditions and wearing sun glasses or
scarf ..... .............. ................ .. 69

7-17 Plots of sum of Ti- T* + TA- T of 30 trials recovered by ten
measures in the first experiment with noise std. 0.1. Numbers 1 to
10 represent p,p,rT,q,a, mMI, pMI, mNMI and pNMI-the ten reg-
istration measures. .............. . ... 72

7 18 Plots of sum of Ti- T* + T T2 of 30 trials recovered by ten
measures in the second experiment with noise 0.2. Numbers 1 to 10
represent p,pr,r,t,a, mMI, pMI, mNMI and pNMI-the ten regis-
tration measures. .................. .......... ..73









7-19 The first row is the set of images before registration; the second row
is the set after registration. [Dataset index: VHD #1080.] ....... 76

7-20 Segmented images before (1st row) and after (2nd row) registration.
[Dataset index: VHD #1080.] .................. ..... 76

7-21 The first row is the set of images prior to registration; the second row
is the set after registration. [Dataset index: VHD #1110.] ...... 77

7-22 Segmented images before (1st row) and after (2nd row) registration.
[Dataset index: VHD #1110.] .................. ..... 78

7-23 The first row is the set of images before registration; the second row
is the set after registration. [Dataset index: VHD #1165.] . 78

7-24 Segmented images before (1st row) and after (2nd row) registration.
[Dataset index: VHD #1165.] .................. ..... 79

7-25 The first row are the images before registration and 2nd row is the
images after registration. .................. ..... 81

7-26 Corresponding MR PD images before and after registration. ..... ..81

7-27 Some slices of 3D MR PD and T2 images before registration. . 84

7-28 Some slices of 3D MR PD and T2 images after registration. . 84

7-29 Anatomical photo and overlap of 3 images before and after registration. 85

7-30 CT image before and after registration and deformed grid with dis-
placement field ............. ........... .. 86

7-31 PD image before and after registration and deformed grid with dis-
placement field. .................. ........... ..86

7-32 Segmented images before registration. ............... 87

7-33 Segmented images after registration. ................... .. 87

7-34 Some slices of 3D MR T2 images (target in the registration). ..... ..91

7-35 Some slices of 3D MR T1 and PD images before registration. ..... ..91

7-36 Some slices of 3D MR T1 and PD images after registration. ....... 92

7-37 Deformed grid with displacement fields of 3D MR T1 and PD images
in registration. . . . . ... . .. .. .92

7-38 Some slices of three MR 3D images before registration. . ... 94

7-39 Some slices of three MR 3D images after registration. . ... 94









7-40 Grids deformed with displacement fields in unbiased multimodality
image registration .. .......... ......... .. 94















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

NEW INFORMATION THEORETIC DISTANCE MEASURES
AND ALGORITHMS FOR MULTIMODALITY IMAGE REGISTRATION

By

Jie Zhang

August 2005

C'!I ir: Anand Rangarajan
Major Department: Computer and Information Science and Engineering

Accurate comparison and alignment of multimodality images give vital

integrated information to clinicians and researchers which has ap l i-off in clinical

practice. A critical stage in this process is the alignment or registration of the

images, which is the topic of my dissertation.

First, we present a B ,i, i i, multimodality non-rigid image registration

method. We prove that the displacement field which minimizes the B i, -i i max-

imum a posteriori (1 AAP) objective also maximizes the true mutual information

(with a small deformation penalty) as the number of pixels tends to infinity. The

criterion imposes an upper bound on the number of permissible configurations of

the displacement field.

Second, we propose a new registration method for multimodality images,

which combines features and intensities of the images in registration. We maximize

the normalized mutual information (NMI) over the "best features" of two images

instead of just using intensity as a feature. The "best fi I i is achieved by

finding the best projection onto a single feature image by maximizing the NMI

between the two registered images (training sets) w.r.t. the projection weights.









Then we use the same projection coefficients on new test images to obtain their

"best features." We show that using the new best iI i re" is more noise resistant

than using image intensity as the default feature.

Finally, we present an extensible information metric for multimodality image

registration. And its normalized version is still a pseudometric and is equivalent

to normalized mutual information in the intermodality case. When compared to

mutual information, it is easier to extend our metric to the registration of multiple

images. After using a new technique to efficiently compute high dimensional

histograms, the metric can be efficiently computed even in the multiple image

case. And we use the metric and high dimensional histogram to affine and nonrigid

multimodality image registration. In nonrigid registration, displacement field is

represented by B-Spline and the multiresolution optimization algorithms are used

for nonrigid intermodality and multimodality image registration. We compare the

results of direct multimodality registration using high-dimensional histogramming

with repeated intermodality registration. We find that registering 3 images

simultaneously with the new metric is more accurate than pair-wise registration

on the images obtained from synthetic magnetic resonance (\!I ) proton density

(PD), MR T2 and MR T1 3D volumes from Brain Web. We perform the unbiased

affine registration of 5 multimodality images of .111 I..nr:J, CT, MR PD, T1 and T2

from Visible Human Male Data and the unbiased nonrigid registration of three

MR 3D images of the brain with the normalized metric and high-dimensional

histogramming Our results demonstrate the efficacy of the metrics and high-

dimensional histogramming in affine and nonrigid multimodality image registration.














CHAPTER 1
INTRODUCTION

Medical image analysis is getting more and more important for diagnosis,

treatment, surgery and healthcare. And medical image analysis techniques can

be used in neuroscience and bioengineering domains. Four important radiological

imaging modalities are computed tomography (CT), magnetic resonance imaging

(!l RI), single photon emission computed tomography (SPECT) and positron

emission tomography (PET). Generally -I'" i:1:- structures are imaged with CT

and MRI, whereas function is measured with SPECT and PET and functional









(a) MR T2 (b) SPECT (c) PET








(d) anatomical photo (e) CT (f) MR PD

Figure 1-1. Examples of multimodality brain images: the photographs in the first
row from left to right are MR T2, SPECT and PET brain images,
which come from The Whole Brain Atlas (http://www.med.harvard.
edu/AANLIB/home.html); the second row from left to right are
anatomical photograph, CT and MR PD Brain images, which are
from Atlas of the Visible Human Male.









MRI (:1IlUI). In addition to these imaging modalities, there are other important

in-vivo modalities such as X-ray, ultrasound, traditional projection radiographs,

digital portal films, etc. Figure 1-1 shows some examples of different brain image

modalities.

Accurate comparison and overlay of these multimodality images will give

integrated information to clinicians and researchers in medicine and biology. A

critical stage in this process of comparison and/or overlay is the alignment or

registration of the images, which is the topic of my dissertation.

1.1 What is Registration?

After motivating the need for image registration, we give the following quasi-

formal definition of image registration. In mathematical language, image













T


(Xp,Yp) (Xq,Yq)


T(Xq,Yq)


Figure 1-2. Multimodality image registration









registration is a mapping T or transformation between the coordinate systems of

two images I(land 1(2) such that image (1) and transformed image I(2)(T) with

the transformation T have similar structures/features at the same position. Since it

turns out to be quite difficult to define image similarity, we call this a quasi-formal

definition. Informally, we call it alignment of images.

For example when we register two images at the first row in Figure 1-2, we

know the point P in the first image should correspond to the point Q in the second

image. Hence we look for a transformation T such that T(xq, yq) = (xp, y). After

we find the proper transformation T, we use the transformation T to transform

the second image to the bottom image in Figure 1-2. This is the process of

registration.

For most current applications of medical image registration, a transformation

T is a mapping from 2D space to 2D space or from 3D space to 3D space but some

special cases require T to be from 3D space to 2D space, such as the registration

of 3D CT to 2D digital radiography. Depending on the purpose of registration and

the property of images, the transformation T can be a rigid transformation, affine

transformation or nonrigid transformation. For a rigid transformation, there are

three free parameters in a mapping from 2D space to 2D space: one rotation and

two translations. For a rigid mapping from 3D space to 3D space, there are six

free parameters: three rotations and three translations. An affine transformation

has more free parameters: scaling and shear besides rotation and translation.

Each affine transformation has six free parameters in mapping from 2D space to

2D space including one scaling, one shear, two rotations and two translations or

has twelve free parameters in mapping from 3D space to 3D space. Hence, a rigid

transformation is an affine transformation without scaling and shear. If T has more

parameters than an affine transformation (for 2D-2D or for 3D-3D), we call it a

nonrigid transformation.









1.2 Contributions of the Dissertation Work

We set up a framework which begins with the conditional probability estimate

and uses it as a likelihood in B ,i, i i, estimation. Because of the popularity

of mutual information, we relate our method to MI-based method and derive a

new criterion-a sufficient condition-which when satisfied, guarantees that the

displacement field which minimizes the B li-, -i 'i maximum a posteriori (A\ P)

objective also maximizes the true mutual information (with a small deformation

penalty) as the number of pixels tends to infinity. Then the question of why the

vanilla image intensity should be used in mutual information-based registration

and if there exists a better feature is motivation for our next work. By maximizing

NMI on registered training images, we find the "best feature combination" and

the new best "feature" is more noise resistant than using image intensity as the

default feature in NMI-based registration. The most important contribution of

the dissertation is that we propose a new information metric and high dimensional

histogram for multimodality image registration. Compared to mutual information

which can even become negative in the multiple image case, our metric can be

easily and naturally extended to multiple images. After using a new technique

to efficiently compute high dimensional histograms, the extensible information

metric can be efficiently computed even for multiple images. The metric and

high dimensional histogram are used to affine and nonrigid multimodality image

registration. And we find that simultaneous multimodality registration of multiple

images is more accurate than intermodality registration of two images. The metric

and the high dimensional histogram are also used to unbiased multiple image

registration.

1.2.1 A Bayesian Multimodality Nonrigid Image Registration Method

propose a new B ,i-, i ,multimodality nonrigid image registration method






5


derive a sufficient condition which guarantees that the displacement field

which minimizes the B ,,-i i maximum a posteriori (1\ AP) objective also

maximizes the true mutual information (with a small deformation penalty) as

the number of pixels tends to infinity

1.2.2 A Unified Feature-based Registration Method for Multimodality
Images

find the best feature combination of images of different modality with NMI

being the criterion, which is more robust to noise than image intensity in

registration

propose a new feature-based multimodality image registration method in

training and boost mode

training mode: extract features from fully registered and noiseless images

bootstrap mode: extract features from not fully registered or noised

images such as registered images by other image registration methods

show some experimental results of affine registration between PD, MR T1 and

MR T2 brain images in training and bootstrap mode

1.2.3 Multimodality Image Registration Using an Extensible Informa-
tion Metric and High Dimensional Histogramming

Present an extensible information metric for multimodality image registra-

tion. Compared to mutual information which can even become negative in

the multiple image case, it is easier to extend our metric to the registration of

multiple images.

Using a new technique to efficiently compute high dimensional histogram, we

show that the sum of the conditional entropies can be efficiently computed

even in the multiple image case.

Multimodality image registration is more accurate than intermodality

registration.









The metric and the high dimensional histogram are also used to unbiased

multiple image registration.

The method has used to affine and nonrigid multimodality image registration.

In the next section, we review some related works in multimodality image registra-

tion.

1.3 Outlines of the Dissertation

The rest of the dissertation is organized as following:

In ('!C lpter 2, we review some related previous work on multimodality image

registration. Depending on what is used in the registration, the works are catego-

rized into two group: intensity- and feature-based methods. In the feature-based

methods, we review some papers which use features such as points, edges, curves or

surface in multimodality image registration. In the intensity-based methods, we re-

view some papers which use different intensity similarity measures in multimodality

image registration. We also review some papers where multiple image are registered

in same time.

In C'!i lpter 3, we present a B ,i-i -i multimodality non-rigid image regis-

tration method. Since the likelihood is unknown in the general multimodality

setting, we use a density estimator as a drop in replacement for the true likeli-

hood. The prior is a standard small deformation penalty on the displacement

field. Since mutual information-based methods are in widespread use for mul-

timodality registration, we attempt to relate the B ,i, -i ,i approach to mutual

information-based approaches. To this end, we derive a new criterion-a sufficient

condition-which, when satisfied, guarantees that the displacement field which

minimizes the B li, -i maximum a posteriori (\1AP) objective also maximizes

the true mutual information (with a small deformation penalty) as the number of

pixels tends to infinity. The criterion imposes an upper bound on the number of

permissible configurations of the displacement field.









In C'!I ilter 4, we propose a new registration method for multimodality images,

which combines features and intensities of the images in registration. We maximize

the normalized mutual information (NMI) over the "best features" of two images

instead of just using intensity as a feature. The "best fi Ii is achieved by

finding the best projection onto a single feature image by maximizing the NMI

between the two registered images (training sets) w.r.t. the projection weights.

Then we use the same projection coefficients on new test images to obtain their

"best features." We show that using the new best liure" is more noise resistant

than using image intensity as the default feature. And we extend the idea to

the bootstrap case, wherein the best feature combination is computed using the

imperfectly registered pair of images (obtained by using NMI on the original

intensity pair) as a training set.

In C'!i Ilter 5, we present an extensible information metric for multimodality

image registration. For the intermodality (2-image) case, given images A and

B, the pseudometric used here is the sum of the conditional entropies H(AIB)

and H(BIA). And we show that the normalized version of the pseudometric [the

pseudometric divided by the joint entropy H(A, B)] is still a pseudometric and is

equivalent to normalized mutual information in the intermodality case. We show

that when compared to mutual information which can even become negative in the

multiple image case, it is easier to extend our metric to the registration of multiple

images. After using a new technique to efficiently compute high dimensional

histograms, we show that the metric can be efficiently computed even in the

multiple image case.

In C'!i Ilter 6, we use the normalized metric and high dimensional histogram-

ming to the nonrigid registration of multimodality images. For recovering local

deformation, we will use B-Splines to represent flow fields of pixels because B-

Splines have good local approximation as long as the grids of B-Splines are fine






8


enough. And we also propose multiresolution optimization algorithm for nonrigid

multimodality image registration.

In C'! lpter 7, we present the experiments to support measures and algorithms

proposed in previous chapters. The most data used in experiments are Brain-

web synthetic MR T1, T2 and PD images and Visible Human Data including

anatomical photo, CT, MR T1, T2 and PD data.

