A Multi-phase Soft Segmentation Based on Bi-direction Projected PDHG Method

Soft segmentation takes an important role in partial volume segmentation for MRI brain image. Soft segmentation is also more flexible than hard segmentation. But the membership functions are usually sensitive to noise. In this paper, we proposed a multiphase soft segmentation model for nearly piecewise constant images based on stochastic principle, where intensities of the image are modeled as random variables with mixed Gaussian distribution. Our contributions lies in two aspects. On the one hand, by introducing mixed Gaussian distribution to the fidelity term, our model is robust to noise and bias. On the other hand, by developing a bi-direction projected primal dual hybrid gradient algorithm (PDHG), the model can be implemented efficiently with simplex constraint.