A variational multiphase model for simultaneous MR image segmentation and bias correction

In this paper, we present a multiphase segmentation model for MR images in the presence of strong intensity inhomogeneity. The problem is formalized as a constraint min-max optimization problem that consists both primal and dual variables. We use the primal dual hybrid gradient (PDHG) algorithm to alternately solve for the optimal solutions. The proposed algorithm is quite efficient in that all the subproblems have closed form solutions. Moreover, the computational complexity is shown to be linear with respect to the size of the image. Numerical experiments on various images demonstrated that our algorithm outperforms recently developed methods in terms of efficiency and accuracy.