Nicolas Charon, “Diffeomorphic registration and metamorphosis in the space of varifolds”
Nicolas Charon, PhD
Assistant Professor
Department of Applied Mathematics
and Statistics
Johns Hopkins University
“Diffeomorphic registration and metamorphosis in the space of varifolds”
Abstract: Building on the versatility of the Large Deformation Diffeomorphic Metric Mapping (LDDMM) model for the registration and metric comparison of geometric objects such as images, point clouds, surfaces…, we introduce an extended formulation of LDDMM on a space of generalized measures known as varifolds. A varifold is essentially a notion of directional measure which provides a convenient representation of any submanifold embedded in an Euclidean space but also encompasses various other and less structured geometric data. By introducing a mathematical framework for the estimation of optimal diffeomorphic transformations between two varifolds as well as the adequate numerical methods to tackle the corresponding optimal control problems, we can extend the scope of the LDDMM registration approach to deal efficiently with situations involving e.g. noisy, incomplete or inconsistent shapes.
The second part of the talk will discuss a varifold metamorphosis model in which the geometric deformation is further complemented with a transformation process on the varifold weight at each point (i.e. its local mass). This is motivated by the limitations of purely diffeomorphic methods in the case of imbalanced, partially observed or topologically inconsistent data. We specifically define and study a new Riemannian metric between varifolds that combine the LDDMM energy with the Fisher-Rao metric of the change in weight. We also tackle the numerical implementation of this model and show a few preliminary results as proof of concept.
This is joint work with Hsi-Wei Hsieh.
Biography: Nicolas Charon is currently an Assistant Professor in the Department of Applied Mathematics and Statistics and the Center of Imaging Sciences at Johns Hopkins University. Prior to this position, Nicolas obtained his PhD in Mathematics from Ecole normale supérieure de Cachan in 2013 under the supervision of Pr. Alain Trouvé, and worked as a post-doctoral researcher at University of Copenhagen in Denmark.
His main research interests are in morphological shape analysis and geometric methods for applications to medical imaging and computational anatomy. Specifically, Nicolas is interested in mathematical and numerical models for the representation, registration and statistical analysis of geometric structures occurring in the anatomy and in biology.
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Meeting ID: 993 0411 4570