ICTEAM > ELEN > ISPGroup > ISPS > Calendar > ABS081014

Title: "Interpolation on Riemannian manifolds with a {$C^1$} piecewize Bézier path"

Speaker: Pierre-Yves Gousenbourger

Location: "Nyquist" Seminar Room (a164, close to Shannon seminar room) Place du Levant 3, Maxwell Building, 1st floor

Date / Time (duration): Wednesday 08/10/2014, 10h00 (~ 45')

Abstract: Nowadays, more and more problems are solved through specific manifold formulation. This often allows important reduction of computation time and/or memory management compared to classical formulations on the classical Euclidean space (because of non-linear constraints like restricting the solutions to a certain subdomain of a larger ambiant space). Interpolation and optimization tools can be useful for solving some of these problems (like defining the optimal trajectory of a humanitory plane dropping supplies, or fitting two objects orientations). However, current procedures are only defined on the Euclidean space. In this presentation, I focus on interpolation methods and, more precisely, I propose a new general framework to fit a path through a finite set of data points lying on a Riemannian manifold. The path takes the form of a continuously-differentiable concatenation of Riemannian Bézier segments. This framework will be illustrated by results on the Euclidean space, the sphere, the orthogonal group and the shape manifold.​ The content of this presentation meets also very recent research carried out in this institute for providing novel efficient manifold-based optimization methods.

(slides)

Last updated October 08, 2014, at 05:08 PM

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