A robust parametric method for bias field estimation and segmentation of MR images

This paper proposes a new energy minimization framework for simultaneous estimation of the bias field and segmentation of tissues for magnetic resonance images. The bias field is modeled as a linear combination of a set of basis functions, and thereby parameterized by the coefficients of the basis functions. We define an energy that depends on the coefficients of the basis functions, the membership functions of the tissues in the image, and the constants approximating the true signal from the corresponding tissues. This energy is convex in each of its variables. Bias field estimation and image segmentation are simultaneously achieved as the result of minimizing this energy. We provide an efficient iterative algorithm for energy minimization, which converges to the optimal solution at a fast rate. A salient advantage of our method is that its result is independent of initialization, which allows robust and fully automated application. The proposed method has been successfully applied to 3-Tesla MR images with desirable results. Comparisons with other approaches demonstrate the superior performance of this algorithm.