PeterHastreiter,ThomasErtl
ComputerGraphicsGroup,UniversityofErlangen–Nuremberg
AmWeichselgarten9,91058Erlangen,Germanyhastreiter,ertl@informatik.uni-erlangen.de
Abstract
Differentimagingmodalitiesgiveinsighttovascular,anatomicalandfunctionalinformationwhichassistdiag-nosisandtherapyplanninginmedicine.Registrationandconsecutivevisualizationallowtocombinetheimagedataandtherebyconveymoremeaningfulimagestotheclini-cian.Applyingavoxelbasedapproachbasedonmutualinformation,accurateandretrospectiveregistrationispro-vided.However,optimizationandconsecutivevisualizationproceduresrequireahugeamountoftrilinearinterpolationoperationstore–samplethedata.Ensuringfastperfor-mancewhichisfundamentalformedicalroutine,wesug-gestanintegratedapproachwhichtakesadvantageoftheimagingandtexturemappingsubsystemofgraphicscom-puters.Alltrilinearinterpolationiscompletelyperformedwithhardwareassisted3Dtexturemapping.The1Dand2Dhistogramsofthedatasetswhicharenecessaryforthecalculationofmutualinformationareobtainedwithdiffer-enthardwareacceleratedimagingoperations.Forthesi-multaneousandinteractivevisualizationoftheregistereddatasetsanewapproachwasdevelopedwhichallowsforversatilefusionoperations.Usingsimilarproceduressup-portedbyhardware,contributesconsiderablytoaccelerateregistrationandvisualization.Implementingourapproachwithinapreviouslypresentedframework[7,16]basedonOpenInventorandOpenGLprovidesintuitivemanipulation.Clinicalexamplesofshowthevalueofourapproachinpractice.
1.Introduction
Avarietyofimagingmodalitiesgiveinsighttodiffer-entparametersandinformationincurrentmedicalpractice[13].Thereisconventionalradiographywhichisoneofthemostwidelyspreadandestablishedmodalities.How-ever,itonlyprovidestwo–dimensional(2D)projectionim-ageswithlimiteddepthinformation.Morerecently,othertechniquesgainedmoreattentionsincetheyprovidethree–
dimensional(3D)informationwithagreatdiversityofstructural,anatomicalandfunctionaldetailsallowingmorecomprehensiveexaminations.Asacommonfeatureallthesemodalitiesproducestacksofequidistantandspatiallyassignablesliceimagesformingavolumedatasetwiththesamplepointstypicallyarrangedonauniformgrid.Us-ingCT(X–rayComputedTomography)the3DdistributionofX–raydensitiesiscalculatedbyreconstructingtheX–raytransmissionmeasurementsfrommanyanglesofview.Completelydifferentimageswithawidevarietyofcharac-teristicsareobtainedwithMRI(MagneticResonanceImag-ing)givingexcellentvisualizationofsofttissuewithhighlydetailedstructuralinformation.Usingalocallyvariablestaticmagneticfieldandlong-waveradiofrequenciesres-onanceabsorptionofmagneticnucleiinbiologicaltissueismeasuredinordertocalculatethespatialdistributionofthenuclearmagnetization.Developmentsreducingmeasure-menttimesandinvestigatingthepotentialofflow(MRA:MagneticResonanceAngiography)andfunctionalimaging(fMR:functionalMagneticResonance)willfurtherincreasetheimportanceofMRIinfuture.Finally,withmodali-tiesofnuclearmedicinesuchasPET(PositronEmissionTomography)andSPECT(SinglePhotonEmissionCom-putedTomography)thedistributionofradio-isotopesinspe-cificorgansorstructuresismeasuredgivinginformationonmetabolismandfunctionality.