In C'! lpter 8, we draw the conclusion for our works and propose some possible

direction, which can be done in the future.














CHAPTER 2
RELATED PREVIOUS WORK

A fundamental distinction made by many researchers working in multimodality

image registration [1, 2, 3] is between intensity- and feature-based methods. We

will review some related works in these two categories.

2.1 Feature-based Methods

Features extracted from images can be points, edges, curves or surfaces.

Generally, feature-based registration involves two things: finding correspondences

between these features and finding a transformation between the features. We will

review some literature on feature-based registration.

2.1.1 Point-based Registration

In point-based registration, we seek a correspondence and transformation of

two point sets which are extracted from two images using some feature extraction

operator: Rohr [4], Alker et al. [5] and Worz and Rohr [6].

Given two point sets with the same cardinality and with known correspon-

dence, if the desired transformation is rigid, the problem is a classical Procrustes

problem (Small [7]). The transformation can be solved using singular-value de-

compositions (SVD) (Dryden and Mardia [8]). If the transformation is affine, the

problem is a standard least squares problem (Golub and Loan [9]). For nonrigid

transformations, the problem gets harder. Thin plate splines (TPS) are used in

Chui and Rangarajan [10] and Belongie et al. [11]. And diffeomorphisms are used

in Joshi and Miller [12].









For a given transformation, the correspondence problem becomes a linear

assignment problem, which can be solved using a Hungarian method (Papadim-

itriou and Steiglitz [13]) or more efficiently using the Shortest Augmenting Path

Algorithm (Jonker and Volgenant [14]).

A popular algorithm for point matching is the iterative closest points algo-

rithm (ICP) (Besl and Mcmay [15]), which alternatively solves for correspondence

by finding the closest point in one point set for each point in another point set and

uses the standard least squares solution for the transformation. The ICP algorithm

is widely used in medical imaging applications (Cuchet et al. [16], Declerck et al.

[17], and Maurer et al. [18]). However, ICP can be quite sensitive to changes in

feature locations and false positives in detection of closest points. This problem

was partially fixed in the adaptive-threshold work of Feldmar and Ayache [19].

In addition, Chui and Rangarajan ([10]) noted the problems with robustness to

noise and outliers and proposed a new nonrigid point matching algorithm based on

clustering and soft assignment known as robust point matching (RPM) which they

used to register 3D cortical anatomical structures [20]. Shape contexts [11] are also

used in nonrigid point matching although it contributes more in object recognition.

The shape contexts approach defines a new energy function with X2 distance of

histograms of radius and angle for each point instead of using Euclidean distances

between points, which makes use of the geometric information of the neighborhood

of each point and has good performance in matching and recognition.

2.1.2 Surface-based Registration

Contours or surfaces in medical images tend to be more distinct than points,

and many segmentation algorithms can successfully locate such high-contrast

surfaces. If equivalent surfaces can be automatically segmented from two images,

then registration can be achieved by matching the extracted and fitted surfaces.









Pelizzari and colleagues [21, 22] proposed a surface fitting technique for regis-

tration of images of the head that became known as the head-and-hat algorithm.

Two surfaces are extracted from two images. One is called the head surface.

Another is called the hat surface. The transformation is iteratively solved by

transforming the hat surface until the square of the distance between a point on

the hat and the nearest point on the head achieves its local minimum. The Powell

method was used for optimization. Because of the deformation of two surfaces, the

nearest point does not alvi1-, lie in the direction of the head centroid. Thus this

algorithm is not robust to cases with high deformation. Using a distance transform

to prelabel all voxels in the image with their distance from the surface of the object

can reduce computation cost in the algorithm; Jiang et al. [23] and Elsen [24] use

the chamfer filter [25] as a distance transformation for rigid registration. Huang

and Mitchell [26] used Euclidean distance transforms to achieve the same goal.

Recently, a promising surface matching algorithm was proposed by Gu et al

[27], in which all surfaces are treated as Riemann surfaces. That means all surfaces

have intrinsic conformal structures and are invariants under globe conformal

transformation groups. A surface can be transformed with a conformal mapping to

a sphere or plane after which subsequent matching on sphere or plane is relatively

easier. This approach was used for cortical surface matching [28].

In the 2D case, contours or curves are also used in registration. Li et al. [29]

proposed two contour-based methods which use region boundaries and other edges

as features. They use correlation and other shape similarity criteria to register

these features. Recently, Klassen et al. [30] proposed a new curve-based method

(closed curve). They proposed new representations of curves using their direction

functions and curvature functions. The curves are matched by solving for the

tangent that connects any two shapes via a geodesic in the shape space.









2.1.3 Edge-based Registration


Instead of using surfaces for registration, edges or ridges can be used as

distinctive features in registration. Maintz et al. [31] used several edge or ridge

detectors for CT and MR images and used cross-correlation to register the feature

images. More detail on their methods can be found in Elsen [24].

2.1.4 Other Feature-based Registration


Liu and Vemuri [32] present a local frequency based registration method.

The local frequency image representation is obtained by filtering the images

with a Gabor filter tuned to a certain frequency/orientation and then computing

the gradient of the phase of the filtered images. To match the local-frequency

representations of the image pair, they minimize the integral of the squared

error between a Gaussian model of the residual and its true density function.

The residual is the difference between the local frequency representations of the

transformed source and target images. They register the misaligned MR brain

images using different protocols. This method has good performance on images

with large nonoverlap region.

Hero and his colleagues [33, 34] use features extracted by independent compo-

nent analysis (ICA) in registration. They use the minimum spanning tree (\!ST)

to estimate the a-entropy after which they minimize the a-Jensen divergence of

two ICA feature sets. They applied their method to MR brain images. Since this is

really an intensity-based similarity measure, we defer discussion of this to the next

section.

2.2 Intensity-based Registration

Intensity-based methods directly use the intensity of original images or

denoised images instead of using features extracted from images. Hence, intensity-

based methods do not need to segment images or detect edges or ridges. The most









important need in intensity-based methods is a good image intensity similarity

measure. For intermodality registration of images, there are several good measures

that have been proposed. In sharp contrast, for multimodality registration which

requires the registration of more than two images, there are not many good

measures.

2.2.1 Mutual Information

Since Viola and Wells [35] and Collignon et al. [36] used mutual information in

image registration, there have been hundreds of papers [37] on image registration

using mutual information.

The definition of mutual information for two random variables X and Y is


MI(X, Y) = H(X) + H(Y) H(X, Y) (2-1)

where H(X) and H(Y) are marginal entropies of X and Y and H(X, Y) is the

joint entropy of X and Y and defined as H(X) = -E(log(p(X)), where p(X) is

the probability mass function (PMF) of X, and E(.) denotes the expectation of a

random variable.

The definition of normalized mutual information [38] for two random variables

X and Y is


H(X) + H(Y)
NMIA(X, Y) (2-2)
H(X,Y)
Mutual information is now used in nonrigid intermodality image registration

along with deformation models such as TPS as used in Kim et al ([39]) elastic

deformation as used in Maintz et al. ([40]) and Hata et al. ([41]), B-Spline or free

form deformation (FFD) as used in Rueckert et al. ([42]) and Rohlfing et al. ([43]),

and Gaussian kernels as used in Gaens et al. ([44]).









2.2.2 Normalized Cross Correlation

Another popular measure of multimodality image registration is normalized
cross correlation (Lemieux et al. [45, 46])
The definition of normalized cross correlation is


cc -i I (1 ( (2)
CC = (2-3)


where I(k) is the intensity value of image I(k) at location i [pixel position (x, y, z)],
k =1, 2,i 1 ,..., N, where N is the total number of pixels in each image and I(k)
is the mean value of {I k)}i.

2.2.3 Entropy of Difference Image and Pattern Intensity

The entropy of the difference image is applied to the difference (I(d)) image of
I(1) and I(2):


j(d) I(1) Sj(2), (2-4)

with the entropy being


H(s) = p(a)logp(a). (2-5)

A histogram is formed from the difference image and p(a) denotes the probability
of obtaining the pixel intensity value a in I(d). This measure has been used in 2D
registration between images of a digital subtraction angiography (DSA) sequence in

[47].
Another measure using the difference image is pattern intensity.

2
P", (s) 2 ( ) d)a2, (2-6)
2 + (Id j- I '









where pixel j is a neighbor of pixel i within a radius r and a is a constant used

to weigh the measure so that small deviations in intensity result in the measure

remaining near its maximum value. The values chosen for the constants were

a = 10 and r = 3 pixels in registration of an X-ray image to a CT image [48].

The scaling factor s for the creation of the difference image should be chosen so

that the difference image has the least contrast. Note that a constant shift between

the image intensities does not affect the similarity measure, as it only assesses

differences in the difference images.

2.2.4 Joint Entropy and Joint Probability

The joint entropy of two images I(1) and 1(2) is defined as


H((l), I(2) = p(a, b) logp(a, b), (2-7)
a b

where a and b are intensity values of image I(1) and I(2) respectively and p(a, b) is

the joint probability mass function of the two images. Joint entropy was simulta-

neously proposed for intermodality image registration by Studholme et al. [49] and

Collignon et al. [50].

A similar measure is the joint probability as used in registration by Leventon

and Grimso [51].

L = log p(Ii,'), 1(2)) (2-8)

where p(Jl), 2)) is the joint probability of intensity () at pixel i and intensity
I,(2) for image 1(2). A Gaussian mixture model was used to estimate the joint

probability mass function.









2.2.5 Other Measures

Wang and Vemuri et al. [52] present a new measure for intermodality image

registration called cross cumulative residual entropy (CCRE):


C(X,Y) = (X)- E(E(Y|X)), (2-9)

where E(X) = Pr(x > A)logPr(x > A)dA, E(YIX) = Pr(y >

AIX) log Pr(y > AIX)dA and E(E(YIX)) is the expectation of E(YIX). They applied

this method to rigid MR brain image registration and got better results than

mutual information.

Hero et al. [33] use the a-Jensen divergence in their MR brain image registra-

tion.

Let fo and fl be two densities and 3 E [0, 1] be a mixture parameter. The

a-Jensen divergence is the difference between the a-entropies of the mixture

f = 3fo + (1 3)fl and the mixture of the a-entropy of fo and fl:


AH(/3, fo, fi) = H(/3fo + (1 3)fi) 3PH(fo) (1 3)H((f1), (2-10)

where Ha is the a-entropy of a density and defined as

1
H(f) log f(x)dx. (2-11)


More detailed comparison of these measures may be found in [53].

2.3 Multimodality Image Registration

In this section, we will review some paper and similarity measure, which have

used or can be used to multimodality image registration.

2.3.1 Mutual Information

While the mutual information measure is popular in intermodality (two

images) registration, it has not been widely used in multimodality (more than two

images) situations. While the mutual information measure between two random









H/B)
H(A) H()











MI(A,B,C) H(A) +H(B) +H(C) H(A,B) -H(B,C) -H(A,C) +H(A,B,C) mMI(A,B,C) = H(A) + H(B) + H(C) -H(A,B,C)
(a) Mutual Information (b) modified Mutual Information

Figure 2-1. Definitions of mutual information and modified MI of three images
(shaded areas)


variables is non-negative, this is not true when more than two random variables

are involved. The mutual information measure between (more than two) random

variables can even become negative Cover and Thomas [54].

Two notable facts emerge after surveying the literature. There is almost no

prior work on using an entropy-based image similarity metric as we have done

here and there are considerable differences of opinion on the extension of mutual

information from the intermodality (two images) case to the multimodality (more

than two images) case. In Cover and Thomas [54], mutual information of three

random variables X,Y and Z is defined as MI(X, Y, Z) = H(X) + H(Y) + H(Z)

H(X, Y) H(X, Z) H(Y, Z) + H(X, Y, Z)((a) in figure 2-1). Unfortunately,

MI(X, Y, Z) is not necessarily nonnegative, which renders it inadequate as an

image similarity measure. In Studholme et al. [55] and Boes and M1. ,i r [56], a

different definition is proposed: mMI(X, Y, Z) = H(X) + H(Y) + H(Z) -

H(X, Y, Z)((b) in figure 2-1)). This definition is nonnegative but it is not a

natural extension of the mutual information of two random variables. In Lynch

et al. [57], three images are registered using yet another different definition of

mutual information. However, all these definitions do not embody the true (in









our eyes) spirit of mutual information: shared information between multiple

images. Hence using mutual information to simultaneously register multiple

images is not appropriate despite the fact that mutual information is a very good

measure (though not a metric) for registering two images. Finally, even if we

had a nonnegative and natural definition for multimodality mutual information,

an efficient computation technique of high dimensional entropy is still needed in

computing multi-variable entropy in mutual information.

In order to compute the Shannon entropy of multiple random variables,

we need to estimate the high dimensional probability mass function (PMF) of

multiple random variables. Due to the curse of dimensionality, and especially when

derivatives of the PMF are required, it is difficult to accurately estimate a high

dimensional probability distribution. The simplest PMF estimation approach is

histogramming and has been used in database research such as multiple-attribute-

data query in Poosala and loannidis [58]. In multimodality image registration,

despite the fact that we only need to estimate the entropy (of the form p logp)

from the PMF, high dimensional histogramming is not prevalent and due to

this, there is almost no previous work on simultaneous, multimodality image

registration.

2.3.2 Jensen Divergence

Jensen divergence has been used to intermodality image registration in

2.2.5. But there is no paper extending Jenson divergence to multimodality image

registration. A possible extension is that for three images X,Y and Z, computing

Jenson divergence between p(X, Y, Z) and p(X)p(Y)p(Z) or


AH(, p(X, Y, Z),p(X)p(Y)p(Z)) = H((p(X, Y, Z) + (1 -)p(X)p(Y)p(Z))

-PH,(p(X, Y, Z)) (1 -3) H,(p(X)p(Y)p(Z)),









where H, is the a-entropy of a density and 3 E [0, 1]. Actually Jensen divergence

has same intuition as Kullback-Leibler distance. They all are measure of the

distance of two density. So maximizing Jensen divergence between p(X, Y, Z) and

p(X)p(Y)p(Z) is equivalent to maximizing Kullback-Leibler(KL) distance of them
in some extent. And KL distance of p(X, Y, Z) and p(X)p(Y)p(Z) is the modified

mutual information of the three images X,Y and Z.

