Solving the Chan-Vese Model by a Multiphase Level Set Algorithm Based on the Topological Derivative

In this work, we specifically solve the Chan-Vese active contour model by multiphase level set methods. We first develop a fast algorithm based on calculating the variational energy of the Chan-Vese model without the length term. We check whether the energy decreases or not when we move a point to another segmented region. Then we draw a connection between this algorithm and the topological derivative, a concept emerged from the shape optimization field. Furthermore, to include the length term of the Chan-Vese model, a preprocessing step is taken by using nonlinear diffusion. Numerical experiments have demonstrated the efficiency and the robustness of our algorithm.