Inmostcasesduringdiagnosisandtherapyplanningto-mographicsliceimagesareinspectedseparately.Ifthespa-tialrelationshipofobjectsisrequiredthedifficulttaskofre-constructingsuccessivesliceimagesmentallycanbeeffec-tivelyassistedby3Dvisualizationtechniques.Theyevenallowforafullunderstandingofdifficultsituationswithcomplextopology[6,8].However,3Dvisualizationtech-niquesareonlyapplicableinclinicalroutineiftheyprovidethenecessaryeaseofinterpretation.Therefore,anychangeofvisualizationparametersmustbeachievedinteractivelyandintuitively[24],anddetailinformationwithinthesliceandaglobaloverviewmustbeaccessibleinacombinedimagerepresentation[7].Inadditiontothat,dependingontheclinicalrequirements,itisoftennotsufficienttocon-
sidervascular,anatomicalandfunctionalinformationsep-aratelybuttosuperimposeimagesofdifferentmodalities.Thisproceduretypicallyrequiresahugeamountofinterpo-lationsandothercalculationsforeveryiterationinordertooptimizetheappliedmeasure.Inclinicalroutinesuchalign-mentproceduresareonlyacceptediftheirprocessingtimeisreducedappropriately.Duetothecloserelationshipofvisualizationandregistrationandthesimilarityofcompu-tationalrequirementsanintegratedapproachwhichmakesextensiveuseofcommonlyavailablespecialpurposegraph-icshardwarewasalogicalconsequence.
Afterashortsurveyofdifferentapproachesforregis-tration,werefertosomeofourpreviouslypublishedworkinsection2anddescribemutualinformationasageneralmeasurewhichleadstoaccurateregistrationresults.Thebasicideaofourapproachisthendescribedinsection3.Itdemonstrateshowtoapplyhardwaresupportedimagingand3Dtexturemappingfunctionalitytovoxelbasedregis-trationusingmutualinformation.Thereby,weillustratethatthetimerequiredtocalculate1Dand2Dhistogramsandtheenormousamountoftrilinearinterpolationoperationsduringanoptimizationprocedureisdramaticallyreduced.Subsequently,wepresentanewmethodallowingforthesi-multaneousandinteractivevisualizationoftworegistereddatasetsbasedon3Dtexturemapping.Finally,usingclini-callyrelevantimagedatasomeofourresultsarepresentedwhichshowthevalueofourapproach.
2.RegistrationApproach
AscanbeseeninFigure1registrationinthemedicalfieldtypicallytriestofindatransformationoftwodifferentdatasetswhichcandifferinthenumberandsizeofvoxelsineverydirection,thepositionandorientationofthescannedobjects,theorientationofthetomographicsliceimages(sagittal,coronal,axial)andscannerdependentdistortions.Inordertofindtheirexactgeometricalrelationshiponedatasetiskeptfixedasreferencewhereastheotherdatasetisdefinedasfloatingimageandmovedduringaniterativealignmentprocedure.Therefore,dependingontheappliedregistrationtechniqueaspecificmeasureisoptimizedwhichtriestomaximizethesimilarityofcorrespondingstructures.Thistypicallyrequirestointerpolatethefloatingdatasetatgridpositionsofthereferencedatasetforeveryiterationde-pendingonthecurrenttransformationwhichfinallyresultsinbothdatasetshavingthesamenumberandsizeofvoxelsifaregistrationsolutionwasfound.Theymaythenbere-gardedasasinglecombineddatasetwithtwoattributesateachgridpositionwhichallowseasyapplicationofvariousfusionprocedures.
2.1.Overview
Registrationalgorithmsinthefieldofmedicalimagingaredividedintotwomaingroups[2,12,20].Thereareapproachesbasedonexternal,fiducialmarkerswhichareclassifiedprospectivesinceregistrationisonlyfeasibleifmarkersareattachedpriortoscanningthepatient.Theseapproachesgenerallyallowveryhighregistrationaccuracywithlandmarkswhicharegenerallyeasytodetectinal-mosteverymodality.However,theyareusuallyinvasiveandthereforeveryinconvenientforthepatientifastereo-tacticframeisusedwhichistightlyfixedtothepatientshead.
RegistrationFusiondata−set 1data−set 3data−set 2Interpolationdata−set 3Figure1.Typicalalignmentprocedureinclud-ingre–slicingandfusionafterfindingtheregistrationsolution.
