A Method for Image Registration via Broken Geodesics

Abstract

Anatomical variabilities seen in longitudinal data or inter-subject data is usually described by the underlying deformation, captured by non-rigid registration of these images. Stationary Velocity Field (SVF) based non-rigid registration algorithms are widely used for registration. However, these methods cover only a limited degree of deformations. We address this limitation and define an approximate metric space for the manifold of diffeomorphisms G. We propose a method to break down the large deformation into finite set of small sequential deformations. This results in a broken geodesic path on G and its length now forms an approximate registration metric. We illustrate the method using a simple, intensity-based, log-demon implementation. Validation results of the proposed method show that it can capture large and complex deformations while producing qualitatively better results than state-of-the-art methods. The results also demonstrate that the proposed registration metric is a good indicator of the degree of deformation.