A new fast multiphase image segmentation algorithm based on nonconvex regularizer

We present a new variational model for the soft multiphase image segmentation. In the model, we introduce a nonconvex regularizer on the membership functions which are used as indicators of different homogeneous regions. The nonconvex regularizer performs better than the usual convex ones in that (i) it well preserves geometric shapes of the homogeneous regions, and (ii) it protects edges from oversmoothing which is a common drawback of the convex regularizer. To solve the nonconvex minimization problem, we design a new fast alternative iteration algorithm, which is robust to the setting of the parameters in the model. We conduct comprehensive experiments to measure the performance of the algorithm in terms of visual evaluation and a variety of quantitative indices for image segmentation. The algorithm achieves more accurate results compared to other well-known convex variational methods for image segmentation.