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1、B-SplineRegistrationof3DImageswithLevenberg-MarquardtOptimizationSvenKabusa,b,ThomasNetschb,BerndFischera,JanModersitzkiaaInstituteofMathematics,UniversityofLubÄeck,Wallstra¼e40,23560LubÄeck,GermanybPhilipsResearchLaboratories,RÄontgenstra¼e24,22335Hamburg,GermanyABSTRACTB-splinesareawell-knownapp
2、roachfornon-rigidimageregistration.Thoughsuccessfullyappliedtovariousmedicalapplicationstheyexhibitahighcomputationalcomplexitymainlybecauseofthelackofdedicatedoptimizationmethods.InthisworkwefocusonaLevenberg-Marquardttypeoptimizationroutine.Asasimilaritymeasureweuseleast-squaresfunctionalssuchas
3、thesumofsquareddi®erences,thecross-correlationandthelocalcorrelationmeasure,respectively.Thelatterisusedformulti-modalityregistrationtasks.Theproposedregistrationalgorithmconsistsofthreemainparts.Ineachiterationsteponehasto(a)buildalinearsystemofequations,(b)solvethissystemandcomputeanupdate,(c)de
4、terminethesteplengthforthefollowingiterationstep.Appropriatestoppingcriteriaensuretheterminationoftheregistrationtask.Astandardapproachfor(c)andseveralmodi¯cationsareinvestigated.Usingaquadraticmodelweareabletoavoidadditionalexecutionof(b)duringthesteplengthadaption.Severalsolvers(Cholesky,CG,pre-
5、conditioning)for(b)havebeenevaluated.Also,modi¯cationsonthemosttimeconsumingtask(a)areinvestigated,leadingtoaspeed-upbyafactorupto30.Finally,thealgorithmisembeddedinamulti-scaleframework(bothonimageandonparameterlevel)providingadditionalregularization,anincreasedcapturerangeandspeed-up.Convergence
6、testshavebeensuccessfullyappliedforaprioriknowntransformations.FeasibilityoftheproposedapproachisalsoshownforclinicalapplicationsincludingPET-CTregistrations(19datasets)andMRmammography.Keywords:3Dimageregistration,B-splines,Levenberg-Marquardtoptimization,multi-scaledecomposition1.INTRODUCTIONThe
7、taskofnonrigidimageregistrationofthree-dimensional(3D)medicalimagevolumesisto¯ndavector¯eldof3Ddisplacementssuchthateachpointinthereferenceimagecanbemappedontoacorresponding(meaning-ful)pointinthetemplateimage.Ty
