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Communication Dans Un Congrès Année : 2017

Optimal matching between curves in a manifold

Résumé

This paper is concerned with the computation of an optimal matching between two manifold-valued curves. Curves are seen as elements of an infinite-dimensional manifold and compared using a Riemannian metric that is invariant under the action of the reparameterization group. This group induces a quotient structure classically interpreted as the ”shape space”. We introduce a simple algorithm allowing to compute geodesics of the quotient shape space using a canonical decomposition of a path in the associated principal bundle. We consider the particular case of elastic metrics and show simulations for open curves in the plane, the hyperbolic plane and the sphere.
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Dates et versions

hal-04374199 , version 1 (08-01-2024)

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Alice Le Brigant, Marc Arnaudon, Frédéric Barbaresco. Optimal matching between curves in a manifold. Geometric Science of Information 2017, 2017, Paris, France. ⟨hal-04374199⟩
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