A variational level set method of multiphase segmentation for piecewise smooth images

A variational level set method of multiphase segmentation for piecewise smooth images is presented in this paper. n-1 level set functions are used to partition n regions using n new characteristic functions via Heaviside functions without overlapping and vacuum problems. The energy functional includes three parts. The first part is a parametric region-based model via generic image noise distributions, but the parameters are not constant in different homogeneous regions to describe the smooth properties based on TV model, the second part is classic edge-based model, the third part is terms used to enforce the constraints of level set functions as signed distance functions. The estimation of parameters is realized through solving a set of PDEs using some concepts of image inpainting, which is different from the method in literatures. The evolution equations of level set functions are solved by a semi-implicit scheme. Some numerical examples for segmentation of synthetic and real images are presented to validate the method suggested in this paper.