Split Method for the Convex Relaxation Model of Image Multi-Phase Segmentation

A general equivalent model is introduced based on the convex relaxation model of a class of vector-valued minimization problems. The presented model can be solved by split-Bregman algorithm. The computational efficiency is greatly improved. The method is applied to the Vese-Chan multi-phase segmentation model and Mumford-Shah model. Numerical experiments show our method has fast computing speed and good segmentation results, and is robust to the initial condition.