A convex variational level set model for image segmentation

In this paper, we propose a strictly convex energy functional in a level set formulation for the purpose of two-phase image segmentation. We prove that the value of the unique global minimizer for the energy functional is within the interval [−1, 1] for any image, and equals to 1 in the object and −1 in the background for an ideal binary image. A pointwise convergent numerical scheme is presented to solve the gradient descent flow equation. The proposed model is allowed for flexible initialization and can set a reasonable termination criterion on the algorithm. The proposed model has been successfully applied to some synthesized and real images with promising results.