2.3.3 Minimum Entropy of Bad Prediction (MEBP)

In Zhao and Belford [59], a new method is proposed for the image sequence

registration. They need a prediction function P to compute the prediction error

I1 J(2) p(j(1)).


Then MEBP is defined as

MEBP(I(1), I(2)) = H(E),


where E = {xx E Ie A x / 0} and H(E) is the Shannon entropy of E. But in

their paper, they just used identity function as the prediction function P. This is

very similar to computing the entropy of difference image in 2.2.3. For the sequence

registration, they use weighted least square to compute a linear regression for

prediction. They used the method to register the image sequence of rabbit brain.

From their results, this method is better than direct using SSD but not good as

mutual information. Actually because of needing prediction function, it is hard to

extend this method to multimodality image registration.














CHAPTER 3
BAYESIAN MULTIMODALITY NON-RIGID IMAGE REGISTRATION VIA
CONDITIONAL DENSITY ESTIMATION

We present a B ,i, i i, multimodality non-rigid image registration method.

Since the likelihood is unknown in the general multimodality setting, we use a

density estimator as a drop in replacement for the true likelihood. The prior is

a standard small deformation penalty on the displacement field. Since mutual

information-based methods are in widespread use for multimodality registration, we

attempt to relate the B ,i, i approach to mutual information-based approaches.

To this end, we derive a new criterion-a sufficient condition-which when satis-

fied, guarantees that the displacement field which minimizes the B li,. -i i, maxi-

mum a posteriori (1\ AP) objective also maximizes the true mutual information

(with a small deformation penalty) as the number of pixels tends to infinity. The

criterion imposes an upper bound on the number of permissible configurations of

the displacement field.

3.1 Conditional Density Estimation

Assume that we have two images I(1)and 1(2), and let I(k) be the intensity

value of image I(k) at location i [pixel position (x, y)], k = 1,2, i = 1,..., N,

where N is the total number of pixels in each image. (While our development

is mainly for 2D, extensions to 3D appear straightforward.) The conditional

probability of I(1) given I(2) at location i is denoted by Pr(l)I } 2)). Also, for the

remainder of the section, non-rigid warps will be applied solely to 1(2) with I(1)

held fixed. Instead of using the original (possibly real-valued) intensity, we will use

the following binned intensity value. This is done for a technical reason which will









become more obvious as we proceed. The binned intensity for each image is

Bk) = (Kk 1) x lI<

From (3-1), we see that the binned intensity values are integers in {1,... ,K(k).
We use (3-2) to compute the conditional probability at location i:


) Pr(B 1), B())
r(B()IB) 2) (3-2)

3.2 Bayesian Non-rigid Registration

As mentioned previously, we seek to register image 1(2) to image (1). To
achieve this, we set up a displacement vector ui at each location i. We denote an
entire cornFil,.i.i, of {ui, i E 1,..., N} by u and the set of allowed configurations
of u by A. A non-rigid warping of 1(2) exists for each configuration u (with the
understanding that interpolation may be necessary to generate a valid warped (2)).
From B -' rule, we get


pu )Pr(B(1) IB(2) u) Pr(u)
Pr(ulB(1) B(2)) ) (33)
Pr(B() IB(2))
from which we get



log Pr(ul(1), B(2)) = log Pr(B(1)B(2),U) +log Pr(u) log Pr(B(1)B(2)). (34)

Since the probability Pr(B(1) B(2)) uEA Pr(B(1) I(2) u) Pr(u) is independent of
u, we have


log Pr(uB( ), B(2)) O log Pr(B(1)I(2) ) + log Pr(u).


(3-5)









Consequently, from a B li-, -i perspective, the non-rigid registration problem

becomes


i argminE(u) argmin log Pr(B(1) B(2), u) log Pr(u). (3-6)
U u

We use a standard small deformation smoothness constraint on u which can

be written as -log Pr(u) oc I|Lul2. Since we use a density estimator for

Pr(B1) IB(2), u), we assume conditional independence of B(1) given B(2) over

the pixel locations. This assumption is clearly not necessary since the image pro-

cessing/computer vision literature is replete with correlated random field image

models (ranging from simplistic to baroque) [60, 61]. However, most random field

models require the estimation of further parameters which increases the estimation

burden considering that we are already saddled with the problem of estimating u.

In addition, EMI-based registration methods have traditionally used very simple

density estimation procedures such as histogramming [62] and Parzen windows [63]

which sets a clear precedent for us. With these simplifications in place, we obtain

the following B i-, -i il maximum a posteriori (\1AP) objective function

N
EMAP(U) =- log Pr(B B (2, u) + A|Lu |2 (3 7)
i=

where we have normalized the negative log-likelihood in the first term of (3-7). The

parameter A is a regularization parameter and L is the regularization operator. In

the 2D case, we choose


|Lu 2 f fa )2 +2( )2 ( )2dxdy (38)

which is a standard thin-plate spline [64] small deformation cost.
which is a standard thin-plate spline [641 small deformation cost.









3.3 Convergence of the Bayesian MAP Minimizer in the General
Setting

In this section, we examine the convergence properties of the minimizer of

the B -I i' MAP objective function in (3-7) as the number of pixels N tends to

infinity. In the non-rigid setting, the cardinality of u scales linearly with N and as

we shall see, this complicates the convergence proof.

We begin by assuming that the chosen density estimator converges to the true

density as N tends to infinity. This is usually true of histogram and Parzen window

estimators. Denote the true density of B(1), B(2) and the pair (B(1), B(2)) by

Pr(B(1)), Pr(B(2)) and Pr(B(1), B(2)) respectively and the corresponding estimated

densities by Pr(B(1)), Pr(B(2)), and Pr(B(1), B(2)). We assume that


lim Pr(B(1)) Pr(B(1)), lim Pr(B(2)) Pr(B(2)) (39)
N-oo N->oo

and

lim Pr(B(1), B(2)) P(B(1), B(2)). (310)
N->oo

With this notation in place, we can write the true mutual information as
K K
MI(u) Pr(a, blu) logPr(alb, u) + terms independent of u (3-11)
a l b=

and the empirical mutual information as
K K
EMI(u) = 1 r(a, blu)log Pr(ab, u) + terms independent of u. (3-12)
a l b=l

The objective function we would like to minimize is


EMI(u) = -MI(u) + A||Lu1|2 (313)


Since we use the framework of statistical learning theory [65] throughout this

dissertation, we call EMI(u) the expected risk. This objective function is not

computable since the true distribution Pr is unknown and is only approached by









our density estimator Pr as N tends to infinity. Instead of minimizing the expected

risk, we minimize the B li, -i i: MAP objective function, a.k.a. the empirical risk

which is the same as (3-7):


EMAp(u) LL(u) + A|Lull2 (314)

where the log-likelihood LL(u) is defined as

1 N
LL(u) def slog PIr(B ) 2), u). (3- 15)
i=i

In (3-15), Pr(B I)|B 2), u) is the estimated distribution from N samples. We are

interested in the relationship between the minimizers of (3-14) and (3-13).

Let the minimum of the expected risk in (3-13) be achieved by the displace-

ment field u, and the minimum of the empirical risk in (3-14) be achieved by

the displacement field u,. The following question is our main concern in this

dissertation:

1. What is EMi(uC) EMi(ur), or how close is the value of the expected risk

attained by the minimizer of the B i-, -i ,i, MAP objective function (empirical

risk) to the maximum value of the true mutual information (expected risk)

which is attained by u,?

We answer this question by proving the following theorem. It turns out that the

theorem requires a specific choice of the density estimator. We pick the estimator

used in [61] which is closely related to histogramming. Assuming an i.i.d. density

for each pixel, our chosen density estimator is
N
p(I) ( 6(- l) (3-16)
j=1

where 6(.) is the Dirac delta function with f_ 6(x)dx 1. Note that p(I) in

(3-16) is a density function and not a discrete distribution as required. Since the









Dirac delta function is not differentiable, we switch to a continuous approximation

6(x) exp (317)
Z-a2 { 2 2j2

This approximation is increasingly exact as a -i 0 and is continuous and differ-

entiable for a > 0. Finally, since we use binned intensities B, we normalize the

above delta function approximation to get the final density estimator used in this

dissertation. The marginal and joint probability distributions are


S(Bl)-B ))2 (B2)_-B2))2
Pr(B')) V exp{- 2' 2 } r(2) ie-, exp-{ 2a2
S K(M) N (-B())2 K(2) N (3-B )2
=31 Yij exp{- 2 }=1 ij=1 iexp{- 2 }
(3-18)
and

N(BB 1 ( )-B )+(B -B 2)- 2))
r(B) B(2) j=1xp- ( 3-9)
Srs K(1) K(2) ( (1)-B )2+ (()-2)B )2
E 3(1)I -(2)1 Nj1 exp{- 2(2
with the understanding that we are dealing with i.i.d. pixels.

As mentioned previously, A = {u} is the set of all possible configurations of u.

For the non-rigid registration problem with N-pixel images, ||A||-the cardinality

of A-is bounded from above by NN, since each pixel can potentially move to

any other location. Since the upper bound for I||A| scales with N, we let I||A| be a
function of N:

IAII = g(N) (3-20)

Theorem 3.1: With the probability distributions estimated as in (3-18) and (3

19), and with the total number of configurations of u as in (3-20), the inequality

K1) K(2) N
Pr(sup(E Pr(a, bu)[-log Pr(a|b, u)] [-log Pr(B ), u))) >
uA a 1 b= i=
292N
< g(N) exp{- (Kl)2 + log(K(1)K( 21)









is valid where c is any given positive small number.

Proof: An abbreviated proof of Theorem 3.1 follows. The basic idea is to calculate

lower and upper bounds of the estimated distribution log Pr(Bj) B '), u) and

then apply Hoeffding's inequality [65] for real-valued bounded functions to get

K(1) K(2) N
Pr{sup( Pr(a, b|u)[- log Pr(a|b, u)] [-logPr(Bl) B2), u)} > c
uEA N
uA a 1 b=l i=
K() K(2) N
< Pr( Pr(a, blu)[- log P1r(ab, u)]- [-logPr(BI) B2), u)]) >
uEA a=1 b = i=1
2IN
< g(N) exp{- 2c2(K( 22)
2, )2 + log(K(1) (2))

which is the desired result. From (3-22), we obtain with probability 1 Tr (where
def 22N }), the inquality
TI exp{ -(K2(1))K(22 log(K(l)K(2)) the inequality

K(1) K(2) N
S> Pr(a, b|u)[-log Pr(a b, u)] [- log r(B)B2), ]
a- b= i=
( (K(1))2 + (K(2))2 l( )) og g(N) log (3-23)
< 22 + og 2N

Adding and subtracting A||Lue| 2 to both terms on the left side of (3-23), we get

(after cutting a few corners),

Em ) E P(U) < (K ())2 + (K(2))2 log2)) log g() log TI
22r 2N
(3-24)

Once again, from Hoeffding's inequality, we have

K(1) K(2) N
>Pr(a, b|u)[-log Pr(a b, u)] > [- log Pr(B) B2), Ur)]
a l b= i=
(K(1))2 + (K(2))2 l0g y
-[ + (K(2))2 + log(K()K(2))] log (3 25)
2j2 2N









Adding A||Lur|2 to both sides of (3-25) we can state more simply that

(Kl) 2 + (K(2))2 log n
EMI(u,) EMAP(Ur) > -[( 2 + log(K()K(2)) (3-26)
2a2 2N

Since u, is the minimizer of the empirical risk (B i-, -i in MAP objective function),

EMAp(U,) > EMAp(ue) and hence

0 < EMI(Ue) EMl(Ur) < [EMI(Ue) EMAP(Ue)] + [EMAP(Ur) EMI(u,)]. (3-27)


Substituting (3-24) and (3-26) in (3-27), we see that


0 < EMI(Ue) EMI(u,)
(Kl()2 + (K(2))2 log g(N) log I log (3
<[ + log(K()K(2))][ 2+ ]2 (328)
2o2 2N 2N

If we assume that

lim lg 0, (3-29)
N-oo N

then we have

lim EMn(ue) EMi(ur)| 0. (3-30)
N->oo

We have shown that the minimizers of the expected risk (true mutual information)

and the empirical risk (B li-, -i i: MAP objective function) coincide as the number

of samples approaches infinity provided that a sufficient condition (3-29) is met.

It is time that we took a closer look at g(N) which is the cardinality of the

number of allowed configurations of u. In non-rigid registration, the upper bound of

g(N) is NN if we allow each pixel to move to any other location. In sharp contrast,

in rigid registration, the upper bound of g(N) is C6 in 2D where we have assumed

6 free parameters (affine) with each parameter quantized into C (independent

of N) bins. It should be obvious that if g(N) = NN, we cannot conclude that

limNoo |EMn(ue) EMn(u,)| = 0. Clearly, from this proof's viewpoint, allowing

every pixel to potentially visit any other location is unreasonable even in large






28


deformation situations. In this dissertation, we already have a B ,-i i prior which

effectively restricts u to small deformations (even though there are no forbidden

configurations). If we set an upper bound for g(N) to be ND where D is a constant

independent of N, then the proofs go through and the empirical and expected risk

minimizers coincide. Consequently, a sufficient condition is that g(N) be O(ND).

An upper bound of O(ND) is equivalent to D (independent of N) free parameters

instead of 6 as in the case of the 2D affine with each parameter quantized into N

bins.















CHAPTER 4
A UNIFIED FEATURE-BASED REGISTRATION METHOD FOR
MULTIMODALITY IMAGES

While mutual information-based methods have become popular for image

registration, the question of what underlying feature to use is rarely discussed.

Instead, it is implicitly assumed that intensity is the right feature to be matched.

We depart from this tradition by first beginning with a set of feature images

the original intensity image and three directional derivative feature images. This

"feature extraction" is performed on both images in a typical intermodality

registration setup. Assuming the existence of a training set of registered images, we

find the best projection onto a single feature image by maximizing the normalized

mutual information (NMI) between the two images w.r.t. the projection weights.

