Solving Mumford-Shah model equation by AOS algorithm

Abstract

The Mumford-Shah model equation uses the global information of the gray level rather than the local gradient information as the stopping criterion in curve evolution. The CFL (Courant-Friedrichs-Levy) condition, which keeps the convergence of the level set method, and restricts the time step size in iterations. So the computational time may be long. In this paper, the AOS (additive operator splitting) scheme, an unconditionally stable numerical algorithm, is introduced to solve the problem. The scheme can use rather large time step size and still maintain the stability of the scheme. In our experiments, the first one shows the fast convergence of the scheme, and the others demonstrate the satisfied segmentation result.