Creative Commons Attribution-ShareAlike 4.0 International
This œuvre, Reparameterization invariant metric on the space of curves, by Marc Arnaudon is licensed under a Creative Commons Attribution-ShareAlike 4.0 International license.

Reparameterization invariant metric on the space of curves


Reparameterization invariant metric on the space of curves
Publication details: 
This paper focuses on the study of open curves in a manifold M, and its aim is to define a reparameterization invariant distance on the space of such paths. We use the square root velocity function (SRVF) introduced by Srivastava et al. in [11] to define a reparameterization invariant metric on the space of immersions =Imm([0,1],M) by pullback of a metric on the tangent bundle T derived from the Sasaki metric. We observe that such a natural choice of Riemannian metric on T induces a first-order Sobolev metric on with an extra term involving the origins, and leads to a distance which takes into account the distance between the origins and the distance between the image curves by the SRVF parallel transported to a same vector space, with an added curvature term. This provides a generalized theoretical SRV framework for curves lying in a general manifold M.
Source et DOI
Vidéo
Voir la vidéo
Reparameterization invariant metric on the space of curves
Groupes / audience: