New Approach to Solving Mumford and Shah Model by Using Level Set Based Optimization

This paper proposes a fast algorithm to solve the piecewise-smooth Mumford and Shah model to speed up convergence. To prevent the active curve from converging to local optimal solutions, the two key functions u⁺ and u^- that have important influence upon segmentation results are studied. At every time step of the original algorithm, after the locations of u⁺ and u^- obtained they are further adjusted and updated by using the level set based optimization algorithm proposed by Song and Chan. Also, a narrowband is defined to control the size of regions to be adjusted to save computational cost. By this way, the convergence speed of the new algorithm is faster than the original one. The proposed algorithm has been demonstrated by several cases.