An Operator-Splitting Approach for Variational Optimal Control Formulations for Diffeomorphic Shape Matching

TL;DR

This paper introduces an operator-splitting numerical method for solving variational diffeomorphic shape matching problems, demonstrated on clinical cardiac data, improving computational efficiency and accuracy.

Contribution

It presents a novel, matrix-free operator splitting algorithm for diffeomorphic shape matching, enhancing existing variational and numerical approaches.

Findings

Successful application to real cardiac data

Improved computational efficiency

Accurate shape matching results

Abstract

We present formulations and numerical algorithms for solving diffeomorphic shape matching problems. We formulate shape matching as a variational problem governed by a dynamical system that models the flow of diffeomorphism $f_t \in \operatorname{diff}(\mathbb{R}^3)$. We overview our contributions in this area, and present an improved, matrix-free implementation of an operator splitting strategy for diffeomorphic shape matching. We showcase results for diffeomorphic shape matching of real clinical cardiac data in $\mathbb{R}^3$ to assess the performance of our methodology.