Inthisworkweconsidertheproblemofshapereconstructionfromanunorganizeddatasetwhichhasmanyimportantapplicationsinmedicalimaging,scientificcomputing,reverseengineeringandgeometricmodelling.ThereconstructedsurfaceisobtainedbycontinuouslydeforminganinitialsurfacefollowingthePartialDifferentialEquation(PDE)-baseddiffusionmodelderivedbyaminimalvolume-likevariationalformulation.Theevolutionisdrivenbothbythedistancefromthedatasetandbythecurvatureanalyticallycomputedbyit.Thedistancefunctioniscomputedbyimplicitlocalinterpolantsdefinedintermsofradialbasisfunctions.SpacediscretizationofthePDEmodelisobtainedbyfiniteco-volumeschemesandsemi-implicitapproachisusedintime/scale.Theuseofalevelsetmethodforthenumericalcomputationofthesurfacereconstructionallowsustohandlecomplexgeometryandevenchangingtopology,withouttheneedofuser-interaction.Numericalexamplesdemonstratetheabilityoftheproposedmethodtoproducehighqualityreconstructions.Moreover,weshowtheeffectivenessofthenewapproachtosolveholefillingproblemsandBooleanoperationsbetweendifferentdatasets.
