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  Thin-Plate Splines Between Riemannian Manifolds

Steinke, F., Hein, M., & Schölkopf, B. (2008). Thin-Plate Splines Between Riemannian Manifolds. Talk presented at HIM Workshop: Geometry and Statistics of Shapes 2008. Bonn, Germany. 2008-06-09 - 2008-06-14.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-C94F-D Version Permalink: http://hdl.handle.net/21.11116/0000-0003-A9F2-D
Genre: Talk

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 Creators:
Steinke, F1, 2, Author              
Hein, M1, 2, Author              
Schölkopf, B1, 2, Author              
Affiliations:
1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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 Abstract: With the help of differential geometry we describe a framework to define a thin-plate spline like energy for maps between arbitrary Riemannian manifolds. The so-called Eells energy only depends on the intrinsic geometry of the input and output manifold, but not on their respective representation. The energy can then be used for regression between manifolds, we present results for cases where the outputs are rotations, sets of angles, or points on 3D surfaces. In the future we plan to also target regression where the output is an element of "shape space", understood as a Riemannian manifold. One could also further explore the meaning of the Eells energy when applied to diffeomorphisms between shapes, especially with regard to its potential use as a distance measure between shapes that does not depend on the embedding or the parametrisation of the shapes.

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 Dates: 2008-06
 Publication Status: Published online
 Pages: -
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 Rev. Method: -
 Identifiers: BibTex Citekey: 5250
 Degree: -

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Title: HIM Workshop: Geometry and Statistics of Shapes 2008
Place of Event: Bonn, Germany
Start-/End Date: 2008-06-09 - 2008-06-14
Invited: Yes

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