Incorporating growth models in Riemannian shape spaces.

24^th February 2024, 14:00
Laurent Younes
Johns Hopkins University, USA

Abstract

We review and introduce some Riemannian metrics and evolution equations in the context of diffeomorphic shape analysis. After a short discussion of various approaches at building Riemannian metrics on shape spaces (with a special focus on the foundations of the large deformation diffeomorphic metric mapping algorithm), we introduce elastic metrics and growth models that can be derived from them. In the latter context, a new class of metrics, involving an infinitesimal growth tensor, is considered and some of its properties are studied.