After discovering the best feature to match using normalized mutual information as

the criterion, we use the same projection coefficients on new test images. We show

that affine NMI-based registration of the test images using the new best "feature"

is more noise resistant than using image intensity as the default feature. Since the

assumption of a registered, training set of images is problematic, we extend the

idea to the bootstrap case, wherein we use imperfectly registered images (obtained

by using NMI on the original intensity pair) as a training set. The best feature

combination is computed using the imperfectly registered pair of images. We show

that subsequent NMI-based registration of the best feature image pair is able to

improve upon the original imperfect registration. Results are shown on 2D coronal,

axial and sagittal slices drawn from a 3D MRI volume of proton density (PD) and

T2- weighted images.









4.1 Feature Combination

The definitions of MI and NMI of two random variables X and Y are


MI(X, Y) = H(X) + H(Y) H(X, Y)


(4-1)


and


H(X) + H(Y)
NMI(X, Y) (4-2)
H(X,Y)
where H(X) and H(Y) are the marginal entropies of X and Y and H(X, Y) is the

joint entropy of X and Y.

Assume that we have two images I(P)and I(2) which are already registered.

Let {JIf)} and {7)},k = 1,..., K be K feature images corresponding to 1)

and 1(2). The feature images correspond to a set of filters that are run on both

images. There is no a priori reason to use the same set of filters on both images.

As mentioned above, given the two sets of feature images, we determine a set of

projection coefficients that map each set of feature images onto a single "b' -1

feature image. Normalized mutual information (NMI) [38] is used as the criterion

to find the single, best dimension of feature projection. The objective function used

is


E(W(1 W(2)) NM((W(1))TF(1) (W(2))TF (2)

Wi
where (W(f))T is the transpose of the column vector Wt) = and

WK


(4 3)


fr)
F(r) = r r


1, 2. We denote by Fl(), the set of feature images of image









I(r),r 1,2. The objective function in (4-3) is maximized to get the best pro-

jection coefficients (W(1), W(2)). By maximizing (4-3), we obtain the best linear

combination of features.

As mentioned in the introduction, we have found that MI is not a good

criterion to determine the best feature combination. MI is biased toward images

with higher entropy and usually favors the original intensity image or an even

noisier image! NMI does not suffer from the same bias.

4.2 Affine Image Registration with the "Best" Feature Images

Assuming that the best feature combination has been discovered, we then
a b 0
proceed with NMI-based affine registration. Let T = c d 0 be a 2D affine

ef 1

a b
transformation, where can be decomposed into shear, scale and rotations
c d

and e f are the x- and y-translations. Assume that images IC1)and I(2)are

two noisy, unregistered images and F(1)and F(2) are two sets of feature images.

Let W('),r e 1, 2 be feature combination coefficients achieved by maximizing the

objective function (4-3) on a representative training set. Then we register images

I(1) and I(2) by maximizing NMI between the best feature images (W(1))TF(1) and

(W(2))TF(2). This is a standard affine registration step using NMI as the criterion.


T* = arg max NMI((W(l))TF(l), (W(2)T (2(T))
T

where F(2)(T) is the set of feature images of image I(2)(T), which is the affine

transformed version of image I(2) with affine transformation T.


(4 4)















CHAPTER 5
SIMULTANEOUS MULTIMODALITY IMAGE REGISTRATION USING AN
EXTENSIBLE INFORMATION METRIC AND HIGH DIMENSIONAL
HISTOGRAMMING

We present an extensible information measure for simultaneous multimodal-

ity image registration. The measure is a pseudometric when restricted to the

intermodality case since it satisfies the properties, i) non-negativity, ii) sym-

metry, iii) triangle inequality and is iv) zero if (but not only if) the two image

intensities are identical. Given images A and B, the metric used here is the sum

of the conditional entropies H(AIB) and H(BIA). We show that the normal-

ized version of the metric [the metric divided by the joint entropy H(A, B)] is

still a metric and is equivalent to the normalized mutual information (NMI).

Information metrics are rarely used in image registration and notably, mutual

information is not a metric. When compared to mutual information which can

even become negative in the multiple image case, it is easier to extend our metric

to the registration of multiple images-the multimodality case. The extension

is straightforward and comes in non-normalized and normalized versions. Given

images A, B, and C, the non-normalized measure is the sum of the conditional

entropies H(AIB, C) + H(BIA, C) + H(CIA, B). The non-normalized measure can

be normalized by either the joint entropy H(A, B, C) or the sum of the marginal

entropies H(A) + H(B) + H(C). The conditional entropies are estimated using

high-dimensional histogramming which (for mostly cultural reasons we think)

is rarely used in the medical imaging community. Finally, we propose another

new measure-an upper bound of the non-normalized measure (along with its

normalized counterparts) for multiple image registration, which does not need the









estimation of high dimensional probability mass functions. We compare the regis-

tration results using the new measure, the normalized measure, the upper bound of

the measure, the normalized upper bound, modified mutual information and mod-

ified normalized mutual information to simultaneously register multiple 2D slice

images obtained from synthetic magnetic resonance (\ll) proton density (PD), MR

T2 and MR T1 3D volumes available from the Brainweb simulator. In addition,

we also perform unbiased registration of multiple images of anatomical slices,

CT and MR PD from the Visible Human Male Data with the normalized metric

and we show the unbiased and simultaneous registration results of 9 synthetic

PD, T1 and T2 MR brain images using the normalized measure computed via

high-dimensional histogramming. Our results demonstrate the efficacy of the new

measures and high-dimensional histogramming for unbiased. affine, multimodality

image registration.

5.1 Multimodality Registration Using the Extensible Metric

5.1.1 Metric Definition

After our brief introduction and review of the different inadequacies of the

mutual information measure, we now turn to the definition of our new information

metric.

The metric p is the sum of two conditional entropies and defined in [54]. For

two random variables X and Y,



p(X,Y) H(XIY) + H(YIX) (5-1)

where H(-) is the entropy of a random variable and defined as H(X) = -E(log(p(X)),

where p(X) is the probability mass function of X, and E(.) denotes the ex-

pectation of a random variable. Hence H(XIY) = -E(log(p(XIY)) and

H(YIX) -E(log(p(Y|X)).

p(X, Y) is a pseudometric since it satisfies the following four properties [54].






34


H(X, Y)




H(.Y Y X H(Y)X)



H(X) Hf(y)


Figure 5-1. Venn diagram for two random variables


1. p(X,Y) >0

2. p(X, Y)= p(Y, X)

3. p(X, Y) = 0 if X = Y. However p(X, Y) = 0 also if X = f(Y). This is why

p(X, Y) is not a true metric.

4. p(X, Y) + p(Y, Z) > p(X, Z)

5.1.2 Relationship between the Information Metric and Mutual Infor-
mation

The definition of mutual information for two random variables X and Y is



MI(X, Y) = H(X) + H(Y) H(X, Y)

where H(X) and H(Y) are marginal entropies of X and Y and H(X, Y) is the

joint entropy of X and Y. Also,



H(XIY) H(X,Y)- H(X)

and


H(YIX) H(X,Y)- H(Y).

















(a) PD image (b) MR T2 image








(c) the metric p (d) Mutual Information

Figure 5-2. The metric p and mutual information between PD and rotated and
scaled T2 images


Hence
p(X, Y) = H(X|Y) + H(YIX)

S2H(X, Y) H(X) H(Y)
(5-2)
SH(X) + H(Y) 2MI(X, Y)

SH(X,Y)- MI(X,Y)

In Figure 5-2, we plot the values of the metric p and MI between a proton

density (PD) MR image and a rotated and scaled MR T2 image, where the

rotation angle ranges from -20 degrees to 20 degrees and scaling ranges from -1 to

1.

5.1.3 Affine Registration by Minimizing the Metric

Assume that we have two images I()and 1(2). We treat the intensity value of

each pixel as an independent random variable. We seek to register image 1(2) to

image (1) by determining the best affine transformation T* which minimizes the









metric (5-2).

T* = arg mnp()C, I(2) (T)) (5-3)
T

a b 0
a b
where T = c d 0 is an affine transformation. In T, the submatrix
c d
ef

can be decomposed into shear, scale and rotation and the vector [ fI contains

the x and y translations. The image (2) (T) is the transformed image of image 1(2)

using the affine transformation T.

5.1.4 Normalized Versions of our Metric

We also proposed two normalized versions of the metric: The first is

-(X, Y) p(X, Y)
Y(X, Y) (5-4)
H(X, Y)'

r(X, Y) is also a pseudometric [66]. And 0 < r(X, Y) < 1, r(X, Y) = 0 if X = Y;

r(X, Y) = 1 if X and Y are independent. The second normalized version of the

metric p(X, Y) is

I(X, Y) p(x) (5-5)
4XY) -H(X)+H(Y) )

And 0 < l(X, Y) < 1, (X, Y) = 0 if X = Y; (X, Y) = 1 if X and Y are

independent. But qr(X, Y) does not satisfy the triangle inequality and hence it is

not a metric (or pseudometric). We give the proofs of the triangle inequality of

the metric p(X, Y) = H(X Y) + H(YIX) and the normalized metric r(X, Y) =
H(XY)+H(YX) and a counterexample for that q(X, Y) = (X (Y) does not satisfy

the triangle inequality in the appendix.

From the definition in (5-1), we see that p is very similar to mutual infor-

mation (M\I) (5-6) in the 2-image case except that the metric has one more joint

entropy term, which means the metric gives joint entropy more weight than the

marginal entropy in comparison to mutual information












MI(X,Y) = H(X) + H(Y) H(X, Y) H(X) H(Y p(X,Y). (5-6)
2

And we have found that minimizing the normalized metric r or rl is equivalent to

maximizing the normalized mutual information (NMI) [38] (5-7) in the 2-image

case



H(X) + H(Y)
NMI(X, H(Y) 2- r(X,Y). (5-7)
H(X, Y)

Consequently, from our perspective, NMI is not ad hoc since it is inversely propor-

tional to a pseudometric.

Now we move to our main topic-multimodality image registration.

5.2 Extension to the Multimodality Case

From the definition of the information metric for two random variables (5-1),

we can .1i.:l, extend the metric to multiple random variables in two different v--v.

The first extension, for n random variables X1, X2, ... X,,


p(Xi,X2,...,X) = Ei H(XIX1,... ,Xi-, Xi+1,... ,X,) (5-8)

and the second is,


p(X, X2,... ,Xn) = i1 H(X1,... Xi,_,Xi+,... ,X, Xi). (5-9)

And after dividing by either the joint entropy H(X1,X2,..., X,) or by the sum of

the marginals l H(Xi), we get their normalized counterparts.

If we want to simultaneously register three images I(1), 1(2) and I(3), we obvi-

ously need to find more transformations. We define the biased case as one where

I(1) is the reference image and fixed in the registration and we seek two optimal

affine transformations-T2* for image I(2) and T3* for image 1(3) by minimizing the









metric (5-10).

{T2,T} = arg min p(() J(2) (T,(3)(T3)). (5-10)
{T2,T1}

We define the unbiased case as one where there is no reference image and we seek

three optimal affine transformations-T, for image (1), T2 for image I(2) and T3*

for image 1(3) by minimizing the metric (5-11).


{T* T, T *} arg min p(I(1(T), I(T2) 2j(3)T3)) (5-11)
{T1, T 2, T3

where I(1)(TI) is the transformed image of image (1) using affine transformation

T1, (2) (T2) is the transformed image of image I(2) using affine transformation T2

and I(3) (T3) is the transformed image of image 1(3) using affine transformation T3.

Equivalent minimizations can be carried out for the normalized counterparts of p

and p.

In Figure 5-3, we plot the values of p, MI and modified MI (lilI) for a PD

image, a rotated MR T2 and a rotated MR T1 image, where both rotation angles

range from -10 degrees to 10 degrees and the values of p, MI and MMI for a MR

PD image, scaled MR T2 and scaled MR T1 image, where both scale ranges are

from -1 to 1. From Figure 5-3, we can see that p and MMI can achieve their

minimum or maximum at the points where rotation or scale is zero. Once again

this anecdotally demonstrates that we can minimize p or maximize MMI to recover

transformations of rotation or scale. MI has two peaks in rotation but both peaks

are not the point where rotation is zero. Although MI achieves its maximum at

the point where scale is zero, it is very noisy compared with p or MMI and it

can assume negative values which are hard to interpret. Hence MI is not a good

measure in multimodality registration of images when compared to p or MMI.

The differences and accuracy in registration of p and MMI will be shown in our

experiments.

























(a) PD image (b) MR T2 image (c) MR T1 image


(d) p with rotation


0 45-
-
S35

)257S
101 8 0
_0 -6 -4 2 0 2 4 6 1 10 10 -10 -10
(e) MI with rotation (f) modified MI with rotation


S253
^ ^ 2:


(g) p with scaling (h) MI with scaling (i) modified MI with scaling

Figure 5-3. p MI and MMI with rotation (2nd row) and scaling (3rd row) of MR
PD, MR T2 and MR T1 images









5.3 Computing the Entropy of Multiple Random Variables

The multimodality image registration measures p, p and their normalized

versions are all entropy-based measures. Consequently, all these measures require

the computation of the joint entropy of many random variables-henceforth termed

"multi-dimensional entropy."

The approach in [34] used minimum spanning trees (\!ST) to estimate the

a-entropy in image registration. The MST-based approach directly estimates

entropy without estimating the high dimensional PMF. But computing an MST for

a graph with many edges is very expensive [O(E log E)] where E is the number of

voxels and furthermore, the method cannot compute the normalized versions of the

information measure. (Also the method computes the Renyi entropy instead of the

Shannon entropy.) Indirect methods compute entropy by first estimating the high

dimensional PMF. While histogramming is a popular approach for estimating the

PMF, it has not been used for computing the high dimensional entropy in image

registration, mainly because naive implementations are exponential in ,..-l'l,. .iii/

in the i.:I ,' ...: .','.,,.:l of random variables. Our technique for computing high

dimensional histograms (to be explained below) overcomes the aforementioned

dimensionality problem. Its computational complexity is O(N) where N is the

number of samples drawn from (corresponding) pixel locations over a set of images.

The 0(N) computational complexity is much smaller than some popular high

dimensional PMF estimation methods such as Parzen windows O(N2), Gaussian

mixture models O(NK) where K is the number of clusters, etc. An approximation

to the Parzen window entropy can be computed in O(NM), M < N using fast

Gauss transforms [67], but you have to first cluster the samples. To our knowledge,

this approach has not been explored in medical image registration. Its advantage

over the high dimensional histogramming technique is that it is analytically

differentiable.









