Efficient Variational Approaches for Deformable Registration of Images

Abstract

Dirichlet, anisotropic, and Huber regularization terms are presented for efficient registration of deformable images. Image registration, an ill-posed optimization problem, is solved using a gradient-descent-based method and some fundamental theorems in calculus of variations. Euler-Lagrange equations with homogeneous Neumann boundary conditions are obtained. These equations are discretized by multigrid and finite difference numerical techniques. The method is applied to the registration of brain MR images of size $65\times 65$. Computational results indicate that the presented method is quite fast and efficient in the registration of deformable medical images.