A variant of the level set method and applications to image segmentation

Abstract

In this paper we propose a variant of the level set formulation foridentifying curves separating regions into different phases. In classicallevel set approaches, the sign of n level set functions are utilizedto identify up to 2" phases. The novelty in our approach is to introducea piecewise constant level set function and use each constant valueto represent a unique phase. If 2" phases should be identified, thelevel set function must approach 2" predetermined constants. We justneed one level set function to represent 2" unique phases, and thisgains in storage capacity. Further, the reinitializing procedurerequested in classical level set methods is superfluous using ourapproach. The minimization functional for our approach is locallyconvex and differentiable and thus avoids some of the problems withthe nondifferentiability of the Delta and Heaviside functions. Numericalexamples are given, and we also compare our method with related approaches.