A new Mumford-Shah type model involvinga smoothing operator for multiphase image segmentation

Variational image segmentation based on the Mumford-Shah model requires to solve the heat diffusion equations in evolving irregular subdomains. It brings about significant difficulties in efficient and accurate segmentation, especially, in multi-phase scenarios. In this paper, we propose a new Mumford-Shah type model involving a smoothing operator, acting a similar role as the diffusion process and avoiding complicated computation. We introduce two simplified numerical models based on the Gaussian operator and the bilateral operator respectively, and provide efficient numerical algorithms to solve both segmentation problems. Numerical validation experiments on various images show better accuracy and robustness over existing methods.