Name
Abstract | ||
|---|---|---|
This article provides an overview of various notions of shape spaces, including the space of parametrized and unparametrized curves, the space of immersions, the diffeomorphism group and the space of Riemannian metrics. We discuss the Riemannian metrics that can be defined thereon, and what is known about the properties of these metrics. We put particular emphasis on the induced geodesic distance, the geodesic equation and its well-posedness, geodesic and metric completeness and properties of the curvature. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1007/s10851-013-0490-z | Journal of Mathematical Imaging and Vision |
Keywords | Field | DocType |
Shape space,Diffeomorphism group,Manifolds of mappings,Landmark space,Surface matching,Riemannian geometry | Mathematical optimization,Scalar curvature,Curvature,Mathematical analysis,Geodesic map,Pure mathematics,Riemannian geometry,Isometry (Riemannian geometry),Exponential map (Riemannian geometry),Geodesic,Homogeneous space,Mathematics | Journal |
Volume | Issue | ISSN |
50 | 1-2 | Journal of Mathematical Imaging and Vision, 50, 1-2, 60-97, 2014 |
Citations | PageRank | References |
21 | 1.01 | 30 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Martin Bauer | 1 | 52 | 10.45 |
| M. Bruveris | 2 | 58 | 4.53 |
| Peter W. Michor | 3 | 33 | 2.36 |