Theothermaingroupcomprisesapproacheswhicharebasedoninternal,anatomicallandmarks.Theyarenamedretrospectivesinceregistrationisfeasibleatanytimeafterscanningthepatientwithoutattachinganymarkers.Overthelastdecadetherewereextensiveeffortstodevelopap-proacheswhichtrytoachievealignmentafterdelineat-ingcorrespondinganatomicalpointlandmarks,structures(lines,surfaces),momentsorgrayvalueinformation.Sincetheavailablemethodsdonotrequireanyspecialprepara-tionofthepatienttheyaremuchmoreconvenient.How-ever,proceduresbasedonanatomicallandmarksareverylaborintensivewiththeiraccuracydependingontheabilityoftheusertoexactlyidentifycorrespondingpointsindiffer-entmodalities.Ifautomaticproceduresareappliedinapre–processingstep,theoverallregistrationaccuracyisalwayslimitedbytheaccuracyofthesegmentation.Fortheregis-trationofMRandCTtypicallyboneistakenasreferencewhichiscomparablyeasilydetectedinCT.However,thisisaverychallengingtaskforMRsinceonlythesurroundingtissueisvisualized.IffunctionaldataisconsideredsuchasPET,itisalmostimpossibletosegmentspecificstructuresduetoitsnoisynature.
Avoidingtheseriousproblemsencounteredwithexplicitsegmentationofcorrespondingfeatures,voxelbasedap-proachesgainedmoreattentionjustrecently.Takinginto
accounttheentiregrayvalueinformationatgeometricallycorrespondinggridpositionstheytrytooptimizethesimi-larityofthefloatingandthereferenceimage.Asageneralfeatureoftheseapproachesthesegmentationisimplicitlyperformedbythefunctionalwhichevaluatesthequalityofalignmentandtherebycontrolstheoptimizationprocedure.Varioussimilaritymeasureslikecorrelationinscalespace[19],conditionalentropy[23]orjointentropy[10,4,17,18]wereinvestigatedextensively.However,allofthemwereeitherrestrictedtoaspecificcombinationofmodalitiesorencounteredmajordifficultieswithpartiallyoverlappingdatasets.Havingproposedmutualinformationamuchmoregeneralandreliablemeasurewasalmostsimultaneouslyin-troducedbyCollignon[5]andViola[21,22]whichprovedtoprovideveryrobustandversatileregistration.
2.2.Method
Originallydefinedininformationtheorymutualinfor-mationdescribesthestatisticaldependenceoftworandom
variablesortheamountofinformationthatonevariable
containsabouttheother.Withadataset(floatingim-age)consistingofdifferentsignalsandadataset(referenceimage)consistingofdifferentsig-nalsthereareandassociated.Applyingthemarginalthecurrentprob-abilitydistributionstransformationthegrayvaluesofthefloatingimageareevaluatedatgridpositionsofthereferenceimagebytrilinearinterpolationforeveryiterationoftheoptimiza-tionprocedure.Thisresultsinthejointprobabilitydistri-butionwhichisidenticalwiththe2Dhistogramofbothdatasets.Forreasonsofconveniencewe
furtherreferto
andasand.Figure2.Dispersionofclusterinthe2D-histogramforCTandMRfortheunregistered
(left)andregistered(right)case.
Consideringthe2Dhistogramtheregistrationsolutionisreachedifthedispersionofsignificantclustersisminimizedwhichcoincideswithmutualinformationreachingamaxi-mum.AscanbeseeninFigure2theregistrationofMRandCTresultsinadominantclusterforthetissueinformation.ThiscomprisesallgrayvaluesinMRandaspecificrange
ofgrayvaluesinCT.InthesamewayhighgrayvaluesinCT(bone)coincidewithlowgrayvaluesinMR(bonenotvisible).
Source
Channel
Drain
ImageH(F|R)FI(R,F)ImageRH(F)H(R|F)H(R)Probability DensityJoint Probability
DensityProbability DensitypF(f)
pRF(r(x), f(T(x)))
pR(r)
Figure3.TheSource–Channel–Drainmodeloftheregistrationapproach.
Incasethereisanexactmappingbetweenthefloatingimageandthereferenceimage(i.e.thesignalsareidentical)thejointprobabilitydistributionsatisfies
(1)
Ifthetwosignalsarestatisticallyindependent,however,the
jointprobabilitydistributionresultsto
(2)
Mutualinformationof
and
isthendefinedbysumming
forallgreyvaluepairs
atcorrespondingpositions
solutionisobtainedifmutualinformationreachesamaximumforagivensetoftransformationparameters:
(5)
Foramoredetailedoverviewconcerningthecalculationoftheentropiesinrelationtotheregistrationoftwoclin-icallyrelevantmedicaldatasetsrefertopreviousexplana-tionsfoundin[11,9].
