Alain Trouvé: Diffeomorphometry, geodesic shooting and the selection of low dimensional manifolds in shape spaces

When facing the nonlinear nature of shapes, the idea of considering shape spaces as infinite dimensional riemannian manifolds is very natural but the proper definition of actual shape spaces equipped with a completely specified metric may be quite challenging. The construction of shape spaces via the action of diffeomorphisms offers the rich and versatile diffeomorphometric framework with applications to computational anatomy in medical imaging. In this talk I will recall the basics of diffeomoprhometry and then explain important issues related to the selection of low dimensional submanifolds in shape spaces. We will see that this goes beyond tangent PCA with interesting relations to the matrix completion problem.