7,566 research outputs found
Why Use Sobolev Metrics on the Space of Curves
We study reparametrization invariant Sobolev metrics on spaces of regular curves. We discuss their completeness properties and the resulting usability for applications in shape analysis. In particular, we will argue, that the development of efficient numerical methods for higher order Sobolev type metrics is an extremely desirable goal
Computing distances and geodesics between manifold-valued curves in the SRV framework
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. The geodesic equations for this metric are
given and exploited to define an exponential map on M'. The optimal deformation
of one curve into another can then be constructed using geodesic shooting,
which requires to characterize the Jacobi fields of M'. The particular case of
curves lying in the hyperbolic half-plane is considered as an example, in the
setting of radar signal processing
The ANTARES Collaboration: Contributions to ICRC 2017 Part III: Searches for dark matter and exotics, neutrino oscillations and detector calibration
Papers on the searches for dark matter and exotics, neutrino oscillations and
detector calibration, prepared for the 35th International Cosmic Ray Conference
(ICRC 2017, Busan, South Korea) by the ANTARES Collaboratio
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