%0 Journal Article
%T A New Multiphase Soft Segmentation with Adaptive Variants
%A Hongyuan Wang
%A Fuhua Chen
%A Yunmei Chen
%J Applied Computational Intelligence and Soft Computing
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/921721
%X Soft segmentation is more flexible than hard segmentation. But the membership functions are usually sensitive to noise. In this paper, we propose a multiphase soft segmentation model for nearly piecewise constant images based on stochastic principle, where pixel intensities are modeled as random variables with mixed Gaussian distribution. The novelty of this paper lies in three aspects. First, unlike some existing models where the mean of each phase is modeled as a constant and the variances for different phases are assumed to be the same, the mean for each phase in the Gaussian distribution in this paper is modeled as a product of a constant and a bias field, and different phases are assumed to have different variances, which makes the model more flexible. Second, we develop a bidirection projected primal dual hybrid gradient (PDHG) algorithm for iterations of membership functions. Third, we also develop a novel algorithm for explicitly computing the projection from to simplex for any dimension using dual theory, which is more efficient in both coding and implementation than existing projection methods. 1. Introduction Image segmentation has played an important role in image processing and computer vision. Recently, variational segmentation models have attracted increasing interest [1¨C8]. With level set technique [9], variational models can be solved efficiently. The technique was originally developed for two-phase segmentation, and then extended to multiphase segmentation [10¨C13]. With carefully choosing the initial values, these methods can achieve an ideal solution for multiphase segmentation. However, the nonconvexity of the energy functional in the level set formulation is an inherent drawback of level set-method. As a result, many level set-based variational segmentation models are sensitive to initial values, especially for multiphase segmentation, and may lead to an inferior local minimum. One way to overcome the drawback is to use fuzzy membership function to replace the Heaviside function of a level set function in level set formulation for modeling a characteristic function, called soft segmentation. With this relaxation (characteristic function can be viewed as a special case of membership function), Chan and Bresson et al. [1, 2, 5] proved that global minimum can be achieved in these models due to the convexity of the energy functional. Unfortunately, this method cannot be easily applied to multi-phase segmentation. Very recently, based on a variational convexification technique developed by Pock et al. [14], Brown et al. [15], and Bae et
%U http://www.hindawi.com/journals/acisc/2013/921721/