We now describe the high dimensional histogramming approach. Assume we
have M images I(m), m E {1,..., M} and the number of histogram bins for the
mth image I(m) is K('), m {1,..., M}. The total number of bins in the multi-
dimensional histogram of M images is HII 1 K(m), which will be very large if M

or K(m) is large. But in the space of the joint histogram of M images, most of the

bins of the joint histogram are empty. Empty bins do not contribute anything when

we compute the high dimensional Shannon entropy (since p logp -- 0 as p -i 0.)
Hence, using I~m 1 K(m) bins in the space of the joint histogram of M images is

impractical and furthermore is unnecessary since we only need know the non-empty
bins.
Assume a bounded range [I(, n) x] for image I('). Let B( ) be the binned

intensity value of image I(m) at location i, i E {1,...,N}:


I( ) mini<, I(m)
B m)= (K -1)x (m) m + 1 ,me{1,...,M}.
maxl N{I -} minl (5-12)

From (5-12), we see that the binned intensity values of image I(") are integers in
{1,..., K()}. Let L(i) be the minimum length of digital bits which can represent

K(), m r {1 ..., M}. Then we get a new code C = B1)B (2) B(M) with

length : 1 L('), which is a concatenation of the binned intensity values of all
images at location i, i E {1,..., N}. The number of different elements of the set

{Ci, i E {1,..., N}} is the number of non-empty bins of the joint histogram of
M images. Hence we can use {Ci, i E {1,..., N}} to generate the joint histogram

of M images by counting the number of identical Cs in the code set. That this is

valid is guaranteed by the following theorem.
Theorem 1: Ci Cj if and only if B(') = B() Vm e {1,..., M},

Vi, jE {1,..., N}. [Proof omitted due to lack of space.]









The number of bins K(m) is the only free parameter in our method but it is

also very important. Below, following [68], we propose a criterion for limiting the

maximum number of bins in the histogram.

Theorem 2: Let U1, U2,..., UN be i.i.d. random variables in RM with PMF

f. Let P be a partition of RM into cubes of size h, and define the histogram PMF

estimator by
N
fN(u) = EA(u)} (5-13)
i=1
where A(u) is the set in P that contains u and I is the indicator function of a

set. Then the estimate is ;,,.:;. i, ,ll j consistent in L1 if h -- 0 and NhM 00

as N -+ o, that is, for any f the LI error of the estimate f IfN((u) f(u)\ du

converges to zero in probability, or equivalently, for any e > 0,


lim Pr f (u) f(u) du> = 0. (5-14)
N-oo j

For our case, the domain of PMF is a bounded subset of RM, namely [0, 1]M

If we use the same number K() = K bins for each image in the set, then h = -

Thus h -- 0 is equivalent to K -- oc and NhM oc is equivalent to -- oo, for

which K < Nk- is necessary. Let K N= aM then as K -- oc, K = N

for any a > 0 as N -- oc, which satisfies the condition of the theorem. Hence we

use K N= NM+ for some a > 0 as a criterion in our high dimensional histogram. In

plain English, Theorem 2 essentially -ziv that if you have more samples, then use

more bins for the histogram but the rate of increase of the number of bins should

be slower than the rate of increase of the number of samples. (The simplification of

K() = K has been used for the sake of exposition. An extension to different K(m)

is straightforward.)

From Theorem 1, we know that to compute the high dimensional histogram,

we only need to count the number of identical Ci in the set {QC, i E {1,..., N}}.

From Theorem 2, we know that for any Ci, i E {1,..., N}, Ci e [1, N]. We can









count the number of identical Ci in the set {Ci, i E {1,..., N}} by traversing N

samples once. Thus the time complexity of computing high dimensional histograms

is 0(N).

5.4 Another Measure for Multimodality Image Registration

Based on the properties of entropy, we propose another measure for multiple

image registration, which is an upper bound of the measure p.

p(X, Y, Z)
SH(XIY, Z) + H(YIX, Z) + H(ZIX, Y)

< (H(X|Y) + H(X|Z))
(5-15)
+(H(YIX) + H(YIZ))

+(H(ZIX) + H(ZIY))

S(p(X, Y) + p(Y, Z) +p(X, Z)).

In the reduction of (5-15), we mainly use the following property of entropy:

H(XY, Z) < H(XIY).

Let

K(X, Y, Z) df (p(X, Y) + p(Y, Z) + p(X, Z)). (5-16)

In multimodality image registration, we may minimize (5-16) instead of minimiz-

ing(5-8).

From the definition of p for three random variables, it can be seen that we

have to estimate the joint PMF p(X, Y, Z) of three random variables X, Y and Z,

which is computationally more expensive than the estimation of the joint PMF of

two random variables. But using K instead of p in registration of three images does

not require the estimation of the joint PMF of three random variables, which will

slightly alleviate the computational burden. This is the main benefit of using the

upper bound.









Finally, we briefly discuss the field of view problem which besets much of

entropy-based image registration. Since the joint PMF between two images is esti-

mated by considering the overlap region of the two images, the trivial minimization

of the information metric and maximization of the mutual information occurs when

the two images are spatially separated with zero overlap. The information metric p

is minimized in that case and the mutual information reaches its maximum value

equal to the sum of the two marginal entropies. A simple, but non-unique way of

fixing this problem is to use normalized version of the measure K. There are two

v--,V of normalizing K:

X Y Zdef (X, Y) + p(Y, Z) + p(X, Z)
(X,Y,Z) 2H(X,Y,Z) (5-17)
2H(X, Y, Z)

and
Y, def p(X, Y) + p(Y, Z) + p(X, Z)
2(H(X) + H(Y) + H(Z))
where it can be shown that 0 < a(X, Y, Z) < 1. If X = Y = Z then a(X, Y, Z) = 0

and if X, Y and Z are independent of each other, a(X, Y, Z) = 1. These also hold

for v(X, Y,Z).

In Figure 5-4, we plot the values of the measure a for a PD image, a rotated

MR T2 and a rotated MR T1 image, where both rotation angles range from -20

degrees to 20 degrees and the values of a for a PD image, scaled MR T2 and scaled

MR T1 image, where both scale ranges are from -1 to 1. From Figure 5-4, the

normalized measure a achieves its minimum at the point where rotation or scale is

zero. Once again this anecdotally demonstrates that we can minimize a to recover

transformations of rotation or scale.






























(b) MR T2 image


(c) MR T1 image


(a) PD image

px^" -~


(d) a with rotation (e) a with scaling

Figure 5-4. a with rotation and scaling of PD, rotated T2 and rotated T1 images















CHAPTER 6
NONRIGID MULTIMODALITY IMAGE REGISTRATION

In our previous work [69], we have proposed a new information metric as

a similarity measure and extend it to multimodality image registration (mul-

tiple image registration). And in [70], we compared ten similarity measures of

multimodality images and found that the normalized metric rl (??) has the best

performance in affine multimodality image registration. In this section, we will

use the normalized metric Tr and high dimensional histogramming to the nonrigid

registration of multimodality images. For recovering local deformation, we will

use B-Splines to represent flow fields of pixels because B-Splines have good local

approximation as long as the grids of B-Splines are fine enough.

6.1 Nonrigid Multimodality Image Registration

Affine registration is good enough for brain images from the same subject.

But when we need to register images from multiple subjects, we have to let

transformation have more freedom. Generally we have to compute a flow field for

each pixel of image.

Suppose we have three images 1(1),1(2) and I(3)

In the biased case, assume I(1) is the reference image. We wish to register I(2)

and I(3) to (1). To achieve registration, we need to find flow fields u(2) for image

I(2) and flow fields u(3) for image 1(3) so as to minimize the normalized metric Tr of

three images in (6-1).




{u(2), u(3)= arg min Tr(1(1),(2) ((2)), I(3) ((3)))+A(||Lu(2) 2+ Lu(3) 2) (6-1)
{u(2),u(3)}









For unbiased case, there is no reference image hence we need to find fields u(')

for image I(1), fields u(2) for image I(2) and flow fields u(3) for image 1(3) so as to

minimize the normalized metric r of three images in (6-2).



{u(), (2), u(3) } argmin u(1) (2) (3)( r(j(1)(u()), (2) (u(2)), (3) (u(3)))
(6-2)
+A(l|Lu(l)||2 + ||Lu(2)1 2 + |Lu(3) 12)

In (6-1) and (6-2), I(l)(u(l)), I(2)(u(2)) and I(3)(u(3)) are transformed images

of j(1),1(2) and 1(3) using flow fields u('), u(2) and u(3).

But optimizing (6-1) or (6-2) is very time consuming and flow fields will

not be smooth if we directly optimize (6-1) or (6-2) over flow field of each pixel.

Hence, researchers use splines to control these flow fields so as to be computa-

tionally efficient and achieve smooth flow fields. A popular spline is the B-Spline

[71].

6.2 B-Splines for Flow Field Representation

In 2D case, the B-Spline has the following form:

3 3
f(,Xy) Bk(s)B(t' ,, ,(j+) (6-3)
k=0 1=0
where i = [x 1, j = Ly] 1, s = x- [x, and t = y Ly]. Bk and Bi are uniform

cubic B-spline basis functions defined as

Bo (1 t)3/6,

B1 = (3t3 6t2 + 4)/6,

B2 (-3t3 +3t2 + 3t + 1)/6,
B3 3/6.

where 0 < t < 1. is the value of the ij-th control point on the grid of image.









If we use B-splines (6-3) for flow fields u, we have
3 3
u(x, y) = Bk0s)B 1 (i+k)(j+1) (6-4)
k=0 1=0

where u(x, y) and yij are two dimensional vectors for 2D image.

For 3D images, we can get similar form:

3 3 3
u (x, y, z) = B1 (r) B. (s) B (t) n (i+1) (j+m)(k+n) (6-5)
1=0 m=0 n=0
where u(x, y, z) and Kijk are three dimensional vectors for the 3D image.

After using B-splines on flow fields, the unbiased registration of three images in

(6-2) becomes

{I(1), CI(2), (3)} argm in (1),(2),(3) T( (1)( (1)), (2)()(2)), (3) ( (3)

+A(l|Lu(l)||2 + I|Lu(2) 12 + I|Lu(3)112)
(6-6)

where 1(1), 4(2) and 4(3) are the value of control points on the grid to compute

flow fields u(l), u(2) and u(3) in (6-4).

Hence the optimization is performed in the space of K instead of the space of

flow fields u. Since the cardinality of K is much less than that of u, the optimiza-

tion will be more efficient. And because of the use of the B-spline, the flow fields

will be smooth.

6.3 Multiresolution Optimization over B-Spline

Before developing an algorithm for multimodality image registration, we first

develop an algorithm based on multiresolution optimization over B-Spline for

intermodality registration. In intermodality registration, the energy function is


E -= (I ), 1(2) (u)) + A(lLu l2) (6-7)


where u are represented by (6-4) for 2D images or (6-5) for 3D images. By

minimizing 6-7, we achieve the best flow field u to register image I(2) to (1). In









the registration process, if the resolution of the grid of B-Spline representing the

flow field is low, the number of parameters 4 will be small so that the optimization

is very efficient but some small local deformation would not be recovered; but

if we select a high resolution, the small deformation will be recovered but the

computation expense will be very high. Thus we use a multiresolution optimization

algorithm, shown in Algorithm 1. The basic idea is that using low resolution of

the grid of B-Spline and efficient computation to recover large deformation at

earlier iterations of optimization then using high resolution to recover small local

deformation. At earlier iteration of the optimization process, the computation will

be efficient because the number of parameters 4 is small and large deformation

will be recovered because the grid is coarse so that each point on the grid will

affect more pixels on the image. Then after improving the resolution, the small

deformation will be recovered if it is not recovered in earlier iterations. For each

resolution, the gradient descent method is used for minimizing the energy function

and to find the best flow field. And the final flow field will be the accumulation of

the best flow field found in each resolution.










Algorithm 1 Multiresolution optimization of intermodality image registration
Initialize total flow fields u with 0;

Repeat

Initialize current grid of B-Spline with the current resolution;

Initialize the parameters 4 with 0;

Repeat

Numerically compute gradient a;

Update = 4 a;

Until E is less than a small constant e;

Compute current flow fields u, with the parameters 4;

Update total flow fields u = u + u,;

Improve the current resolution of the grid of B-Spline

Until the current resolution reaching the preset value;


Then we extend the Algorithm 1 to multimodality image registration. Suppose

we try to unbiasedly register three images and the energy function is


E = (I(l)(u(1)), (2) ((2)), J(3) ((3))) + A(IILu(1)I2 + ||Lu(2)1 2 + ||Lu(3)1|2) (6 8)


where u(), (2) and u(3) are represented by (6-4) for 2D images or (6-5) for

3D images. Similar to intermodality registration but we have to find 3 sets of

flow fields for 3 images, which minimize the energy function (6-8). The process

of finding the 3 sets of flow fields is similar to Algorithm 1, which is shown in

Algorithm 2. At each resolution level, we find the best 3 sets of flow fields which

minimize the energy function (6-8). Each best flow field is found by gradient

descent method with fixing other two flow fields. Then the final 3 sets of flow fields

are the accumulation of 3 sets of the best flow fields found in each resolution level.










Algorithm 2 Multiresolution optimization of multimodality image registration

Initialize 3 sets of total flow fields u(), u(2) and u() with 0;

Repeat

Initialize current grid of B-Spline with the current resolution;

Initialize the parameters 4(1), 4(2) and 4(3) with 0;

For image m = 1 to 3

Repeat

SNumerically compute gradient 5W

SUpdate 4(m) (m) $5W

Until 9E is less than a small constant e;

Compute current flow fields um with the parameters ("m);

Update total flow fields u(m) u(m) + um)

-End

Improve the current resolution of the grid of B-Spline

Until the current resolution reaching the preset value;














CHAPTER 7
EXPERIMENTAL RESULTS

7.1 Experimental Results on the Bayesian Multimodality Nonrigid
Image Registration

In this section, we compare four different multimodality registration methods

on synthetic data and simulated T1 and T2 2D MR images. The four methods

used are i) B li, MAP, ii) empirical mutual information, iii) empirical joint

probability and iv) empirical joint entropy with a small deformation penalty added

to each one. The objective functions corresponding to the four methods are

1. B ,li -, ,i MAP: EMAP(U) N 1logPrf ) I ),u) + ALu||2

2. Mutual information: EEMI(u) = -K Pr(a, bIu) logPr(a|b, u) +

A||Lu1|2

3. Joint probability: EEJp(U) = 1 logPr 1(B1 ) u) + A|Lu|2
K(1) K(2) Lu
4. Joint entropy: EEJE(U) = 1 Lb Pr(a, b|u) logPr(a, bu) + ALu2

For each method, we use essentially the same optimization approach as described

below:

Multimodality Non-rigid registration

Set n = 0.

