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

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 $f_t\in \mathrm{diff}({\mathbb{R}}^3)$. 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.