Variational Second-Order Interpolation on the Group of Diffeomorphisms with a Right-Invariant Metric

Abstract

In this note, we propose a variational framework in which the minimization of the acceleration on the group of diffeomorphisms endowed with a right-invariant metric is well-posed. It relies on constraining the acceleration to belong to a Sobolev space of higher-order than the order of the metric in order to gain compactness. It provides the theoretical guarantee of existence of minimizers which is compulsory for numerical simulations.

Publication
Mathematics of shapes and applications