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 for identifying curves separating regions into different phases. In classical level set approaches, the sign of n level set functions are utilized to identify up to 2n phases. The novelty in our approach is to introduce a piecewise constant level set function and use each constant value to represent a unique phase. If 2n phases should be identified, the level set function must approach 2n predetermined constants. We just need one level set function to represent 2n unique phases and this gains the storage capacity. Further, the reinitializing procedure requested in classical level set methods is superfluous using our approach. The minimization functional for our approach is convex and differentiable and thus avoid some of the problems with the non-differentiability of the Delta and Heaviside functions. Numerical examples will be given and we shall also compare our method with related approaches.