Computing distances and geodesics between manifold-valued curves in the SRV framework

Understand

This paper focuses on the study of open curves in a Riemannian manifold M, and proposes a reparametrization invariant metric on the space of such paths.

• We use the square root velocity function (SRVF) introduced by Srivastava et al.
• to define a Riemannian metric on the space of immersions M'=Imm([0,1],M) by pullback of a natural metric on the tangent bundle TM'.
• This induces a first-order Sobolev metric on M' and leads to a distance which takes into account the distance between the origins in M and the L2-distance between the SRV representations of the curves.