Constructing reparameterization invariant metrics on spaces of plane curves
نویسندگان
چکیده
منابع مشابه
Constructing Reparameterization Invariant Metrics on Spaces of Plane Curves
Metrics on shape spaces are used to describe deformations that take one shape to another, and to define a distance between shapes. We study a family of metrics on the space of curves, which includes several recently proposed metrics, for which the metrics are characterised by mappings into vector spaces where geodesics can be easily computed. This family consists of Sobolev-type Riemannian metr...
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Metrics on shape space are used to describe deformations that take one shape to another, and to determine a distance between them. We study a family of metrics on the space of curves, that includes several recently proposed metrics, for which the metrics are characterised by mappings into vector spaces where geodesics can be easily computed. This family consists of Sobolev-type Riemannian metri...
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We focus on the study of time-varying paths in the two-dimensional hyperbolic space, and our aim is to define a reparameterization invariant distance on the space of such paths. We adapt the geodesical distance on the space of parameterized plane curves given by Bauer et al. in [1] to the space Imm([0, 1],H) of parameterized curves in the hyperbolic plane. We present a definition which enables ...
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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...
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ژورنال
عنوان ژورنال: Differential Geometry and its Applications
سال: 2014
ISSN: 0926-2245
DOI: 10.1016/j.difgeo.2014.04.008