Level set methods and image segmentation

In this paper we discuss some questions for applying the level,el set methods to image segmentation. During image segmentation, it has been found that the level sets function could be changed into a non-distance function with the initial level set function defined as a distance function. This causes some applications in fail, such as Coupled Surfaces Propagation, et al. In addition, the solution existence and uniqueness of the evolving equation in level set method has not been discussed in detail. In this paper, we firstly proved that the signed distance function could de preserved to the level set function during the evolution of the level set function through the methods presented in [1,7]. Furthermore, the solution existence and uniqueness of the level set function evolution equations are analyzed in detail under the distance function restriction. And it has been proved that the solutions exist but not unique. Finally, this conclusion can be validated in the results of implementation on image segmentation.