3.HardwareAcceleration
3.1.Registration
Inordertofindtheregistrationsolutionalocallyorglob-allyoptimizingproceduremustbeappliedwhichtriestovaryalltransformationparametersiteratively.Sincethisre-quirestheevaluationofmutualinformationforeveryiter-ationstepthemarginalandjointprobabilitydensities(e.g.the1Dandthe2Dhistograms)ofbothdatasetsmustbere-calculatedforeverychangeoftheregistrationparameters.Duetothetypicalsizeofmedicaldatasetswhichliesinarangeupto100Mbytesahugenumberofinterpolationsisrequiredforre–samplingthefloatingdataset.Sincethisisthemostimportanttimefactorcontributingtotheoverallprocessingtimeitmainlydecidesonwhetheraregistrationprocedureisconsideredforaroutineapplicationsupposedtheaccuracyissufficient.
Inordertoovercomethisproblemsomesoftwarebasedapproacheswereproposed.AccordingtothesuggestionofViola[22],astochasticapproximationoftheentropiesandanoptimizationprocedureusingthegradientofmutualin-formationisapplied.Takingonlyaverylimitednumberofsamplesforeveryiterationthenumberofinterpolationsisreducedconsiderably.Recently,Pokrandt[14]reportedgoodresultsusinganothertechniqueofselectingfewsam-plepointsrandomlywhichachievedcomparableresults.Contrarytosoftwarebasedapproachesweproposetousecommonlyavailablegraphicshardware.Takingad-vantageoftheimagingandtexturemappingsubsystemofgraphicscomputersthealignmentprocedureisacceleratedtremendously.Duetotheapplicationofidenticalalgorith-micmethodsregistrationiscloselyrelatedtovisualization.Withtheavailabilityofhardwareassisted3Dtexturemap-pingatechniqueproposedbyCabral[3]becameapowerfuloptionfordirectvolumerendering.Usingtheinterpola-tionandblendingcapabilitiesofhardwareassistedtexturemappinginteractiveframeratesareachieved(seeFigure4).Afterloadingadatasetto3Dtexturememoryequidis-tantplanesparalleltotheviewportareclippedagainsttheboundingboxofthevolumedataset.Volumerenderingisthenperformedbyblendingtheresultingandtexturedpoly-gonsback-to-frontwithanappropriateblendingfunction.
3D−TexturePlanes Parallelto ViewportRenderedImageInterpolationTrilinear Compositing(Blending)Figure4.Directvolumerenderingusingtheinterpolationandblendingcapabilitiesofgraphicshardware.
Correspondingtothevisualizationprocessourregistrationapproachusestheimagingandtexturemappingsubsysteminordertore–slicethevolumedataandtocalculatethehistograms(seeFigure5):
1.Afterconvertingthefloatingdatasettoan8bitrepre-sentationitisloadedto3Dtexturememory.Varioustestsshowedthatthisissufficientfortheregistrationprocedureandkeepsthehistogramssmall.Contrarytothatafterconversiontoan8bitrepresentationthereferenceimageisadditionallyshiftedby8bitstotheleft.2.Inaloopoverallsliceimagesofthereferencedataseteverysliceistransferredtoapbufferwhichisanaux-iliaryrenderingbuffer.ProvidedbythepixelbufferextensionofOpenGLitallocatesnon-visibleframebuffermemoryforhardwareacceleratedrendering.3.Thecurrentregistrationtransformationisthenappliedtotheplaneverticesofthereferencedatasetinordertoobtainitslocationrelativetothecoordinatesystemofthefloatingdataset.Thecorrespondingtexturecoor-dinatesarethenobtainedbyclippingtheplaneagainsttheboundingboxofthefloatingdataset.Sincethisrequiresthesamestrategyasinvolumerenderingtheidenticalprocedureisapplied.4.Priortoblendingthegrayvaluesoftherectangulartex-tureareaontothepbufferitsup-vectormustbecor-rected(seeFigure6).Thisensuresthattheorientationofboththesliceimageofthereferenceimageandthecorrespondingsliceofthefloatingimagecoincide.Asaresultthepbuffernowcontainsanimagewhichcon-tainsthefloatingimageinthelower8bitsandtheref-erenceimageintheupper8bitsofa16bitdatarepre-sentation.
