This method uses deformable registration to produce a dense vector 64257eld describing the point correspondences between two images of bilaterally paired structures The deformation vector 64257eld properties are clustered to detect and describe regi ID: 47581
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andfemaleanimals,allapproximately28-30daysoldtoreduceeffectsofageonsizeandshape.Thescanswereperformedatanisotropicresolutionof18microns,theneachdatasetreducedbyafactorof3tosimplifydatahandlingandcomputationtime.Toquantifythesymmetryofthemandibles,theexternalcontourofeachhemi-mandiblewasrstextractedfromtheimage.Ourmethodbasedongeodesicactivecontours[6]wasusedtoremovescannoiseintheimages,clarifyindistinctbordersbetweentheobjectandthebackground,andtollgapsandholes.Oncethecontourswereextracted,thelefthemi-mandiblesweremirroredtoper-mitcomparisontotherightsidesandanafnetransformationappliedtoaligntheimagesandremoveposedifferences.IV.METHODOLOGYThegoalofthetoolpresentedinthisworkistoprovideaexiblewaytoanalyzetheasymmetriesbetweenbilaterallypairedstructures–inthiscase,theleftandrighthemi-mandibleofindividualmice,andtocomparetheseasym-metriespairwiseacrossindividuals.Thistoolprovidesthreeprimarymodesofanalysis:1)theglobalasymmetrymeasurequantiesasymmetryacrossthesurfaceofthemandibleforanindividual,2)thelocalasymmetrymeasurequantiesasymmetryatuser-denedregionsofinterest,3)theasymmetrysimilaritymeasurequantiespairwisesimilarityofindividualasymmetry.A.DeformableRegistrationTherststepinthismethodisadeformableregistrationthatisappliedtoassesslocaldifferencesateverypointbetweenalignedimagesofanindividual'srightandmir-roredleftmandible.Thisregistrationdeterminesthespatialtransformmappingpointsfromasourcetohomologouspointsonanobjectinatargetimage.Theoutputisadensedeformationvectoreldinwhichthevectorateachpointdescribesthespatialtransformationofthatpoint.Whenappliedtotwoimages,thesevectorsreectthestructuraldifferencesbetweenthesourceandtargetimages.Forthisapplication,aB-splinedeformabletransformusingamutualinformationmetricwaschosen,sinceitiswidelyapplicableandcomputationallyefcient[2].B.VectorFieldFeaturesTointerpretthedeformationvectorsinameaningfulway,itisnecessarytoidentifyandquantifyregionsofbiologicallyrelevantdifferences.Forthisapplication,twolow-levelvec-torpropertieswerechosen:thedeformationvectormagnitudeandthecosinedistancebetweenthedeformationvectorandthesurfacenormalvector.C.ClusteringandClusterFeaturesThetwolow-levelfeaturesareindividuallyclusteredtondregionswithsimilartransformationproperties.Ourspa-tiallyconstrainedK-meansclusteringalgorithmdescribedin[6]isusedtoidentifytheregionsforeachlow-levelfeature.AsymmetricclustersaredenedasthosewithanaveragedeformationmagnitudegreaterthanT,whereTisonestandarddeviationabovethemeandeformationmagnitudeofallvoxels.Theclusterfeaturesusedtogeneratethefeaturevectorarethe:1)locationofclustercenter,2)numberofvoxelsincluster,3)averagemagnitudevalue,and4)averagenormalangledifference.Eachfeatureisnormalizedoverthedatasettoremovedifferencesinscaleanddistributionsothatonefeaturedoesnotdominatethefeaturevector.D.GlobalAsymmetryScoreTherstanalysismethodprovidedbythistoolistheglobalasymmetryscore.Thisscoreisusedtoquantifythemagnitudeofthedeformationbetweentheleftandrighthemi-mandibles.Thegoalwastoproducescoresthatwouldcorrelatehighlywiththeratingsassignedbyanexpert.Itwasnecessarytouseamoreexiblemethodthanasimplemetricliketheaverageenergyofthetransformation,becausetheexpertrankingincorporatespriorknowledgesuchastherelativeimportanceofsmallregionsofhighmagnitudedifferencesandtheneedtoexcludespecicregions,suchastheteethbecauseofvariationduetowear.Theglobalsym-metryscoreprovidestheuserwiththeabilitytoincludethisinformationinthescores.Thescoreiscalculatedusingonlydeformationmagnitudeclusterfeatures,sincethedirectionofthedeformationwasnotusedintheexpertrankings.Thetwoglobalmagnitudefeaturesusedare:1)Umax,themaximumclustermean,and2)Vdef,thetotalnumberofvoxelsinclusterswithmeanhigherthanthethresholdT,whereTisonestandarddeviationabovethemeandeformationmagnitudeofallvoxels.Theseglobalfeaturesarenormalizedoverthedatasetandthescoreisdenedas:Sglobal= Umax+(1� )Vdef;(1)where isaconstantspecifyingthecontributionofthemaximumdeformationrelativetotheoveralldeformation.Thevalueofthisconstantisspecictotheapplicationandallowstheusertoincorporatepriorknowledgeabouttherelativeimportanceofsmallregionswithhighmagnitudetransformationscomparedtolargerregionswithsmallermagnitudetransformations.Inaddition,thetoolallowsclus-terswithacenterinaregionselectedbytheusertobeexcluded,forexample,ifdeemednottobebiologicallyrelevanttotheparticularquestionbeingconsidered.E.LocalAsymmetryScoreThelocalasymmetryscoreisasecondasymmetrymeasurethatprovidesanadditionalwaytoaddpriorknowledgetothesymmetryscore.Thelocalasymmetryscoreusesonlyfeaturesfromthedeformationvectorsinaneighborhoodaroundthelandmarkpointsplacedbyanexpert.ThelocalasymmetryscoreisdenedasSlocal= Nmax+(1� )Naverage;(2)whereNmaxismaximumneighborhoodaverage,Naverageistheaveragedeformationmagnitudeoverallneighborhoods, Tomotivatetheusefulnessofthemagnitudeandnormalangledifferenceasymmetrymeasures,twosamplequeriesareshown.InFig.3asamplequeryisshownforthemagnitudeclusters,usingtheclustercenterandaveragemagnitudefeatures.Thequeryimagechosenisthemostasymmetriccase:Fig.3(a).Intheleft/rightoverlayinFig.3(d),thelefthemi-mandible,showninblue,isclearlylongerthantherighthemi-mandible,showninred.ThetoptwomatchesformagnitudeofasymmetryarealsoshowninFigures3(b)and3(c).Bothshowasimilarmagnitudeofasymmetryinthecondyloidandangularprocesses.TheseregionsarealsocircledinFigures3(d),3(e),and3(f).Notethatinthe“result”images,theleftmandibleisshorterthantheright.Thisisexpectedsincethedirectionoftheasymmetryisignoredandonlythemagnitudeoftheowvectorsisconsidered.Thistypeofquerycanbeusedtondmandibleswithasymmetriessimilarinmagnitudebutindependentofdirection. (a)Magnitudeheatmapforquery (b)Magnitudeheatmapforresult1 (c)Magnitudeheatmapforresult2 (d)L/Roverlayofquery (e)L/Roverlayofresult1 (f)L/Roverlayofresult2Fig.3.Heatmapsandleft/rightoverlayfromasamplemagnitudequeryusingthemostasymmetricmandible.Inthetoprowthehighmagnitudeisrepresentedbyredandthelowbyblue.Inthelowerrowtherighthemi-mandibleisshowninblueandtheleftinred.InFig.4,thesamplequeryisshownforthenormalangleclusters,usingtheclustercenterandaveragenormalangledifferencefeatures.Thequeryimageisthesameasinthepreviousexampleandthetoptwomatchesfornormalangleasymmetryareshown,butnotablyaredifferenttothoseidentiedbythemagnitudequery.Comparedtothemagnitudequeryresults,thedifferenceismuchsmallerfortheresultimageswhenusingthesefeaturesasaquery.Forthisexample,inbothmatches,thelefthemi-mandibleisshorterthantherightlikethequerymandible.Thistypeofquerycanbeusedtondasymmetrieswhicharesimilarindirectiondespitedifferencesinmagnitude.VI.CONCLUSIONANDFUTUREWORKInthispaper,anewtoolisintroducedandshowntobecapableofassigningasymmetryscoresbasedonglobalfeaturesandfeaturesfromuser-denedlocations.Regionsofsignicantasymmetryaredetected,described,andusedtoquantifythesimilarityofasymmetryacrossindividuals.Thesemethodswereevaluatedonmousemandibleswithvaryingamountsofasymmetryandtheresultsare (a)Angleheatmapforquery (b)Angleheatmapforresult1 (c)Angleheatmapforresult2 (d)L/Roverlayofquery (e)L/Roverlayofresult1 (f)L/Roverlayofresult2Fig.4.Heatmapsandleft/rightoverlayfromanormalangledifferencequeryusingthemostasymmetricmandible.Inthetoprowthelargestnormalangledifferenceisrepresentedbyredandthelowestbyblue.Inthelowerrowtherighthemi-mandibleisshowninblueandtheleftinred.TABLEISUMMARYOFASYMMETRYSCORINGRESULTS Method CorrelationtoExpertRanking GlobalAsymmetryScore 0.92 LocalAsymmetryScore 0.91 Magnitudesimilaritytomostasymmetriccase 0.91 summarizedinTableI.Plannedfutureworkwillcreateanonlineuserinterfacetoexiblyuseandcombinethemethodsprovidedbythistool.Thiswillallowthetooltobeeasilyaccessedbymultipleresearcherstoquantifyandcharacterizetheasymmetryofanybilaterallypairedstructure.Acknowledgment:ThisresearchwassupportedbyNIH/NIDCRundergrantnumbers1U01DE020050-01(PI:LShapiro)andHD061335(PI:TCox),andinpartbyagrantfromtheJ¨orgePosadaFoundation(PI:TCox).REFERENCES[1]B.CombesandS.Prima.Newalgorithmstomapasymmetriesof3dsurfaces.MedicalImageComputingandComputer-AssistedIntervention–MICCAI2008,pages17–25,2008.[2]WRCrum,T.Hartkens,andDLGHill.Non-rigidimageregistration:theoryandpractice.Britishjournalofradiology,77(SpecialIssue2):S140,2004.[3]T.A.Darvann,N.V.Hermann,P.Larsen,H.´Olafsd´ottir,I.V.Hansen,H.D.Hove,L.Christensen,D.Rueckert,andS.Kreiborg.Automatedquanticationandanalysisofmandibularasymmetry.InBiomedicalImaging:FromNanotoMacro,2010IEEEInternationalSymposiumon,pages416–419.IEEE,2010.[4]J.L.Lancaster,P.V.Kochunov,P.M.Thompson,A.W.Toga,andP.T.Fox.Asymmetryofthebrainsurfacefromdeformationeldanalysis.Humanbrainmapping,19(2):79–89,2003.[5]H.Olafsdottir,S.Lanche,T.A.Darvann,N.V.Hermann,R.Larsen,B.K.Ersboll,E.Oubel,A.F.Frangi,P.Larsen,C.A.Perlyn,etal.Apoint-wisequanticationofasymmetryusingdeformationelds:applicationtothestudyofthecrouzonmousemodel.InProceedingsofthe10thinternationalconferenceonMedicalimagecomputingandcomputer-assistedintervention,pages452–459.Springer-Verlag,2007.[6]SMRolfe,LGShapiro,TCCox,AMMaga,andLLCox.Alandmark-freeframeworkforthedetectionanddescriptionofshapedifferencesinembryos.InEngineeringinMedicineandBiologySociety,EMBC,2011AnnualInternationalConferenceoftheIEEE,pages5153–5156.IEEE,2011.