A method for large diffeomorphic registration via broken geodesics

TL;DR

This paper introduces a novel approach for large diffeomorphic registration by decomposing complex deformations into smaller steps, resulting in improved accuracy and a new metric for measuring deformation extent.

Contribution

It proposes a method to break down large deformations into finite compositions of small ones, forming a broken geodesic path that better captures complex deformations.

Findings

Method captures large, complex deformations effectively.

Produces qualitatively better registration results than existing methods.

Registration metric correlates well with deformation degree.

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. SVF based methods form a metric-free framework which captures a finite dimensional submanifold of deformations embedded in the infinite dimensional smooth manifold of diffeomorphisms. However, these methods cover only a limited degree of deformations. In this paper, we address this limitation and define an approximate metric space for the manifold of diffeomorphisms $\mathcal{G}$. We propose a method to break down the large deformation into finite compositions of small deformations. This results in a broken geodesic path on $\mathcal{G}$ 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 the state-of-the-art methods. The results also demonstrate that the proposed registration metric is a good indicator of the degree of deformation.