A method for large diffeomorphic registration via broken geodesics
This work provides an improved method for large deformation registration, which is crucial for medical image analysis in longitudinal or inter-subject studies, addressing a limitation for researchers and practitioners in this field.
The paper addresses the limitation of Stationary Velocity Field (SVF) based non-rigid registration algorithms in capturing large deformations. It proposes a method to decompose large deformations into finite compositions of smaller deformations, forming a broken geodesic path, which allows for capturing large and complex deformations and produces qualitatively better results than state-of-the-art methods.
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.