A sub-riemannian metric from constrained deformations

Appears in collection : Journée sous-riemannienne 2018

A general method to study a population of objects (images, meshes) is to examine how these objects can be deformed by a chosen class of diffeomorphisms. When these objects satisfy some constraints (for instance biological constraints), it can be relevant to incorporate them in the choice of diffeomorphisms. We developed a generic framework to build constrained diffeomorphisms and showed that it allows to define a sub-riemannian structure on the space of objects under study. I will present this framework and show how it can be used in several situations.