Soft segmentation is more flexible than hard segmentation. But the membership functions are usually sensitive to noise. In this\r\npaper, we propose amultiphase soft segmentation model for nearly piecewise constant images based on stochastic principle, where\r\npixel intensities are modeled as random variables with mixed Gaussian distribution. The novelty of this paper lies in three aspects.\r\nFirst, unlike some existingmodels where the mean of each phase ismodeled as a constant and the variances for different phases are\r\nassumed to be the same, the mean for each phase in the Gaussian distribution in this paper is modeled as a product of a constant\r\nand a bias field, and different phases are assumed to have different variances, which makes the model more flexible. Second, we\r\ndevelop a bidirection projected primal dual hybrid gradient (PDHG) algorithm for iterations of membership functions. Third, we\r\nalso develop a novel algorithm for explicitly computing the projection from RK to simplex ? K-1 for any dimension K using dual\r\ntheory, which is more efficient in both coding and implementation than existing projection methods.
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