CONSTRUCTION OF GEOMETRIC PARTIAL DIFFERENTIAL EQUATIONS FOR LEVEL SETS

Geometric partial differential equations of level-set form are usually constructed bya variational method using either Dirac delta function or co-area formula in the energyfunctional to be minimized.However,the equations derived by these two approaches arenot consistent.In this paper,we present a third approach for constructing the level-setform equations.By representing various differential geometry quantities and differentialgeometry operators in terms of the implicit surface,we are able to reformulate three classesof parametric geometric partial differential equations (second-order,fourth-order and sixth-order)into the level-set forms.The reformulation of the equations is generic and simple,and the resulting equations are consistent with their parametric form counterparts.Wefurther prove that the equations derived using co-area formula are also consistent with theparametric forms.However,these equations are of much complicated forms than thesegiven by the equations we derived.