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1、GeodesicActiveRegions:AnewframeworktodealwithframepartitionproblemsinComputerVision1NikosParagiosSiemensCorporateResearch,755CollegeRoadEast,Princeton,NJ08540,USAE-mail:nikos@scr.siemens.comRachidDericheI.N.R.I.A.(RobotVis)2004RoutedesLucioles,06902SophiaAntipolis,FranceE-mail:der@sophia.
2、inria.frThispaperpresentsanovelvariationalframeworkfordealingwithframepartitionproblemsinComputerVisionbythepropagationofcurves.Thisframeworkintegratesboundaryandregion-basedframepartitionmodulesunderacurve-basedenergyframework,whichaimsat ndingasetofmin-imallengthcurvesthatpreservethreem
3、ainproperties:(i)theyareregularandsmooth,(ii)theyareattractedbytheboundarypoints(boundary-basedinformation),(ii)andtheycreateapartitionthatisoptimalaccord-ingtotheexpectedregionpropertiesofthedi erenthypotheses(region-basedinformation).Thede nedobjectivefunctionisminimizedusingagradientde
4、scentmethod.Accordingtotheobtainedmotionequations,thesetofinitialcurvesispropagatedtowardsthebestpartitionunderthein-
uenceofboundaryandregion-basedforces,andbeingconstrainedbyaregularityforce.Thechangesoftopologyarenaturallyhandledthankstothelevelsetimplementation.Furthermore,acoupledmul
5、ti-phasepropa-gationisproposedthatimposestheideaofmutuallyexclusivepropagatingcurves,andincreasestherobustnessaswellastheconvergencerate.TheproposedframeworkhasbeenvalidatedusingthreeimportantapplicationsinComputerVision,thetasksofimageandsupervisedtexturesegmenta-tioninlow-levelvisionand
6、thetaskofmotionestimationandtrackinginmotionanalysis.1Thisworkhasbeencarriedoutduringtheappointment(doctoralresearch)ofthe rstauthorwiththeComputerVisionandRoboticsGroup(RobotVis)ofI.N.R.I.A.SophiaAntipolisfromOctober1,1996toNovember1,1999andwasfundedinpartundertheVIRGOresearchnetwork(ECC
7、ontractNoERBFMRX-CT96-0049)oftheTMRProgram.1.INTRODUCTIONDuringthelasttwentyyearsawidevarietyofmathematicalandcomputationalframeworkshavebeenproposedtodealwithComputerVisionproblems.Theirclassi cationisnotaneasytask.Mostofthem,arebasedonthefactthatmanyofthecomputerv
