A method for large diffeomorphic registration via broken geodesics

• URL: http://arxiv.org/abs/2011.14298v2
• Date: Sun, 3 Jan 2021 05:49:37 GMT
• Title: A method for large diffeomorphic registration via broken geodesics
• Authors: Alphin J. Thottupattu, Jayanthi Sivaswamy, Venkateswaran P. Krishnan
• Abstract summary: Anatomical variabilities seen in longitudinal data or inter-subject data are usually described by the underlying deformation. Non-rigid registration algorithms are widely used for registration. We propose a method to break down the large deformation into finite compositions of small deformations.
• Score: 3.2188961353850187
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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