A multiphase image segmentation model for piecewise smooth images on implicit surfaces

To segment piecewise smooth images on implicit surfaces, Potts model which is a general variational model for planar multiphase image segmentation is extended to the one for image segmentation on implicit surfaces. Potts model is reformulated not only on implicit closed surfaces but also on implicit open surfaces. An improved dual method is proposed to speed up the computation process. Some numerical experiments are presented to give qualitative and quantitative comparisons among our method and the other two fast methods, that is, Split Bregman method and dual method. The results show that these methods can all segment piecewise smooth images on implicit surfaces effectively while the improved dual method is more efficient than Split Bregman method and dual method.