A New Variational Shape-from-orientation Approach to Correcting Intensity Inhomogeneities in Magnetic Resonance Images

A new intensity inhomogeneity correction algorithm based on a variational shape-from-orientation formulation is presented. Unlike most previous methods, the proposed algorithm is fully automatic, widely applicable and very efficient. Since no prior classification knowledge about the image is assumed in the proposed algorithm, it can be applied to correct intensity inhomogeneities for a wide variety of medical images. In this paper, a finite-element method is used to model the smooth bias-field function. Orientation constraints for the bias-field function are computed at the nodal locations of the regular discretization grid away from the boundary between different class regions. The selection of reliable orientation constraints is facilitated by the goodness of fit of a first-order polynomial model to the neighborhood of each nodal location. The automatically selected orientation constraints are integrated in a regularization framework, which leads to minimization of a convex and quadratic energy function. This energy minimization is accomplished by solving a linear system with a large, sparse, symmetric and positive semi-definite stiffness matrix. We employ an adaptive preconditioned conjugate-gradient algorithm to solve the linear system very efficiently. Experimental results on a variety of magnetic resonance images are given to demonstrate the effectiveness and efficiency of the proposed algorithm.