A Lie-Group Approach to Rigid Image Registration

Abstract: The task of image restration is to find the spatial correspondence of two or more given images. In this paper we assume that the correspondence is given either by an Euclidean, or by an affine volume-preserving transformation. Since the registration problem can be seen as an optimization problem on a finite dimensional Lie group, we use a recently developed framework of approximate-Newton methods on manifolds, which leads to locally quadratically convergent algorithms. To reduce numerical costs, we present two strategies: One makes use of the quasi Monte Carlo Method and the other ends up with an algorithm acting on spline function spaces. An extension for multi-modal image registration is given as well.