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1、2FuzzyEnergy-BasedActiveContoursSteliosKrinidisandVassiliosChatzisAbstract—Thispaperpresentsanovelfastmodelforactivelocalminimawhencomparedtosimpleredge-basedenergycontourstodetectobjectsinanimage,basedontechniquesoffunctionals.Ingeneral,region-basedmodel
2、s[19]−[30]utilizecurveevolution.Theproposedmodelcandetectobjectswhoseimageinformationnotonlyneartheevolvingcontour,butboundariesarenotnecessarilydefinedbygradient,basedontheimagestatisticsinsideandoutsidethecontour.Chanandminimizationofafuzzyenergy,whichca
3、nbeseenasaparticularcaseofaminimalpartitionproblem.ThisfuzzyenergyisusedasVese[21]proposedanactivecontourbasedonaregion-basedthemodelmotivationpowerevolvingtheactivecontour,whichenergyfunctionalinspiredbyMumford-Shahfunctional.Thiswillstoponthedesiredobje
4、ctboundary.However,thestoppingenergycanbeseenasaparticularcaseoftheminimalpartitiontermdoesnotdependonthegradientoftheimage,asmostofproblem,andinthelevelsetformulationtheactivecontourtheclassicalactivecontours,butinsteadisrelatedtotheimageisevolved.Thismo
5、del,aswellasmostoftheregion-basedcolorandspatialsegments.Thefuzzinessoftheenergyprovidesabalancedtechniquewithastrongabilitytoreject“weak”localenergyfunctionals,canhandleobjectswithboundariesnotminima.Moreover,thisapproachconvergestothedesiredobjectnecess
6、arilydefinedbygradient,butassumehighlyconstrainedboundaryveryfast,sinceitdoesnotsolvetheEuler-Lagrangemodelsforpixelintensitieswithineachregionhavinghighequationsoftheunderlyingproblem,but,instead,calculatesthecomputationalcost.fuzzyenergyalterationsdirect
7、ly.Thetheoreticalpropertiesandvariousexperimentspresenteddemonstratethattheproposedfuzzyenergy-basedactivecontourisbetterandmorerobustthanGibouetal[28],aswellasotherresearchersintheliteratureclassicalsnakemethodsbasedonthegradientorotherkindof[25],propose
8、anumbervariationsoftheChanandVese[21]energies.methodinordertoovercomeitslimitations,especiallytheIndexTerms—Activecontour,deformablecurve,segmentation,highcomputationalcost.Someofthemutilizethesimplicitycurveevoluti
