Probe Trajectory Interpolation for 3D Reconstructi

ProbeTrajectoryInterpolationfor3DReconstructionofFreehandUltrasoundPierrickCoupea;b;d;,PierreHelliera;b;dXavierMorandia;b;d;cChristianBarillota;b;daUniversityofRennesI,CNRS,IRISA-UMR6074,CampusdeBeaulieu,F-35042Rennes,FrancebINRIA,VisAGeSU746Unit/Project,IRISA,CampusdeBeaulieu,F-35042Rennes,FrancecUniversityHospitalofRennes,DepartmentofNeurosurgery,rueH.LeGuillou,F-35043Rennes,FrancedINSERM,VisAGeSU746Unit/Project,IRISA,CampusdeBeaulieu,F-35042Rennes,FranceAbstractThree-dimensional(3D)FreehandultrasoundusestheacquisitionofnonparallelB-scanslocalizedin3Dbyatrackingsystem(optic,mechanicalormagnetic).UsingthepositionsoftheirregularlyspacedB-scans,aregular3Dlatticevolumecanbereconstructed,towhichconventional3Dcomputervisionalgorithms(registrationandsegmentation)canbeapplied.Thispaperpresentsanew3Dreconstructionmethodwhichexplicitlyaccountsfortheprobetrajectory.Experimentswerecon-ductedonphantomandintra-operativedatasetsusingvariousprobemotiontypesandvariedslice-to-sliceB-scandistances.Resultssuggestthatthistechniqueim-provesonclassicalmethodsattheexpenseofcomputationaltime.1IntroductionUltrasonographyhasbecomeaverypopularmedicalimagingmodalitythankstoitslowcost,realtimeimageformationcapabilityandnoninvasivenature.Duetoitsmanyattributes,ultrasoundhasbeenusedinneurosurgeryforthelasttwodecades[1].SeveralstudiesdemonstratedthatultrasonographycanCorrespondingauthor.Emailaddress:[e-mail](PierrickCoupe).PreprintsubmittedtoMedicalImageAnalysis14June2007beusedinthelocationoftumors,denitionoftheirmargins,dierentiationofinternalcharacteristicsanddetectionofbrainshiftandresidualtumoraltissue[2].Despiteitsadvantages,thelackof3Dinformationintraditional2Dultrasoundimagingpreventsreproductivityofexaminations,longitudinalfollow-upandprecisequantitativemeasurements.Toovercometheselimitsandproducea3Drepresentationofthescannedorgans,severalstechniquesexist:mechanically-sweptacquisitions,freehandimaging[3],mechanicalbuilt-inprobesand2Dphased-arrayprobes[4].Thetworstapproachesarebasedonthereconstruc-tionofa3Dregularlatticefrom2DB-scansandtheirpositions,whereas3Dprobesdirectlyacquire3Dimages.Themainadvantagesoffreehandimaging,comparedtoother3Dapproaches,areexibility,lowcostandlargeorgansex-aminationcapabilities.Moreover,comparedto3Dprobes,theimagequalityandtheeldofviewarebettersuitedtoclinicalapplications[5,6].Freehandimagingtechniquesconsistoftrackingastandard2Dprobebyusinga3Dlocalizer(magnetic,mechanicaloroptic).Thetrackingsystemcontinu-ouslymeasuresthe3Dpositionandorientationoftheprobe.This3DpositionisusedforthelocalizationofB-scansinthecoordinatesystemofthelocal-izer.InordertoestablishthetransformationbetweentheB-scancoordinatesandthe3Dpositionandorientationoftheprobe,acalibrationprocedureisnecessary[7,8].Calibrationisneededtoestimatethetransformationmatrixlinkingthedierentcoordinatesystems(spatialcalibration),butalsothela-tencybetweenimageandpositiontimestamps(temporalcalibration).ThelocalizationaccuracyofB-scanpixelsinthe3Dreferentialsystemdependsonthecalibrationprocedure.Areviewofcalibrationtechniquesispresentedin[9].ToanalyzethesequencesofB-scans,twotypesofapproachescanbeused:thereslicing(withoutreconstruction)orthetrue3Dreconstructionincludinginterpolationstep.TherstisusedbytheStradXsystem[10]andenablestheanalysisofthedatawithoutreconstruction.ThesequenceofB-scanscanbearbitrarilyreslicedanddistance/volumemeasurementsareperformedwith-outreconstruction.Thisstrategyisverypowerfulformanualanalysisof3Ddatasets.However,3Disotropicreconstructionisstillnecessaryintheclinicalcontextwhenautomaticsegmentationorregistrationproceduresarerequired.ThesecondapproachisbasedontheinterpolationoftheinformationwithintheB-scanstollaregular3Dlatticethuscreatingavolumetricreconstruc-tion.DuetothenonuniformdistributionoftheB-scans,thisstepisacutelyexpensivewithrespecttocomputationtimeandreconstructionquality:anecientreconstructionmethodshouldnotintroducegeometricalartifacts,de-gradenordistorttheimages.Toresolvethisproblemseveralmethodswereproposed.ThemostcommononesarePixelNearest-Neighbor(PNN)[11],VoxelNearest-Neighbor(VNN)[10,12]andDistance-Weightedinterpolation2(DW)[13,14].Duetoitssimplicityofimplementationanditsreducedcomputationtime,themoststraightforwardreconstructionalgorithmisthePNNmethod.Thisalgorithmisdividedintotwostages:thebin-llingandthehole-lling[15].Thebin-llingstageconsistinsearching,foreachpixelineveryB-scan.Thenearestvoxelwhichislledwiththevalueofthepixel.Secondly,theremain-inggapsinthe3Dvoxelarrayarelledviaahole-llingmethod.Usually,thehole-llingmethodisalocalaverageoflledvoxels.AlthoughthePNNmethodisfastandsimpletoimplement,thisapproachgeneratesartifacts.ContrarytothePNNmethod,theVNNapproachdoesnotrequirethehole-llingstagebecauseallvoxelsarelledinonestepusingthevalueofthenearestpixelobtainedbyorthogonalprojectiononthenearestB-scan.IntheDWinterpolationapproach,eachvoxelislledwiththeweightedaverageofpixelsfromthenearestB-scans(seesection2.1andFig.1foradetailedexplanation).Thesetofpixelsorinterpolationker