Metrics, Shapes and Deformations
Thursday, November 16, 2000 - 11:00am - 12:00pm
Using a Riemannian point of view to design comparison methods and evaluate variations within high dimensional spaces such as shapes is a conceptually simple and quite generic approach. Adding robustness or invariance with respect to a group action in this framework leads, by projecting into orbits, to interesting theoretical issues and nice results, especially when groups of diffeomorphims come into the picture. After a quick review on how this approach may relate to known examples in the literature (Kendall's shape space, Grenander's deformable templates,...) we show how to design geodesic distances, and estimate diffeomorphisms between configurations of points in space, or between grey-colored images.