Indirectly regularized variational level set model for image segmentation

• Present a novel indirectly regularized variational level set model.
• We give a rigorously analytical study on the proposed model.
• Present an alternating minimization algorithm and give its convergence analysis.
• The indirect regularization term can be easily integrated into existing variational level set methods.

In this paper, we propose a variational level set model with indirect regularization term for image segmentation. Instead of using direct regularization on level set function, we introduce an auxiliary function to regularize indirectly the level set function. Our energy functional consists of a data term, a link term of level set function with the auxiliary function and a regularization term of the auxiliary function. We prove that the energy functional is convex in L2(Ω)×W1,2(Ω)L2(Ω)×W1,2(Ω) and give the convergence analysis of the alternating minimization algorithm that we utilized. We show that the indirect regularization has some advantages over direct regularization theoretically and experimentally. Experimental results illustrate that the proposed model can better handle images with high noise, angle and weak edges.