New variational formulations for level set evolution without reinitialization with applications to image segmentation

Interface evolution problems are often solved elegantly by the level set method, which generally requires the time-consuming reinitialization process. In order to avoid reinitialization, we reformulate the variational model as a constrained optimization problem. Then we present an augmented Lagrangian method and a projection Lagrangian method to solve the constrained model and propose two gradient-type algorithms. For the augmented Lagrangian method, we employ the Uzawa scheme to update the Lagrange multiplier. For the projection Lagrangian method, we use the variable splitting technique and get an explicit expression for the Lagrange multiplier. We apply the two approaches to the Chan-Vese model and obtain two efficient alternating iterative algorithms based on the semi-implicit additive operator splitting scheme. Numerical results on various synthetic and real images are provided to compare our methods with two others, which demonstrate effectiveness and efficiency of our algorithms.