A New Variational Formulation for Image Segmentation without Re-initialization

In the traditional variational level set model for image segmentation, the evolving level set function needs periodical re-initialization to keep it close to a signed distance function during the evolution. Li presented a variational formulation that forces the level set function to be close to a signed distance function by adding a internal energy into the energy functional, and therefore completely eliminates the need of the expensive re-initialization procedure. In this paper, we experimentally testify that the evolving level set function doesn't need to keep to a signed distance function, and as long as relatively smooth. Based on this idea, we present another variational formulation that forces the level set function to be smoother, and it also completely eliminates the need of the re-initialization. The experimental results are then presented to validate the proposed our new model.