New Algorithm for Level Set Evolution without Re-initialization and Its Application to Variational Image Segmentation

Traditionally variational level set model for image segmentation is solved by using gradient descent method, which has low computational efficiency and needs complex re-initialization of level set functions as signed distance functions. In this paper, we first reformulate the variational model as a constrained optimization problem. Then we present an augmented Lagrangian projection method to preserve signed distance functions and accelerate the implementation. By introducing auxiliary variables, we convert derivative constraints to algebraic equations with simple projection. We apply the proposed algorithm to the two-phase/multiphase Chan-Vese models. Numerical results are provided to compare our algorithm with some others, which demonstrate effectiveness and efficiency of our approach.