A review of geometric transformations for nonrigid body registration

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1、IEEETRANSACTIONSONMEDICALIMAGING,VOL.27,NO.1,JANUARY2008111AReviewofGeometricTransformationsforNonrigidBodyRegistrationMarkHoldenAbstract—Thispaperprovidesacomprehensiveandquantita-Spatialtransformation,referstothemappingtivereviewofspatialtransformationsmodelsf

2、ornonrigidimagefromthespaceofthesourceimagetothespaceregistration.Itexplainsthetheoreticalfoundationofthemodelsofthetarget.andclassifiesthemaccordingtothisbasis.Thisresultsintwocat-Directsum.egories,physicallybasedmodelsdescribedbypartialdifferentialequationsofco

3、ntinuummechanics(e.g.,linearelasticityandfluidDisplacementvectorofpointinthespaceofflow)andbasisfunctionexpansionsderivedfrominterpolationandthesourceimagewithcomponents(u,v,w).approximationtheory(e.g.,radialbasisfunctions,B-splinesandVelocityvector.wavelets).Rece

4、ntworkonconstrainingthetransformationsothatitpreservesthetopologyorisdiffeomorphicisalsodescribed.TheVorticitytensor.finalsectionreviewssomerecentevaluationstudies.Thepapercon-cludesbyexplainingunderwhatconditionsaparticulartransfor-mationmodelisappropriate.D:EFI

5、NITIONSIndexTerms—Fluidflowregistration,linearelasticregistration,nonrigidimageregistration,parametrictransformationmodels,spatialtransformations,splinebasedregistration,waveletbasedCapturerangeTherangeofattractionoftheregistrationregistration.function.Thespatial

6、extentofthesetofmisregistrationsfromwhichconvergencetotheoptimaltransformationispossible.M:ATHEMATICALNOTATIONCSFCerebrospinalfluid.DiffeomorphismAdifferentiablehomeomorphismTargetimage,isanimagelocation.withadifferentiableinverse(nonzeroSourceimagetobealignedwit

7、h.determinantoftheJacobianmatrix).ItisahomeomorphismthatmapsoneTherateofdeformationtensor.differentiablemanifoldtoanother.Straintensor.EulerianThesedescribethemotionofabodyofMasssourceterm.coordinatesparticlesrelativetoasetoffixedpointsinspacethroughwhichparticle

8、spass.Bodyforceperunitvolumeactingat.TheEuleriancoordinateframerefersto,Cartesiancomponents.thecurrentstateofthesystem.Identitymatrix.HomeomorphismAcontinuousbijectiv