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1、LEVELSETMETHODSANDTHEIRAPPLICATIONSINIMAGESCIENCERICHARDTSAIANDSTANLEYOSHERInthisarticle,wediscussthequestion"WhatLevelSetMethodscandoforimagescience".Weexaminethescopeofthesetechniquesinimagescience,inparticularinimagesegmentation,andintroducesomereleva
2、ntlevelsettechniquesthatarepotentiallyusefulforthisclassofapplications.Wewillshowthatimagesciencedemandsmulti-disciplinaryknowledgeandexiblebutstillrobustmeth-ods.ThatiswhytheLevelSetMethodhasbecomeathrivingtechniqueinthiseld.Webeginbyreviewingsometypi
3、calPDEbasedapplicationsinimageprocess-ing.IntypicalPDEmethods,imagesareassumedtobecontinuousfunctionssam-pledonagrid.Wewillshowthatthesemethodsallshareacommonfeature,whichistheemphasisonprocessingthelevellinesoftheunderlyingimage.Theimpor-tanceoflevellin
4、eshasbeenknownforsometime.Seee.g.,[2].Thisfeatureplacesourslightlygeneraldenitionofthelevelsetmethodforimagescienceincontext.Insectiontwo,wedescribethebuildingblocksofatypicallevelsetmethodinthecontinuumsetting.Eachimportanttaskthatoneneedstodoisformula
5、tedasthesolutiontocertainPDEs.Then,insectionthree,wequicklydescribethenitedif-ferencemethodsdevelopedtoconstructapproximatesolutionstothesePDEs.Insectionfour,wedescribedtheChan-Vesesegmentationalgorithmandtwonewfastimplementationmethods.Finally,insectio
6、nve,wedescribesomenewtechniquesdevelopedinthelevelsetcommunityasourprospectusforthefuture.1.LEVELSETMETHODSANDIMAGESCIENCEThelevelsetmethodforcapturingmovingfrontswasintroducedbyOsherandSethian[72]in1987.(Twoearlierconferencepaperswhichcontainedsomeofth
7、ekeyideas,haverecentlycometolight[28],[29]).Overtheyears,themethodhasproventobearobustnumericaldeviceforthispurposeinadiversecollectionofproblems.Onesetofproblemsliesintheeldofimagescience.Inthisarticle,wewillemphasizenotonlywhathasbeendoneinimagescienc
8、eusinglevelsettech-niques,butalsoinotherareaofsciencesinwhichthelevelsetmethodsareappliedsuccessfully—theideaistopointouttherelatedformulationsandsolutionmeth-odstotheimagesciencecommunities.Thesecommunitiesincludeimage/vi
