Fast marching the global minimum of active contours

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1、FASTMARCHINGTHEGLOBALMINIMUMOFACTIVECONTOURSLaurentD.COHENRonKIMMELCEREMADE,U.R.A.CNRS749LawrenceBerkeleyLaboratoryUniversiteParis9-DauphineUniversityofCalifornia75775Pariscedex16,FranceBerkeleyCalifornia94720,USAcohen@ceremade.dauphine.frron@csr.lbl.govABSTRACTexternalpotentialterminanaturalway.T

2、heenergyE(C)ofthenewmodelhasthefollowingform:AnewapproachofedgeintegrationforshapemodelingZZZispresented.Itisusedtondtheglobalminimumofan@C2~wkk+P(C)ds=P(C)ds=wL+P(C)ds(1)activecontourmodel'senergybetweentwopoints.Ini-@stializationismadeeasierandthecurveisnottrappedwherePisthepotentialassociatedto

3、theexternalatalocalminimumbyspuriousedges.Wemodifytheforces.HereCisinthespaceofallcurvesconnectingsnake"energybyincludingtheinternalregularizationtwogivenpoints(restrictedbyboundaryconditions):termintheexternalpotentialterm.OurmethodisC(0)=pandC(L)=p,whereListhelengthofthebasedontheinterpretationo

4、fthesnakeasapathof01curve.Contrarytotheclassicalsnakeenergy,heresminimallengthinaRiemannianmetric,orasapathrepresentsthearc-lengthparameter,whichmeansthatofminimalweighteddistance.Wethenmakeuseofa@C2newnumericalmethodtondtheshortestpathwhichk(s)k=1.Theregularizationtermwithw,now@sistheglobalminimu

5、moftheenergyamongallpathsexactlymeasuresthelengthofthecurve.Weshowedjoiningthetwoendpoints.Weshowexamplesofoursomeregularizationpropertiesofthisparameterin[4].methodappliedtorealaerialandmedicalimages.2.PATHSOFMINIMALACTION1.INTRODUCTIONMotivatedbyanapproachofminimalpathestimationVariationsoftheact

6、ivecontourmodel(`snakes')foronasurface[5],weuseanevolutionschemethatpro-boundaryintegrationandfeaturesextraction,intro-videsateachimagepixelanoutputoftheenergyalongducedin[1],havebeenconsiderablyusedandstudiedthepathofminimalintegratedenergyjoiningthatpixelduringthelastyears.Althoughthesmoothingee

7、cttothegivenstartpoint.Thesearchforaglobalmin-ofthesnakesmayovercomesmalldefaultsinthedata,imumisthendoneeciently.Whilethisminimumisspuriousedgesgeneratedbynoiseorinacomplexim-restrictedtostartandendbetwee