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arXiv · 2401.04743

Optimal matching between curves in a manifold

Alice Le Brigant·Marc Arnaudon·Frédéric Barbaresco
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Abstract

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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Alice Le Brigant, Marc Arnaudon, Frédéric Barbaresco. 2024-01-09. Optimal matching between curves in a manifold. https://arxiv.org/abs/2401.04743

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