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Applied Computational Intelligence and Soft Computing
Volume 2013 (2013), Article ID 921721, 9 pages
Research Article

A New Multiphase Soft Segmentation with Adaptive Variants

1School of Information Science & Engineering, Changzhou University, Changzhou 213164, China
2Department of Natural Science & Mathematics, West Liberty University, West Liberty, WV 26074, USA
3Department of Mathematics, University of Florida, Gainesville, FL 36011, USA

Received 19 February 2013; Accepted 9 May 2013

Academic Editor: Zhang Yi

Copyright © 2013 Hongyuan Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.