Perform Gaussian smoothing (with smooth) on the two images.

Begin A: Do A until |AE| < 6 or n > T.

Initialize u to zero. This is equivalent to an identity transformation.
u(f+1) = u-)- c(n+l). C(!....-. a > 0 such that AE("+1) < 0.

Perform bilinear interpolation.

n n+ 1


* End A













Figure 7-1. Left and middle: two simple shape images. Right: final registration
result.


In the above, T is an iteration cap, 6 is a convergence threshold and a is a stan-

dard step-size parameter. We use numerical differentiation (with c = 1) for

computing It should be understood that the objective function E in the al-

gorithm is a placeholder for any of the four methods mentioned above. In all the

experiments below, T = 20, 6 = 0.01, a = 0.1, smooth = 0.5, K() K(2) = 8, and

A = 0.05.

7.1.1 Experiments on Simple Multimodality Shape Images

We first create two images as shown in Figure 7-1. The circle and square

shapes are swapped and the intensities of each shape differ between the two images.

The B ,i, in MAP approach was used to register the right image to the left

image. A small amount of isotropic Gaussian smoothing was performed prior to

registration. At each iteration, we also observe the values of the empirical mutual

information (EMI), empirical joint probability (EJP) and empirical joint entropy

(EJE). From Figure 7-2, we see that the likelihood and mutual information plots

are very similar whereas the joint probability and negative joint entropy actually

decrease which is counter intuitive. (We also observe that the likelihood does not

increase monotonically which is perhaps due to a) bilinear interpolation factors and

b) the deformation penalty.) The algorithm was able to convert the circle and the

square to approximately a square and a circle in about 6 iterations.













Figure 7-2. The changes in i) log-likelihood, ii) mutual information, iii) joint prob-
ability and iv) negative joint entropy when minimizing the B li- i i_
MAP objective function.







Figure 7-3. Leftmost: transverse T2 image. Left middle: transverse T1 image.
Middle: Deformed T1. Right middle: Intensity difference between orig-
inal T1 and deformed T1 prior to registration. Right: Unwarped final
T1 image


7.1.2 Experiments on Simulated T1 and T2 2D MR Images

In our next experiment, we chose two frames generated by the powerful

Brainweb MR simulator [72]. The 2D T1 and T2 axial images are shown in

Figure 7-3. We used a ;:'. noise level for the simulation which uses the ICBM

protocol. The advantage of using the Brainweb simulator is that the ground truth

is known. Any non-rigid deformation applied to a T1 image can be simultaneously

applied to its T2 counterpart.

In our experiments, we used a Gaussian radial basis function (GRBF) spline

as the non-rigid parameterization. The deformed T1 image and the intensity

difference between the original T1 and the deformed T1 image are shown in

Figure 7-3. The registration algorithm attempts to register the deformed T1 image

to the original T2 image. The deformed T1 image is gradually unwarped during

registration. During the execution of the B li, -i i, MAP algorithm, we also observe

the values of the empirical mutual information (EMI), empirical joint probability

(EJP) and empirical joint entropy (EJE). The results are shown in Figure 7-4.













Figure 7-4. The changes in i) log-likelihood, ii) mutual information, iii) joint prob-
ability and iv) negative joint entropy when minimizing the B l-, -i i'
MAP objective function.







Figure 7-5. Difference images between original T1 and unwarped T1. Left: MAP.
Left middle: EMI. Right middle: EJP. Right: EJE. The SSDs were 609
before registration, 20.38 (\!MAP), 20.74 (EMI), 52.49 (EJP) and 52.47
(EJE).


In this case, all four curves mostly show an increase which is somewhat different

from the behavior in Figure 7-2. Once again, the MAP and EMI curves are in

lockstep as are EJP and EJE. As a comparison between the different algorithms,

we executed all four approaches on the same data. The difference images (between

original T1 and unwarped T1) shown in Figure 7-5 clearly indicate that the MAP

and EMI algorithms are superior to the EJP and EJE algorithms.

We performed another experiment on the pair of T1 and T2 simulated 2D

MR images. This time, the deformation on the original T1 image was much larger.

The original and deformed T1 images are shown on the left in Figure 7-6. The

results of executing the B li-, -i ,i MAP algorithm on the deformed T1 and T2

images are shown on the right in Figure 7-6. Clearly, despite errors near high

gradient boundaries (which are mostly caused by interpolation artifacts), the MAP

algorithm is up to the task of recovering a reasonably large global deformation.
















Figure 7-6. Leftmost: Original T1 image, Left middle: deformed T1 image. Mid-
dle: Intensity difference between original T1 and deformed T1 before
registration. Right middle: Intensity difference between original T1 and
unwarped T1 after registration. Right: Unwarped final T1 image. The
before and after SSDs were 647 and 59 respectively.


7.2 Experimental Results on the Unified Feature-based Registration
Method for Multimodality Images

Our experimental results use the powerful Brainweb simulated MRI volumes

for a normal brain [72]. The simulations are based on an anatomical model of the

normal brain with the main advantage being that the ground truth is known and

can be used for validation.

7.2.1 Robustness of Feature Images to Noise

In our experiments, we use pairs of 2D slices from 3D PD and T2 MR brain

images. The basic feature set includes image intensity I, x-direction derivative

VI, y-direction derivative Vy,, cross derivative VcI and their product I VIJ, I*

VyI,I V7I,V1I VyI, V1I V7I,VVy VJI. The best projection onto a single

dimension of the best feature combination of features W(),r = 1,2 is obtained

by maximizing the objective function (4-3). The original intensity range of the

PD and T2 images is in [0 1]. We add different levels of Gaussian noise with mean

zero and varying standard deviations (0.1, 0.2 and 0.4) to the images. As a simple

example, we rotate the T2 image within a range from -20 degrees to 20 degrees and

compute the NMI between the single best pair of feature images. This is compared

to the NMI obtained from the original intensity pair. The NMI plots shown in









Figure 7-7 demonstrate that the single best feature found is more robust to noise

than the original intensity.

7.2.2 Affine Registration of PD and T2 2D Image Slices

We demonstrate results on 2D slices of PD and T2-weighted MR images. The

affine transformation is decomposed into a product of shear, scale and rotations.
ab0
Let T = c d 0 be an affine transformation.

ef 1


a b 2t 0 2] 0
R(o0) R(W)
c d 0 2-" 0 2t

where s and t are scale and shear parameters, R(O) and R(b) are two rotation

matrices with rotation angle 0 and 4. In the experiments, the range of the shear

and scale parameters is [-1 1], the range of rotation parameters are [-45 45] degrees

and the range of translations is [-10 10] pixels. We used 2D slices drawn at sagittal,

coronal and axial orientations. The best linear combination is first estimated by

maximizing the NMI on the feature sets of noiseless registered PD and T2-weighted

images, whose noised and transformed version are used in following registration.

We then transform the T2-weighted image with an affine transformation T.

The shear and scale parameters are 0.5 and the two rotation parameters are 10

degrees, with the translations along the x and y directions being 5 pixels. Hence
1.9095 -0.5130 0
T 0.2565 0.4548 0 s 0.5,t 0.5,0 10, 10,e 5 and

5 5 1
f =5. Gaussian noise with mean 0 and standard deviation 0.2 is added to PD and

transformed T2 images. NMI is subsequently used as the criterion to register these

two images. We used a coarse-to-fine search strategy to find the best T* in (4-4).



























(a) intensity image


Figure 7-7. Left: From top to bottom, NMI between the original intensity pair
with rotation. Right: From top to bottom, NMI between the best fea-
ture image pair with rotation. The rotation range is from -20 degrees
to 20 degrees. From top to bottom: added Gaussian noise with mean 0
and deviation 0, 0.1, 0.2 and 0.4.


(b) feature image















(c) recovered T2


Table 7-1.


Figure 7-8. Sagittal 2D slices

Registration results of 2D sagittal PD and T2 slices using intensity and
best feature pair


ground truth results from intensity results from feature
s 0.5 0.45 0.5
t 0.5 0.45 0.5
0 10 12 10
10 11.5 10
e 5 5 5
f 5 4 5


NMI is computed only on the overlap area of the two images with nearest neighbor

interpolation used for the transformation of the image in all experiments.

Figure 7-8 shows 2D sagittal PD, transformed T2 slices and results recovered

using the best feature images. Table 7-1 shows the registration results using

intensity and the best features.Figure 7-9 shows 2D coronal PD, transformed T2

slices and results recovered using the best feature images. Table 7-2 shows the

registration results using intensity and the best feature image pair. Figure 7-10

shows 2D axial PD, transformed T2 slices and results recovered using the best


(a) PD


(b) T2


(c) recovered T2


Figure 7-9. Coronal 2D slices


(a) PD












Registration results of 2D coronal PD and T2 slices using intensity and
best feature pair


ground truth results from intensity results from feature
s 0.5 0.45 0.48
t 0.5 0.45 0.52
0 10 11.5 10.6
10 11 9.4
e 5 5 5
f 5 5 5


(a) PD


(b) T2

Figure 7-10. Axial 2D slices


(c) recovered T2


Registration results of 2D axial PD and T2 slices using intensity and
best feature pair


ground truth results from intensity results from feature
s 0.5 0.4 0.5
t 0.5 0.4 0.5
0 10 12 10
10 11 10
e 5 5 5
f 5 5 5


Table 7-2.


Table 7-3.









Table 7-4. Registration results of 2D sagittal PD and T2 slices before and after
bootstrap

ground truth results before bootstrap results after bootstrap
s 0.5 0.45 0.5
t 0.5 0.45 0.5
0 10 12 10.6
10 11.5 10.2
e 5 5 5
f 5 4 5


feature images. Table 7-3 shows the registration results using intensity and the

best feature image pair.

From the registration results above, we observe that better results are achieved

using the feature image pair than using the original intensity pair. The feature

image sets were combined using projection coefficients obtained from noiseless,

registered, training images. However, it would be much more interesting to see if

the above approach extends to the case where we do not have registered, training

images. We turn to this case, next.

7.2.3 Bootstrapping the Feature Combination With Imperfect Regis-
tration


We now describe a bootstrap approach wherein NMI is used to register two

images using intensity as the feature after which we apply the above technique to

get the best set of projection coefficients. These projection coefficients are used to

get the best feature pair. NMI is then used on the best feature pair after which

the process can be repeated (if necessary). In this experiment, we register images

(same images used in section 3.2) using image intensity at the first step. Then

we use these imperfectly registered images as training images to extract the best

projection coefficients. After projecting the feature images onto the single best

dimension, we use the new feature images as input to a new NMI-based registration

to boost the registration results achieved by maximizing NMI on image intensity.









Table 7-5.


Table 7-6.


Registration results of 2D coronal PD and T2 slices before and after
bootstrap


ground truth results before bootstrap results after bootstrap
s 0.5 0.45 0.5
t 0.5 0.45 0.52
0 10 11.5 9
10 11 11
S 5 5 5
f 5 5 5


Registration results of 2D axial PD and T2 slices before and after boot-
strap


ground truth results before bootstrap results after bootstrap
s 0.5 0.4 0.52
t 0.5 0.4 0.52
0 10 12 9.4
10 11 9.6
e 5 5 5
f 5 5 5


The second columns of Table 7-4, 7-5 and 7-6 are registration results obtained

by maximizing NMI between the original image intensity pairs. These are used

to extract the best projection coefficients of features. The third columns of Table

7-4, 7-5 and 7-6 are registration results obtained by maximizing NMI between the

best feature image pairs.We see that maximizing NMI between the best feature

image pairs is able to improve upon the registration result obtained by using NMI

on the original image intensities. Despite the fact that the best feature images

were obtained from images which were somewhat mis-registered, we were able to

improve upon the original registration result using the imperf. /;/, registered images

as a training set.









Table 7-7. Results of 2D slice along sagittal direction

T on MR T2 T on MR T1
ground truth results ground truth results
s 0.1 0.1 0.2 0.18
t 0.1 0.1 0.2 0.18
0 5 5 10 9.4
5 5 10 9.8
e 3 3 5 5
f 3 3 5 5


7.3 Experimental Results on the Affine Image Registration Using the
Upper Bound of the Information Metric

7.3.1 Affine Registration of PD, T2 and T1 MR 2D Images

In all our medical imaging experiments, we use the powerful Brainweb simu-

lated MRI volumes for a normal brain [72]. The simulator is based on an anatom-

ical model of a normal brain. The main advantage of using simulated MR data is

that the ground truth is known.

We decompose an affine transformation matrix into a product of shear, scale
ab0
and rotations. Let T = c d 0 be an affine transformation.

ef


a b 2t 0 2' 0
R(o0) R(W)
c d 0 28 0 2-t


where s and t are scale and shear parameters, and R(0) = cos(0) sin(0)
sin(0) cos(0)

cos((Q) sin(0)
R(0) = cos(Q) -sin() are two rotation matrices. In our experiments, the
sin(O) cos(O)
range of shear and scale parameters is [-1 1], the range of rotation parameters are

[-45 45] and the range of translations is [-10 10].















(a) PD


(e) recovered T2


(f) recovered T1


Figure 7-11. Sagittal 2D slice


In the experiments we use 3 triplets of 2D slices of 3D PD, T2 and T1 MR

brain volume images. The slices are chosen in sagittal, coronal and axial directions.

