Image segmentation and smoothing by using improved Mumford-Shah model

In this work, we propose a minimizing functional based on Mumford-Shah model, which provides a model for image segmentation and smoothing. The paper analyzes the physical characteristics of the related modified Poisson equation in local coordinates and explains that diffusion behavioral is superior to isotropic diffusion in essence. Thus our model is more suitable for segmentation and smoothing of noisy images with intensity inhomogeneities while simultaneously preserving edges than the piecewise smooth Mumford-Shah (PSMS) model proposed by Chan and Vese. Moreover we establish solution existence of the minimizing functional. Then effective numerical scheme is designed to handle its computation. The model is finally applied on a wide variety of image segmentation and smoothing. All these results show that the proposed model is effective.