5.Theauxiliarypixelbuffersallowforvariouscolorbufferoperationsorimageprocessingalgorithms.Readingthepbuffercontentsafterblendingasliceim-ageofthereferencedatasetanditscorrespondingtex-tureofthefloatingdatasettheextensionforcalculating1Dhistogramsisenabled.Duetotheinitialconversionandshiftoperationsthereturnedarraycontainsthe2Dhistogramofbothdatasets.Additionally,thecalcula-tionofmutualinformationaccordingtoequation(3)requiresthe1Dhistogramsofthedatasets.Sincetheyarethemarginaldistributionsofthe2Dhistogramtheirentriesarecalculatedbykeepingtherespectivegrayvaluesoftherespectivedatasetconstantandsummingforallentriesinthe2Dhistogramoftheotherdataset.
Reference Image
in Main Memory
in 3D Texture MemoryFloating Image
v1v2Registrationt1t2v4v3t4t3vertex coordinatesPolygon withv1, v2, v3, v4texture coordiantesCut plane witht1, t2, t3, t4BlendingreferenceImaging Extension
OpenGL
image1D and 2D histogramsPixel−Buffer
Auxiliary floating+078
15
imagefloatingimage
referenceimage
Figure5.Surveyoftheregistrationapproachusinghardwareassistedimagingandtexturemappingoperations.
3.2.VisualizationofRegisteredVolumes
Oncetheregistrationprocedurefinishedsuccessfullythefloatingimageisfinallyre–slicedaccordingtothereferenceimage.Sincethisresultsinacombineddatasetwithtwoat-tributesateachgridpositionsimultaneousvisualizationisenvisaged.Inordertointegrateregistrationandvisualiza-tionanapproachwasdevelopedwhichallowstorendertworegistereddatasetsusinghardwareaccelerated3Dtexturemapping.
Inthebeginning,bothdatasetsareloadedto3Dtexturememorysimultaneouslyinordertoensureinteractiveframerates.Similartothecaseofconsideringonlyonedataset,aspresentedinsection3.1,planesparalleltotheviewportare
t1Transformation of up−vectort2t2t1t4t4t3t3Texture planeof floating image
PBufferReferenceSlice ofupBlendingImage
vectorCopyreferenceimage+texture offloating imageFigure6.Correctionofup–vectortogetiden-ticalorientationofthereferenceandthefloat-ingimage.
clippedagainstthesharedboundingbox.Eachresultingpolygonisthenappropriatelytexturedwithbothregistereddatasetsbybindingthemalternately.Compositingisfinallyperformedbyblendingalltexturedpolygonsback-to-front.Ifthesizeoftheregistereddatasetstogetherexceedsthesizeoftheavailabletexturememory,sub-volumescalledbricksarecreated.Inordertoloadcorrespondingbricksofbothdatasetsto3Dtexturememoryeverypairofbricksisassignedapriority.Thiscausesonlythosetostayintexturememorywhichareusedforthecutplanecurrentlyclippedagainsttheboundingbox.
Inordertoallowformorecomplexfunctionsforfus-ingthedatasetsafterregistration,correspondingcutplanesaremergedinaseparatepbufferpriortothefinalrender-ing.Thisisaveryusefulfeatureincaseofangiographicorfunctionaldatainrelationtosofttissueinformation.
4.Results
Theapproachofintegratedregistrationandvisualizationisimplementedinaframeworkalreadypublishedprevi-ously[7,16].DuetothefullintegrationintotheOpen-InventorclasshierarchyandtheextensiveuseofOpenGLavarietyoffunctionalityisavailable.Thiscomprisessepa-rateclippingplanesandindividualcolorlook-uptablesforbothdatasets.Additionally,ifsegmentationwasperformedinapre–processingstepthedatasetscanbeloadedastaggedvolumes.Thisallowsforseparatecolorlook-uptablesforeverytag.
AllourtestswereperformedonanIndigoMaximumImpactandaSGIOnyxRealityEngineIIwhichprovide4Mbytesand16Mbytesof3Dtexturememoryrespectively.Concerningthetrilinearinterpolationstheunderlyinghard-wareofbothworkstationshasthesameorderofmagnitude.Fortheevaluationofourapproachweusedfourdifferentmulti-modalcombinationsofdatasetswhichwereroutinely
,,usedinclinicalpractice(
,).Asanexampledemon-stratingtheresultsweachievedwithourapproachFigure8
andafterapplyingourshowsthefusionof
registrationproceduretotheinitialsituationdemonstratedproblems.Comparedtotypicalsoftwarebasedimplementa-tionsofray–castingalgorithmslikeVolVis[1],ourhardwarebasedapproachisalreadyconsiderablyfaster.
