Sobolev metrics on shape space of surfaces

Event details
Date | 01.04.2014 |
Hour | 16:15 › 17:15 |
Speaker | Philipp Harms |
Location |
MA A3 31
|
Category | Conferences - Seminars |
Geometry and Dynamics Seminar
Abstract: Many procedures in science, engineering and medicine produce data in the form of geometric shapes. Mathematically, a shape can be modeled as an unparameterized submanifold of some fixed ambient space. Endowing shape space with a Riemannian metric opens up the world of Riemannian differential geometry with geodesics, gradient flows, parallel transport and curvature. The Riemannian metric can be induced from metrics on the diffeomorphism group of the ambient space (outer metrics) or from metrics on the space of parameterized immersions (inner metrics). I will give an introduction to both approaches and discuss the second one in more detail. More specifically, I will define Sobolev-type inner metrics, discuss properties of the resulting geodesic distance and geodesic equation, and present some simple numerical examples of geodesics.
Abstract: Many procedures in science, engineering and medicine produce data in the form of geometric shapes. Mathematically, a shape can be modeled as an unparameterized submanifold of some fixed ambient space. Endowing shape space with a Riemannian metric opens up the world of Riemannian differential geometry with geodesics, gradient flows, parallel transport and curvature. The Riemannian metric can be induced from metrics on the diffeomorphism group of the ambient space (outer metrics) or from metrics on the space of parameterized immersions (inner metrics). I will give an introduction to both approaches and discuss the second one in more detail. More specifically, I will define Sobolev-type inner metrics, discuss properties of the resulting geodesic distance and geodesic equation, and present some simple numerical examples of geodesics.
Practical information
- Expert
- Free
Organizer
- Martins Bruveris, Sonja Hohloch, Marc Troyanov
Contact
- sonja.hohloch@epfl.ch