A Lie-Group Approach to Rigid Image Registration

TL;DR

This paper introduces a Lie-group based framework for rigid image registration, utilizing approximate-Newton methods on manifolds to achieve efficient and locally quadratically convergent algorithms, with extensions for multi-modal images.

Contribution

It develops a novel Lie-group approach for image registration, applying approximate-Newton methods on manifolds and proposing strategies to reduce computational costs.

Findings

Quadratic convergence of the proposed algorithms.

Effective strategies using quasi Monte Carlo and spline functions.

Extension capability for multi-modal 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.