Fast projection algorithms for level set evolution in Potts model

Potts model is a basic variational model for multiphase image segmentation. Under the variational level set framework, the model is usually implemented by solving a gradient descent equation derived from energy functional minimization together with re-initialization process to preserve the level set function as a signed distance function. Because of the existence of complicated curvature terms in the PDE equations and the time-consuming re-initialization process, this method is with low computation efficiency. In this paper, we combine the Split Bregman algorithm, Dual method together with a very simple projection method to overcome the problems mentioned above. We name these two methods as Split Bregman Projection Method(SBPM) and Dual Split Bregman Projection Method(DSBPM). They naturally preserve the level set function as a signed distance function during the evolution without the initialization process. These methods are compared with traditional method and the ones proposed by other authors according to some numerical experiments. These examples demonstrate that our proposed methods are of higher efficiency than the other ones and can segment images quickly.