Level set methods and image segmentation

Abstract

In this article, some basic problems on the level set methods are discussed, such as the method used to preserve the distance function, the existence and uniqueness of the solutions for the level set equations and the analysis of the singular points. It is presented that if the solutions of the level set equations with the distance function restriction exist, they must be the signed distance function to the evolving surface. And it is presented that there exists a unique solution in a neighborhood of the initial zero level set. However, the uniqueness of the solutions is hard to be guaranteed away from the initial zero level set. An important property of the singular points is given, which is a sufficient and necessary condition in distinguishing the singular points from ordinary points. The above results consummate the theoretical base of the level set methods. At meantime, the estimate method of the width of the narrow band is presented in order to avoid the singular points during the iterative process of the level set methods. The implementations of our theory are shown on real images and synthetic images.