A new variational shape-from-orientation approach to correcting intensity inhomogeneities in MR images

A new algorithm based on shape from orientation formulation in a regularization framework is proposed for correcting intensity inhomogeneities in MR images. Unlike most previous methods, this algorithm is fully automatic and very efficient. In addition, it can be applied to a wide variety of images since no prior classification knowledge is assumed. In this algorithm, the authors use a finite element basis to represent the bias field function. Orientation constraints are computed at the nodes of the finite element discretization away from the boundary between different regions. The selection of reliable orientation constraints is facilitated by the goodness of fitting a first-order polynomial model to the neighborhood of each nodal location. The selected orientation constraints are integrated in a regularization framework, which leads to the minimization of a convex and quadratic energy function. This energy minimization is achieved by solving a linear system with a large, sparse, symmetric and positive semi-definite stiffness matrix. The authors employ an adaptive preconditioned conjugate gradient algorithm to solve the linear system efficiently. Experimental results on a variety of MR images are given to demonstrate the effectiveness and efficiency of the proposed algorithm.