Automatic Construction of 3-D Statistical

1014IEEETRANSACTIONSONMEDICALIMAGING,VOL.22,NO.8,AUGUST2003

AutomaticConstructionof3-DStatistical

DeformationModelsoftheBrainUsingNonrigidRegistration

DanielRueckert*,AlejandroF.Frangi,AssociateMember,IEEE,andJuliaA.Schnabel

anatomicalandfunctionalvariationsofindividualsubjects,italsooffersapowerfulframeworktofacilitatethecomparisonofanatomyandfunctionovertime,betweensubjects,betweengroupsofsubjectsandacrosssites.Consequently,anumberofdifferentelastic[1]–[3]andfluid[4],[5]warpingtechniqueshavebeendevelopedforthispurpose.Recentreviewsofdifferentnonrigidregistrationtechniquescanbefoundin[6]and[7].Traditionalmedicalatlasescontaininformationaboutanatomyandfunctionfromasingleindividualfocusingprimarilyonthehumanbrain[8].Eventhoughtheindividualsselectedfortheseatlasesmaybeconsiderednormal,theymayrepresentanextremumofanormaldistribution.Toaddressthisproblem,researchershavedevelopedvariousprobabilisticandstatisticalapproacheswhichincludeinformationfromagroupofsubjects,makingthemmorerepresentativeofthepopulationunderinvestigation[9]–[12].A.StatisticalShapeModels

Statisticalmodelsofshapevariabilityhavebeensuccessfullyappliedtoperformvariousimageanalysistasksintwo-dimen-sional(2-D)andthree-dimensional(3-D)images.Inparticular,theirapplicationforimagesegmentationinthecontextofactiveshapemodels(ASMs)hasbeenverysuccessful[13].Inbuildingthosestatisticalmodels,asetofsegmentationsoftheshapeofinterestisrequiredaswellasasetoflandmarksthatcanbeunambiguouslydefinedineachsampleshape.AnextensionofASMsaretheso-calledactiveappearancemodels(AAMs)[14]whichhavebeenusedforatlasmatching.AAMsincorporatenotonlyinformationaboutthespatialdistributionoflandmarksandtheintensityinformationatthelandmarks,butalsoabouttheirunderlyingtexturedistribution.Anumberofauthorshaveusedstatisticalmodelsofshapeinformationaspriorsforsegmenta-tionviadeformablemodels[15]–[17],deformableregistration[18]orshapeanalysis[19].However,afundamentalproblemwhenbuildingthesemodelsisthefactthattheyrequirethedeterminationofpointcorrespondencesbetweenthedifferentshapes.Themanualidentificationofsuchcorrespondencesisatimeconsumingandtedioustask.Thisisparticularlytruein3-Dwheretheamountoflandmarksrequiredtodescribetheshapeaccuratelyincreasesdramaticallycomparedto2-Dapplications.Asimplebutefficientwayofestablishingcorrespondencesfortheconstructionofstatisticalshapemodelsistheuseofdis-tancetransformationswhichhasbeenproposedbyanumberofauthors[16],[20],[21]:Forexample,Leventonetal.[16]pro-posedanapproachinwhichthestatisticalanalysisiscarriedoutdirectlyonthesigneddistancemapsofasetofalignedshapes.

Abstract—Inthispaper,weshowhowtheconceptofstatisticaldeformationmodels(SDMs)canbeusedfortheconstructionofaveragemodelsoftheanatomyandtheirvariability.SDMsarebuiltbyperformingastatisticalanalysisofthedeformationsre-quiredtomapanatomicalfeaturesinonesubjectintothecorre-spondingfeaturesinanothersubject.TheconceptofSDMsissim-ilartostatisticalshapemodels(SSMs)whichcapturestatisticalin-formationaboutshapesacrossapopulation,butoffersseveralad-vantagesoverSSMs.First,SDMscanbeconstructeddirectlyfromimagessuchasthree-dimensional(3-D)magneticresonance(MR)orcomputertomograohyvolumeswithouttheneedforsegmenta-tionwhichisusuallyaprerequisitefortheconstructionofSSMs.Instead,anonrigidregistrationalgorithmbasedonfree-formde-formationsandnormalizedmutualinformationisusedtocomputethedeformationsrequiredtoestablishdensecorrespondencesbe-tweenthereferencesubjectandthesubjectsinthepopulationclassunderinvestigation.Second,SDMsallowtheconstructionofanatlasoftheaverageanatomyaswellasitsvariabilityacrossapop-ulationofsubjects.Finally,SDMstakethe3-Dnatureoftheun-derlyinganatomyintoaccountbyanalysingdense3-Ddeforma-tionfieldsratherthanonlyinformationaboutthesurfaceshapeofanatomicalstructures.WeshowresultsfortheconstructionofanatomicalmodelsofthebrainfromtheMRimagesof25differentsubjects.Thecorrespondencesobtainedbythenonrigidregistra-tionareevaluatedusinganatomicallandmarklocationsandshowanaverageerrorof1.40mmattheseanatomicallandmarkposi-tions.WealsodemonstratethatSDMscanbeconstructedsoastominimizethebiastowardthechosenreferencesubject.

IndexTerms—Free-formdeformation,imageregistration,mor-phometry,shapeanalysis.

I.INTRODUCTION

HEsignificantintersubjectvariabilityofanatomyandfunctionmakestheinterpretationofmedicalimagesaverychallengingtask.Atlas-basedapproachesaddressthisproblembydefiningacommonreferencespace.Mappingdatasetsintothiscommonreferencespacenotonlyaccountsfor

ManuscriptreceivedSeptember19,2002;revisedMarch27,2002.TheworkofD.RueckertwassupportedinpartbyEPSRCunderGrantGR/N/24919.TheworkofA.F.FrangiwassupportedinpartundertheRamónyCajalResearchFellowshipandtheMCYTProjectunderGrantTIC2002-04495-C02.TheworkofJ.A.SchnabelwassupportedbyPhilipsMedicalSystemsEV-AD.TheAs-sociateEditorresponsibleforcoordinatingthereviewofthispaperandrecom-mendingitspublicationwasR.Leahy.Asteriskindicatescorrespondingauthor.*D.RueckertiswiththeVisualInformationProcessingGroup,Depart-mentofComputing,ImperialCollege,LondonSW72AZ,U.K.(e-mail:dr@doc.ic.ac.uk).

A.F.FrangiiswiththeComputerVisionLaboratory,,AragonInstituteofEngineeringResearch,UniversityofZaragoza,ZaragozaE-50018,Spain.J.A.SchnabeliswiththeComputationalImagingScienceGroup,Guy’sHos-pital,King’sCollege,LondonSE19RT,U.K.

DigitalObjectIdentifier10.1109/TMI.2003.815865

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0278-0062/03$17.00©2003IEEE

RUECKERTetal.:AUTOMATICCONSTRUCTIONOF3-DSDMsThisapproacheffectivelyassumesthatthecorrespondingpointsoftwoshapesaretheclosestpoints.Thestatisticalshapein-formationisthenusedaspriorinformationtoguidealevel-setsegmentationapproach.Gollandetal.[20]haveshownthattheresultingstatisticalmodelcanbeusedfortheclassificationofshapesfromdifferentpopulations.Anothersolutiontothepointcorrespondenceproblemistoconstructcorrespondencesim-plicitlyviatheshapeparameterization,i.e.,byusingsphericalharmonics[15].Otherapproachesincludetheuseofgeodesicdistanceandsurfacecurvaturetoes …… 此处隐藏：22746字，全部文档内容请下载后查看。喜欢就下载吧 ……