Providingveryfastregistrationandsuccessiveinterac-tivevisualizationwithOpenInventorbasedintuitivemanip-ulationourapproachprovidesagoodfoundationforfurtherclinicalevaluation.
inFigure7.Inordertoallowforthenavigationwithintheregistereddatasetsindividualclipplaneswereapplied.An-otherexamplepresentedinFigures9–12showsthefusion
of
and.Itillustratesthediversityofopera-tionswhichareapplicableafterregistration.Bothdatasetsweresegmentedinapre–processingstepandloadedastaggedvolumes.Individualcolorlook-uptablesforevery
tagofthe
dataallowforagoodvisualizationofthebrainandtheventricles.Pre–segmentationofthebrainin
allowstosuppresstheskinandgivesgoodoverviewoftheintracranialvesselsituationinrelationtothetissue
visiblein
.Fortheregistrationprocedurearigidtransformation(3rotationand3translationparameters)wasappliedexclu-sively.Thisrestrictstheapproachtoheaddatasetsorotherimagedatawithoutdeformationsordistortions.InordertocalculatethealignmentwithmutualinformationPowell’salgorithm[15]isappliedasaprocedureforlocaloptimiza-tion.
Comparingourhardwareorientatedapproachtotheper-formanceofpuresoftwarebasedimplementations,weareafactorof2–3fastercomparedtothesuggestionofCollignon[5].Iftheapproachbasedonstochasticapproximationofentropies,asproposedbyViola[22]isusedforcompari-son,ourapproachachievessimilarexecutiontimes.Thisresultsmainlyfromthefactthatthestochasticapproxima-tiononlyusesasmallamountofsamplepointsforeveryiterationwhereaswritingtoandreadingfromthepbufferre-quiressomeadditionalprocessing.Therefore,ourapproachisslightlydependentonthenumberofsliceimageswithinthereferencedataset.However,accordingtoourevaluationweseemtohavehigheraccuracyandfasterconvergenceduetoapplyingtheentiregrayvalueinformation.
Lookingattheconsecutivevisualizationoftworegis-tereddatasetsourapproachachievesinteractiveframeratesduetotheinterpolationcapabilitiesofthe3Dtexturemap-pinghardware.Incaseofpre–segmenteddatasetstaggedvolumescanbeloadedwhichleadstofurtherflexibilitysincesegmentedobjectsaredifferentiatedwithseparatecolorlook-uptables.Additionally,itismoreeffectivecon-cerningmemoryrequirementsifonlyonedatasetisusedforseveralsegmentedobjetcs.Inordertoprovidethefullfunctionalityonallplatformsequippedwiththerespectiveimagingand3Dtexturemappinghardware,furthertun-ingiscurrrentlyperformedduetoimplementationspecific
Figure7.FusionofMR(T1)andCTbeforereg-istration.
Figure8.FusionofMR(T1)andCTafterreg-istration.
5.Conclusion
Wepresentedanintegratedapproachforfastregistra-tionbasedonmutualinformationandconsecutiveinterac-tiveandintuitivevisualizationofmedicaldatasets.Foratremendousaccelerationofallcalculationssimilarmethods
wereappliedmakinguseofspecialpurposehardwareavail-ableindesktopgraphicsworkstations.Inthiswayprocess-ingtimeforthehugenumberoftrilinearinterpolationsisnegligible.Acomparisonwithsoftwarebasedregistrationproceduresshowsthatourhardwareacceleratedapproachachievesprocessingtimessimilartothoseobtainedwithstochasticapproximationofentropies.DuetovisualizationatinteractiveframeratesandthefullintegrationintoOpen-Inventorcontrolofvisualizationparametersandevaluationofregistrationresultsisveryintuitive.Clinicalexamplesshowthevalueofourapproachinpractice.Theplanningofinterventionalproceduresisimprovedbythefusionofangiographicandanatomicinformation.Goodlocalizationofcentersofactivityisprovidedbycombiningfunctionalinformationandanatomicstructures.
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Figure9.VisualizationofMR(T1)andMRAafterregistration. Figure11.VentriclesofMR(T1)relativetovesselofMRAFigure10.TissueofMR(T1)relativetoves-selsofMRAaftersuppressionofskin.
Figure12.VesselsofMRArelativetoventri-clesofMR(T1)
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