Based on sparse regularization to the membership functions

this paper proposes a novel multiphase variational model and corresponding algorithm for image segmentation.The proposed model and algorithm has three main advantages.Firstly

the sparse regularizer performs better than total variation regularizer.It protects edges from oversmoothing which is a common drawback of the total variation regularizer.Secondly

the multi-scale geometric analysis tool well preserves geometric shape of the segmentation regions.Finally

the proposed algorithm is simple and has rapid running speed.A series of experimental results demonstrate the feasibility and effectiveness of the proposed method.