Reparameterization invariant metric on the space of curves
LE BRIGANT, Alice
Institut de Mathématiques de Bordeaux [IMB]
Thales Research and Technology [Palaiseau]
Institut de Mathématiques de Bordeaux [IMB]
Thales Research and Technology [Palaiseau]
LE BRIGANT, Alice
Institut de Mathématiques de Bordeaux [IMB]
Thales Research and Technology [Palaiseau]
< Reduce
Institut de Mathématiques de Bordeaux [IMB]
Thales Research and Technology [Palaiseau]
Language
en
Document de travail - Pré-publication
English Abstract
This paper focuses on the study of open curves in a manifold M , and proposes a reparameterization invariant metric on the space of such paths. We use the square root velocity function (SRVF) introduced by Srivastava et ...Read more >
This paper focuses on the study of open curves in a manifold M , and proposes a reparameterization invariant metric 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 M' = Imm([0,1], M) by pullback of a metric on the tangent bundle TM' derived from the Sasaki metric. We observe that such a natural choice of Riemannian metric on TM' induces a first-order Sobolev metric on M' 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 SRV representations of the curves. The geodesic equations for this metric are given, as well as an idea of how to compute the exponential map for observed trajectories in applications. This provides a generalized theoretical SRV framework for curves lying in a general manifold M .Read less <
English Keywords
reparameterization invariance
shape analysis
trajectories on manifolds
square-root velocity function
Origin
Hal imported