Level set methods and image segmentation

We discuss some questions for applying level 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 to fail, such as coupled surfaces propagation. In addition, the solution existence and uniqueness of the evolving equation in the level set method has not been discussed in detail. We firstly prove that the signed distance function could be presented to the level set function during the evolution of the level set function through the methods presented in (Sethian, 1999; Gomes and Faugeras, 2000). Furthermore, the solution existence and uniqueness of the level set function evolution equations are analyzed in detail under the distance function restriction. It has been proved that the solutions exist, but are not unique. Finally, this conclusion can be validated in the results of implementation on image segmentation