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Thin-Plate Splines Between Riemannian Manifolds




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.

Author(s): Steinke, F. and Hein, M. and Schölkopf, B.
Year: 2008
Month: June
Day: 0

Department(s): Empirical Inference
Bibtex Type: Talk (talk)

Digital: 0
Event Name: Workshop on Geometry and Statistics of Shapes 2008
Event Place: Bonn, Germany
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: Web


  title = {Thin-Plate Splines Between Riemannian Manifolds},
  author = {Steinke, F. and Hein, M. and Sch{\"o}lkopf, B.},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  month = jun,
  year = {2008},
  month_numeric = {6}