We then transform the T2 image with an affine transformation Ti. The scale and

shear parameters are 0.1 and 0.1 respectively, and the two rotation parameters are

5 and 5 degrees respectively, with the two translations along the x and y direction
1.1324 -0.1866 0

being 3 and 3 pixels respectively. Hence T = 0.1866 0.9837 0 with

3 3 1
si = 0.1, t = 0.1, 01 = 5, 01 = 5, el = 3 and fl = 3. We then transform the

T1 MR image with an affine transformation T2. The scale and shear parameters

are 0.3 and -0.1 respectively and the two rotation parameters are 10 and -5 degrees

respectively, with the translations along the x and y directions being 5 and -3
1.2496 -0.3967 0

pixels respectively. Hence T2 = 0.3967 0.9301 0 with s2 = 0.2, 2 = 0.2,

5 5 1
02 = 10, Q2 = 10, e2 = 5 and f2 5. We add Gaussian noise with zero mean and

standard deviation 0.1 to the PD, transformed T2 and transformed T1 MR images

and register the three images simultaneously. (The original intensity range of all


(c) T1















(a) PD


(e) recovered T2


(f) recovered T1


Figure 7-12. Coronal 2D slice

Table 7-8. Results of 2D slice along coronal direction

T on MR T2 T on MR T1
ground truth results ground truth results
s 0.1 0.1 0.2 0.16
t 0.1 0.1 0.2 0.22
0 5 5.4 10 10.6
5 5.4 10 10.4
e 3 3 5 5
f 3 3 5 5


images is normalized to the [0 1] interval). We use a coarse-to-fine search strategy

to find the optimal T* and T*. The registration measure a is computed only in

the overlap area of the three images with nearest neighbor interpolation used for

transforming the image intensities.

In all results shown here, the normalized measure a was used. Figure 7

11 shows 2D PD, transformed T2 and transformed T1 slices along the sagittal

direction and the registration results. Table 7-7 shows the registration results of

these sagittal slices. Figure 7-12 shows 2D PD, transformed T2 and transformed

T1 slices along coronal direction and registration results. Table 7-8 shows the

registration results of these coronal slices. Figure 7-13 shows 2D PD, transformed


(b) T2


(c) T1















(b) T2


(e) recovered T2


(f) recovered T1


Figure 7-13. Axial 2D slice

Table 7-9. Results of 2D slice along axial direction

T on MR T2 T on MR T1
ground truth results ground truth results
s 0.1 0.12 0.2 0.18
t 0.1 0.1 0.2 0.2
0 5 5 10 9.4
5 5.4 10 10.2
e 3 3 5 5
f 3 3 5 5


T2 and transformed T1 slices along axial direction and registration results.

Table 7-9 shows the registration results of these axial slices.

These experiments above demonstrate a proof of concept of our approach

to multimodality image registration since T1 and T2 are being simultaneously

determined. Future work will focus on validation studies from which we hope to

elicit capture range and tolerance to noise, etc.

7.3.2 Matching Face Images Obtained under Different Illuminations

In the following experiments, we use face images from the AR Face Database

[73]. We simultaneously register three face images with different illuminations.

Essentially, either one side of the face or the other or none are exposed to a


(c) T1


(a) PD











Cr LI]
(a) left light on (b) right light on




(e) recovered right light on
(e) recovered right light on


(c) no light on




(f) recovered no light on


Figure 7-14. Images under different lighting conditions (left light on, right light on,
and no light on) and wearing sun glasses

Table 7-10. Results under different lighting conditions (left light on, right light on,
and no light on) and wearing sun glasses


T on right light on T on no light on
ground truth results ground truth results
s -0.2 -0.22 0.2 0.14
t -0.2 -0.2 0.2 0.14
0 -10 -9.6 10 9.6
-10 -10 10 10.6
e -5 -5 5 5
f -5 -5 5 5


0.7
0.3(


light source. We use affine transformations T1


049 0.3006 0
306 0.9740 0 and
5 -5 1


1.2496 -0.3967 0
T = 0.3967 0.9301 0 to transform two of the face images. Registration
5 5 1
is performed against the one untransformed image. The true affine transformation


parameters are sl


-0.2, ti


-0.2, 01


10, 01


10, ei


5, fl


S2 = 0.2, t2 = 0.2, 02 = 10, 02 = 10, e2 5 and f2 5.
In all subsequent results, the normalized measure a was used. Figure 7
14 shows left-light-on, transformed right-light-on and no-light-on face images













(a) left light on


(b) right light on
(b) right light on


(e) recovered right light on


(c) no light on


(f) recovered no light on


Figure 7-15. Images under different lighting conditions (left light on, right light on,
and no light on) and wearing a scarf

Table 7-11. Results under different lighting conditions (left light on, right light on,
and no light on) and wearing a scarf

T on right light on T on no light on
ground truth results ground truth results
s -0.2 -0.20 0.2 0.16
t -0.2 -0.22 0.2 0.2
0 -10 -10.6 10 10.2
-10 -9.6 10 10.2
e -5 -5 5 5
f -5 -5 5 5

wearing sun glasses and the corresponding registration results recovered using
the normalized measure a. Table 7-10 shows the registration results of these face
images wearing sun glasses under different light conditions. Figure 7-15 shows
left-light-on, transformed right-light-on and no-light-on face images wearing a scarf
and the registration results. Table 7-12 shows the registration results of these
face images wearing a scarf under different light conditions. Figure 7-16 shows
left-light-on, transformed right-light-on and no-light-on face images wearing sun
glasses or a scarf and results recovered using the normalized measure a. Table 7-12
shows the registration results of these face images wearing sun glasses or a scarf
under different light conditions.


L:;-0-04













(a) left light on


(b) right light on
(b) right light on


(e) recovered right light o
(e) recovered right light on


(c) no light on





(f) recovered no light on


Figure 7-16. Images under different lighting conditions and wearing sun glasses or
scarf

Table 7-12. Results under different lighting conditions (left light on, right light on,
and no light on) and wearing sun glasses or a scarf


T on right light on T on no light on
ground truth results ground truth results
s -0.2 -0.24 0.2 0.14
t -0.2 -0.2 0.2 0.14
0 -10 -9.4 10 9.6
-10 -9.6 10 10.6
e -5 -5 5 5
f -5 -5 5 5


Once again, these three experiments demonstrate a proof of concept with

more validation experiments required to better understand the performance under

different illuminations.

7.4 Experimental Results on the Affine Multimodality Image
Registration using the Information Metric and High Dimensional
Histogramming

7.4.1 Multimodality vs. Intermodality: Simultaneous Registration of 3
Images and Pair-wise Registration on Synthetic PD, T2 and T1
MR Images

In the registration experiments of this section, we use the powerful Brainweb

simulated MRI volumes for a normal brain [72]. The main advantage of using









simulated MR data is that the ground truth is known. The size of each image is

256mm x 256mm.

We decompose an affine transformation matrix into a product of shear, scale
a b 0
a b
and rotations. Let T c d 0 be an affine transformation.
c d
ef 1

28 0 2' 0
R(0) R( ), where s and t are scale and shear parameters,
0 28 0 2-'

cos(O) sin(6) cos(p) sin(p)
and R(0) = R() are two rotation
sin(0) cos(O) sin()) cos()
matrices. In our experiments, the range of shear and scale parameters is [-1 1], the

range of rotation parameters are [-45 45] degrees and the range of translations is

[-10 10] mm. In this decomposition of an affine transformation, reflections are not

allowed.

In the experiments, we use the following ten measures to register 3 triplets of

2D slices of 3D PD, T2 and T1 MR brain volume images.

1. p(X, Y, Z) = H(X|Y, Z) + H(Y|X, Z) + H(Z|X, Y)

2. p(X, Y, Z) = H(X, YZZ) + H(Y, Z(X) + H(Z, XY)

3. r(X, Y, Z) p(x,Yz)
H(X,Y,Z)

l H(X)+H(Y)+H(Z)
5. m(X, Y, Z) ;(x,Yz
H(X,Y,Z)
6. uo(X, Y, Z) P(x,YZ)
H(X)+H(Y)+H(Z)
7. modified mutual information: mMI(X, Y, Z) = H(X) + H(Y) + H(Y) -

H (X, Y, Z)

8. sum of pair-wise mutual information: pMI(X, Y, Z) = MI(X, Y)+MI(Y, Z)+

MI(Z, X)

9. modified normalized information: rNMI(X, Y, Z) H(X)-H(Y)+H(Y)
H(X,YZ)









10. sum of pair-wise normalized mutual information: pNMI(X, Y, Z)

NMI(X, Y) + NMI(Y, Z) + NMI(Z, X)

The slices are chosen in the axial direction. We then transform the MR T2 image
1.2496 -0.39666 0
with an affine transformation T = 0.39666 0.93006 0 with si 0.2,

4 4 1
t1 = 0.2, 01 = 10, 1 = 10, el = 4 and fli 4. We also transform the MR T1
1.4205 -0.88097 0
image with an affine transformation T2 = 0.88097 0.67935 0 with s2 = 0.4,

8 8 1
t2 = 0.4, 02 = 20, 2 = 20, e2 = 8 and f2 8. We have done two experiments with

these data. Each experiment is repeated 30 times with different Gaussian noise.

We add Gaussian noise with zero mean and standard deviation 0.1 in the first

experiment and zero mean and standard deviation 0.2 in the second experiment.

(The intensity range of all images is normalized to the [0,1] interval.) We use a

coarse-to-fine brute force search strategy to find the optimal TI* and T2*. The finest

search resolution of scale and shear is 0.05. The finest search resolution of rotation

is 0.5 degrees in the first experiment and 1 degree in the second experiment. The

finest search resolution of translation is 1 mm. The registration measures are

computed only in the overlap area of the three images with bilinear interpolation

used for transforming the image intensities.

To compare each measure and validate the registration results, we compute

the mean error of each parameter of two affine transformations recovered by

ten measures and the sum of T1 T* + T2 T2 of 30 experiments in each

experiment.

Table 7-13 is mean error of each parameter of two affine transformations

recovered with ten measures of 30 experiments in the first experiment. Figure 7-17

depicts the sum of Ti T* + T2 T2 of 30 noise trials in the first set of















Table 7-13. Mean errors on different affine parameters in the first experiment with
noise 0.1


error of transformation on MR T2 error of transformation on MR T1
measures s t 0 ( e f s t 0 e f
p 0 0 0.83 0.77 1.8 0.17 0 0 1.22 0.62 1.57 0.87
tp 0 0 0.75 0.77 1.87 0.17 0 0 1.35 0.97 1.1 0.93
T 0 0 0.83 0.77 1.9 0.17 0 0 1.08 0.47 1.63 0.7
l 0 0 0.62 0.63 1.67 0.17 0 0 1.02 0.55 1.53 0.8
h 0 0 0.67 0.68 1.9 0.2 0 0 1.38 0.63 1.47 0.83
a 0 0 0.67 0.68 1.9 0.2 0 0 1.38 0.63 1.47 0.83
mMI 0 0 0.68 0.63 1.87 0.2 0 0 1.31 0.62 1.4 0.87
pMI 0 0 0.7 0.78 1.9 0.17 0.0083 0.0017 2.93 0.62 1.4 0.73
mNMI 0 0 0.67 0.68 1.9 0.2 0 0 1.38 0.63 1.47 0.83
pNMI 0 0 0.73 0.8 1.9 0.17 0.0083 0.0017 2.87 0.63 1.47 0.77


Figure 7-17. Plots of sum of Tj + T- T2* of 30 trials recovered by ten
measures in the first experiment with noise std. 0.1. Numbers 1 to 10
represent p,pr,rl,K,o-, mMI, pMI, mNMI and pNMI-the ten registra-
tion measures.


8 9 10


-3 fc






73






Table 7-14. Mean errors of different affine parameters in the second experiment
with Gaussian noise with mean 0 and std. 0.2


error of transformation on MR T2 error of transformation on MR T1
measures s t 0 e f s t 0 ( e f
p 0.24 0.01 2.53 1.53 2.53 0.7 0.11 0.02 3.77 2.4 1.73 1.2
tp 0.64 0.06 10.57 3.03 5.93 1.57 0.42 0.08 4.87 3.53 2.97 2.03
7 0 0 1.1 1.33 1.93 0.43 0.0033 0.0083 3.83 1.67 1.833 0.97
r/ 0 0 0.97 1.33 1.93 0.33 0.0017 0.0083 2.8 1.23 1.77 0.93
h 0 0 1.03 1.2 2.07 0.37 0.005 0.0117 3.53 1.43 2.13 0.7
a 0 0 1.03 1.2 2.07 0.37 0.005 0.0117 3.53 1.43 2.13 0.7
mMI 0 0 1.1 1.2 2.03 0.37 0.005 0.0117 3.93 1.4 2 0.9
pMI 0 0 1.2 1.37 2.17 0.3 0.005 0.013 7.43 1.8 2 0.67
mNMI 0 0 1.03 1.2 2.07 0.37 0.005 0.0117 3.53 1.43 2.13 0.7
pNMI 0 0 1.16 1.37 2.17 0.3 0.005 0.0133 7.4 1.8 2.23 0.77


Figure 7-18.


Plots of sum of T TI* + T T2 of 30 trials recovered by ten
measures in the second experiment with noise 0.2. Numbers 1 to 10
represent p,p,,r,Tl,,a,, mMI, pMI, mNMI and pNMI-the ten registra-
tion measures.









experiments. From the results, we see that multimodality registration is more

accurate than repeated pair-wise (intermodality) registration. And the normalized

metric r] has best performance. Table 7-14 shows the mean error of each parameter

of two affine transformations recovered with the ten measures of 30 noise trials

in the second experiment. Figure 7-18 shows the sum of T- T1I + T- T2

of 30 noise trials in the second experiment. From the results, we see that the two

non-normalized metrics p and p failed in recovering scale because of high noise.

But the normalized metric T] (which is based on p) still has best performance. And

multimodality registration is more accurate than repeated pair-wise registration.

With these experiments on synthetic PD, T2 and T1 MR 2D images, we

see that these ten measures have similar performance in low noise experiments.

Generally, they can correctly recover scale and shear parameters but have error in

recovering rotation and translation. And we see that multimodality registration

is more accurate than repeated pair-wise registration. In the high noise case,

the two non-normalized metrics failed to recover scale because they prefer small

overlaps of images. The normalized metric r] still has best performance. And these

experimental results also show that minimizing the normalized metric K or a is

equivalent to maximizing the modified normalized mutual information.

In our following experiments, we will only use the normalized measure r].

7.4.2 Unbiased Multimodality Image Registration of Visible Human
Data

In this section, we register pentads of images of head slice from Visible Human

Male Data. For the pentad, the first image is the photograph of anatomical slice,

the second is the CT image, the third is an MR PD image, the fourth is an MR

T1 image and the fifth is an MR T2 image. The slice number of the pentads in

the Visible Human Male Data is 1165. Because ground truth is unknown, we

register 5 images simultaneously without bias. That means that each image gets









an affine transformation and we minimize the normalized metric r] on five affine

transformations:


Algorithm 3 Iterated sequential search
1. sequentially search ten translations which minimize r] corresponding to 5

images;

2. sequentially search ten scaling and shear parameters which minimize ] for 5

images;

3. sequentially search ten rotations which minimize r] for 5 images;

4. if rT decreases in this iteration then go to 1; else end.





{T*, T2)T3T4T5} = argmm9r(I (l TI),I(2) T2 (3) T3, (4) (T4), (T (7-1)

where T = {T, T2, T3, T4,T5} and T1, T2, T3, T4 and T5 are five affine transforma-

tions. I() (Tm) is the transformed image of image I(m) using affine transformation

Tm, m E {1, ..., 5}. Since the time complexity of searching for 30 parameters of 5

affine transformations is high, we used iterated sequential search using algorithm 3

for each parameter until the normalized measure qT achieves the minimum. The

color images of the anatomical slice are converted to gray images and the intensity

of images is normalized to the interval [0, 1] prior to registration. The normalized

measure TI is computed only in the overlap area of the three images with bilinear

interpolation used for transforming the image intensities. The image size is 256

by 256. (The pixel size is 0.32mm square for a photograph of anatomical slice and

1mm for MR and CT images.) The histogram of each image used 8 bins. High

dimensional histograms are computed using the technique in 5.3.

In figures 7-19, 7-21 and 7-23, we show the images before and after regis-

tration. In order for human perception to gauge the results of registration, we













(c) MR PD (d) MR T1 (e) MR T2 (f) overlap


Figure 7-19. The first row is the set of images before registration; the second row is
the set after registration. [Dataset index: VHD #1080.]

Table 7-15. Results of unbiased registration of anatomical slice, CT, MR PD, T1
and T2 images. [Dataset index: VHD #1080.]


Anatomic CT MR PD MR T1 MR T2
s -0.1 0.1 0 0 0
t -0.05 0 0 -0.1 0.04
0 0 -4 0 0 2
3 6 1 -18 20
e 2 -1 0 -1 0
f -3 6 0 0 0


Dunr


M


(a) anatomical (b) CT (c) MR PD (d) MR T1 (e) MR T2 (f) overlap
Figure 7-20. Segmented images before (1st row) and after (2nd row) registration.
[Dataset index: VHD #1080.]


(a) anatomical (b) CT











Table 7-16.


Number of pixels in nonoverlap region of segmented images before
and after registration. Upper triangle is before registration and lower
triangle is after registration. [Dataset index: VHD #1080.]


nonoverlap Anatomic CT MR PD MR T1 MR T2
Anatomic 0 7330 5054 8196 7635
CT 1730 0 3762 6214 5595
MR PD 1910 776 0 6258 6219
MR T1 2023 833 571 0 8543
MR T2 3385 2221 1889 2182 0


(a) anatomical


(b) CT (c) MR PD


(d) MR T1 (e) MR T2


Figure 7-21. The first row is the set of images prior to registration; the second row
is the set after registration. [Dataset index: VHD #1110.]


Table 7-17. Results
and T2


of unbiased registration of anatomical slice, CT MR PD, T1
images. [Dataset index: VHD #1110.]


Ain i..i CT MRPD MRT1 MR T2
s -0.09 0.07 0.01 0.01 0.01
t 0 0 0 0.01 0.05
0 0 0 0 0 0
2 -19 0 20 0
e 3 -1 0 0 0
f -3 6 0 0 0


(f) overlap










n


NI


ND


(a) anatomical (b) CT


NM

A
IE]dM
ONME


mi
Mi


(c) MR PD (d) MR T1 (e) MR T2 (f) overlap


Figure 7-22. Segmented images before (1st
[Dataset index: VHD #1110.]


row) and after (2nd row) registration.


Table 7-18. Number of pixels in nonoverlap region of segmented images before
and after registration. Upper triangle is before registration and lower
triangle is after registration. [Dataset index: VHD #1110.]


nonoverlap Anatomic CT MR PD MR T1 MR T2
Anatomic 0 6992 8129 8432
CT 2844 0 4299 5580 4689
MR PD 3442 1320 0 4413 2593
MR T1 3445 1281 699 0 5481
MR T2 4590 2524 1464 1615 0


(a) anatomical (b) CT


(c) MR PD


(d) MR T1 (e) MR T2


Figure 7-23. The first row is the set of images before registration; the
the set after registration. [Dataset index: VHD #1165.]


(f) overlap
second row is











Table 7-19. Results
and T2


of unbiased registration of anatomical
images.[Dataset index: VHD #1165.]


slice, CT, MR PD, T1


Ainin._ CT MR PD MR T1 MR T2
S -0.1 0.01 0.02 -0.03 0.07
t -0.01 0.09 -0.01 0.08 -0.02
0 -7 3 20 0 0
-1 -2 0 0 0
e 4 2 -1 0 0
f -9 1 0 0 0


(a) anatomical (b) CT


(c) MR PD


(d) MR T1


(e) MR T2 (f) overlap


Figure 7-24. Segmented images before (1st
[Dataset index: VHD #1165.1


row) and after (2nd row) registration.


Table 7-20. Number of pixels in nonoverlap region of segmented images before
and after registration. Upper triangle is before registration and lower
triangle is after registration. [Dataset index: VHD #1165.]


nonoverlap Anatomic CT MR PD MR T1 MR T2
Anatomic 0 8250 8721 7719 9449
CT 2372 0 4173 1915 3853
MR PD 2984 1530 0 4446 3632
MR T1 2980 1234 1118 0 4292
MR T2 3390 1700 1434 800 0









add a grid to the images. A careful examination of the images before and after

registration reveals that the images are indeed better aligned. For a quantita-

tive evaluation of the registration, we coarsely segment these images by basically

segmenting the object from the background in the images. Then we represent

these segmented images as binary images as shown in figures 7-20, 7-22 and 7-24.

(Object is with intensity value 1 and background is with intensity value 0.) We

evaluate the quality of the registration by comparing the number of pixels in the

nonoverlap region of pairwise segmented images before and after registration. From

these results in tables 7-16, 7-18 and 7-20, we see that the number of pixels in the

nonoverlap region of segmented pairwise images after registration is much less prior

to registration. Provided that the segmentation errors are not significant and these

can also be gauged by human perception, we see the images are better aligned after

registration. Also, from the segmented images in figures 7-20, 7-22 and 7-24, we

see that these images are better aligned after registration.

From the affine transformations achieved in the registration as shown in

tables 7-15, 7-17 and 7-19, we see that the affine transformations of all three

images include a certain amount of shear. This serves as a very preliminary

justification for using an affine mapping.

From these evaluation results which are admittedly anecdotal, we see that

minimizing the normalized measure r] and computing high dimensional histograms

works well for the simultaneous (and unbiased) registration of multimodality

images.

7.4.3 Multimodality Image Registration on Synthetic MR Data

In this section, we will conduct an experiment to register 9 multimodality

images, which include 3 MR PD images, 3 MR T2 images and 3 MR T1 images,

simultaneously without bias. We perform this experiment mainly for testing the

ability of the normalized measure r] to work with many multimodality images and
















Figure 7-25. The first row are the images before registration and 2nd row is the
images after registration.


Figure 7-26. Corresponding MR PD images before and after registration.


to test the ability of our multi-dimensional histogram computing technique to

compute a high dimensional histogram. This is not an arbitrary exercise. When

we seek to estimate an atlas from a set of multimodality images, the first step is

to register all images. This experiment is designed for this practical purpose. In

the experiment, we give each image an affine transformation and minimize the

normalized measure Tr defined on 9 images for 9 affine transforms. Despite the

considerable computational expense of this approach, we still use the iterated

sequential search algorithm in section II because we do not want to be affected by

the vagaries of a particular suboptimal search technique. The images before and

after registration are shown in figure 7-25.

For the validation of the registration, we transform the corresponding MR PD

images of MR T2 and MR T1 used in registration with these affine transformations

obtained in the registration shown in figure 7-26. Then we compute the SSDs of

the intensity of pairwise MR PD images before and after registration as shown in

table 7-21. From these results, we see the maximum decreasing rate of the these

SSDs is 94.31 the minimum decreasing rate is 43.5 !'. and the mean decreasing

rate is 67.5;:' ~ Hence these images are got better alignment after registration.









Table 7-21. SSDs of intensity of pairwise MR PD images before and after regis-
tration. upper triangle is before registration and lower triangle is after
registration

SSD before and after Registration
1 2 3 3 5 6 7 8 9
1 0 1519.3 2140.7 2677.4 2820.8 2934 2688.1 3172.9 3566.8
2 482.14 0 812.28 2846.7 2692 2737.9 3156.7 2684.6 2866
3 923.06 411.65 0 2932.8 2747.3 2680.5 3540.4 2842.7 2732.7
4 316.93 413.95 878.21 0 885.33 1259.1 4329.4 4439.1 4517
5 160.56 503.67 917.61 291.24 0 609.84 4445.3 4322.6 4329.2
6 258.91 534.18 1007.6 506.27 344.33 0 4515.2 4338 4259.1
7 '-1 522.9 496.31 1004.6 1033.1 949.24 0 2370.4 3275.8
8 937.78 448.48 364.34 948.83 976.48 933.76 205.73 0 1279.4
9 900.75 451.6 228.26 906.27 890.14 982.63 544.96 414.66 0


7.5 Experimental Results on the Nonrigid Multimodality Image
Registration Using the Information Metric and High Dimensional
Histogramming

7.5.1 Validity of Multiresolution Optimization Algorithms over B-
Spline

In this section, we test the validity of the Multiresolution Optimization

Algorithm 1 for intermodality registration and Algorithm 2 for multimodality

registration. For intermodality image registration, we use Brainweb synthetic 3D

MR data and for multimodality image registration, we use Visible Human Data

including 2D anatomical photo, CT and MR data.

7.5.1.1 Validity of intermodality registration with synthetic PD and T2
3D MR images

We use synthetic 3D MR PD and T2 image in this experiment. The image size

55 x 65 x 55 and the pixel size is 1mm. The intensity of all images are normalized

in the range [0 1]. At the beginning, two images are registered and we use artificial

displacement field u to deform T2 image. We register the deformed T2 to PD

images. In intermodality registration, we find the displacement field Uinter, which

registers the deformed T2 image to PD image by minimizing energy function (6-7)

and using Algorithm 1. The resolutions used in Algorithm 1 are 16mm and 8mm.









Table 7-22. DDF, ADF and SSD of intermodality registration of synthetic 3D MR
PD and T2 images before and after registration.

image MR T2
Measure of Error DDF(mm) ADF(degree) SSD
Before Registration 2.91 10004
Intermodality Registration 0.92 13.9 949


In order to validate the registration result from intermodality registration, we

use three error measure: difference of displacement field (DDF), angle between

displacement fields (ADF) and sum of square difference of intensity (SSD). 1

The DDF before registration is the mean of 2-norm of u and the DDF of

intermodality registration is the mean of 2-norm of the difference between the

inverse of Uinter and u. The ADF of intermodality registration is the mean of

angles between the inverse of Uinter and u. SSD before registration is the intensity

difference between the original undeformed MR T2 image and the deformed MR

T2 image and the SSD of intermodality registration is the intensity difference

between the registered MR T2 image with Uinter and the original undeformed MR

T2 image.

In table 7-22, we show DDF and SSD before registration and after intermodal-

ity registration. We can see DDF and SSD after intermodality registration are

much less than those before registration. And a careful examination of the images

before (figure 7-27) and after registration (figure 7-28) reveals that the images

are indeed better aligned. Hence the multiresolution optimization algorithm for

nonrigid intermodality image registration or Algorithm 1 is valid.



1 In general case, let u be original displacement fields, u be recovered displace-
ment fields and v be the inverse of u, then
DDF j- E,. jv, u.11 and ADF E' Y ** S, Let I be original im-
2
age and I be recovered image, then SSD I,- Il; where N is the number
of image pixels and x represents a pixel in the image.

















(a) MR PD slices (b) MR T2 slices before registration
Figure 7-27. Some slices of 3D MR PD and T2 images before registration.











(c) deformed grid using displacement field (d) MR T2 slices after registration
Figure 7-28. Some slices of 3D MR PD and T2 images after registration.


AA
AAAAAAA
AA99999
Adaaaaa
AAAAAAA
AAAAAAA
























Figure 7-29. Anatomical photo and overlap of 3 images before and after registra-
tion.


7.5.1.2 Validity of multimodality registration with Visible Human Data
including 2D anatomical photo, CT and MRPD

In this experiment, we use a 2D slice of Visible Human data (Dataset index:

VHD #1080), which includes Anatomical Photo, CT and MRPD image. The image

size is 256 x 256. The pixel size is 0.32mm square for a photograph of anatomical

slice and 1mm for MR and CT images. The intensity of all images are normalized

to range [0 1]. At the beginning, 3 images are not registered hence ground truth is

unknown. Then we use artificial displacement field u(1) to deform CT image and

use u(2)to deform PD image. We will register the deformed CT and deformed MR

PD images to the anatomical image. In multimodality registration, we find the

displacement field umulti(1), which register the deformed CT image to anatomical

image, and umulti(2), which register the deformed PD image to anatomical image,

by minimizing energy function (6-1) and Algorithm 2. The resolutions used in

Algorithm 2 are 32mm, 24mm and 16mm.

(a) in figure 7-29 is the anatomical photo, which is target in registration. (d)

in figure 7-30 and (g) in figure 7-31 are CT and MR PD images, which are the

source images in the registration. (b) in figure 7-29 is the overlap of anatomical