An operator-splitting approach for variational optimal control formulations for diffeomorphic shape matching

Andreas Mang, Jiwen He, Robert Azencott

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 ft∈diff(R3)<math><msub is="true"><mrow is="true"><mi is="true">f</mi></mrow><mrow is="true"><mi is="true">t</mi></mrow></msub><mo is="true">∈</mo><mtext is="true">diff</mtext><mo stretchy="false" is="true">(</mo><msup is="true"><mrow is="true"><mi mathvariant="double-struck" is="true">R</mi></mrow><mrow is="true"><mn is="true">3</mn></mrow></msup><mo stretchy="false" is="true">)</mo></math>. 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 R3<math><msup is="true"><mrow is="true"><mi mathvariant="double-struck" is="true">R</mi></mrow><mrow is="true"><mn is="true">3</mn></mrow></msup></math> to assess the performance of our methodology.

External IDs:dblp:journals/jcphy/MangHA23