Abstract

The accelerated development of imaging techniques in biomedical engineering is challenging mathematicians and computer scientists to develop appropriate methods for the representation and the statistical analysis of various geometrically structured data like submanifolds.

We will first explain how the concepts of homogeneous spaces and riemannian manifolds embedded in the large deformation diffeomorphic metric mapping setting (LDDMM) and the introduction of mathematical currents by Glaunes and Vaillant in this setting have been a powerful and effective framework to support local statistical analysis in more and more complex shape spaces.

We will then discuss a new extension when the submanifolds are the supports of informative fields that need to be also analyzed in a common geometrical-functional representation (joint work with Nicolas Charon).