Séminaire : Martin Bauer, Department of Mathematics - Florida State University

Shape Analysis: the challenge of geometric data

Abstract

The past decades have seen tremendous advances in imaging techniques, which have led to a significant growth in the quantity and complexity of data in fields such as biomedical imaging, neuroscience and medicine. 
Naturally, this prompted the emergence of new mathematical and algorithmic approaches for the analysis of such data, which led to the emergence and growth of fields such as geometric shape analysis and topological data analysis. Infinite dimensional Riemannian geometry has proven to be a powerful tool to deal with the challenges that arise in this context. In my talk I will give a short introduction to the general concept of infinite dimensional Riemannian geometry, where I will discuss several of the striking phenomena that might arise in this situation. I will then focus on reparametrization invariant  structures on spaces of immersions and, in particular, I will introduce the class of Sobolev metrics on spaces of surfaces. For this class of Riemannian metrics I will discuss the local and global well-posedness of the geodesic equations and properties of the geodesic distance. Finally, to show how we can use this setup in practice, I will discuss the numerical implementation of a statistical framework based on such metrics. 

Short biography

Martin Bauer is currently Associate Professor at Florida State University. Previously he was a PostDoc at the University of Vienna, where he completed his PhD under the supervison of Peter W. Michor. His research lies within the the field of infinite dimensional Riemannian geometry.

In particular Martin Bauer is interested in the study of manifolds of mappings, shape spaces and diffeomorphism groups.