Split-Bregman Method and Dual Method for Multiphase Image Segmentation

The variational level set method can be used to design general frameworks for multiphase image segmentation,but its drawbacks of local minimization and low efficiency are two problems of their applications in different areas.In this work,firstly,the global convex minimization method for two-phase image segmentation is extended to variational multiphase image segmentation,which results in an alternating convex minimization problem.Secondly,the Split-Bregman method and dual method are designed for the proposed model to improve the computation efficiency.The Split-Bregman method is implemented by introducing auxiliary variables which transform the relaxed convex variational model into solving simple Poisson equations and exact soft thresholding formulation,the dual method is implemented by introducing dual variables which lead to semi-implicit iterative scheme of dual variables and exact formulation of primal variables.The proposed model can be used for image segmentation of any phase,is under the same formulation for both 2D and 3D image segmentation.It is suitable for 3D shape recovery from 3D images.Experiments demonstrate its high efficiency of our proposed model in comparison with the traditional methods.