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  Manifold-valued Thin-plate Splines with Applications in Computer Graphics

Steinke, F., Hein, M., Peters, J., & Schölkopf, B. (2008). Manifold-valued Thin-plate Splines with Applications in Computer Graphics. Computer Graphics Forum, 27(2), 437-448. doi:10.1111/j.1467-8659.2008.01141.x.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-C9CB-4 Version Permalink: http://hdl.handle.net/21.11116/0000-0003-3112-1
Genre: Journal Article

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 Creators:
Steinke, F1, 2, Author              
Hein, M, Author              
Peters, J1, 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: We present a generalization of thin-plate splines for interpolation and approximation of manifold-valued data, and demonstrate its usefulness in computer graphics with several applications from different fields. The cornerstone of our theoretical framework is an energy functional for mappings between two Riemannian manifolds which is independent of parametrization and respects the geometry of both manifolds. If the manifolds are Euclidean, the energy functional reduces to the classical thin-plate spline energy. We show how the resulting optimization problems can be solved efficiently in many cases. Our example applications range from orientation interpolation and motion planning in animation over geometric modelling tasks to color interpolation.

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 Dates: 2008-04
 Publication Status: Published in print
 Pages: -
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 Table of Contents: -
 Rev. Method: -
 Identifiers: DOI: 10.1111/j.1467-8659.2008.01141.x
BibTex Citekey: 4944
 Degree: -

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Title: Computer Graphics Forum
  Other : Computer Graphics Forum : journal of the European Association for Computer Graphics
  Abbreviation : Comput. Graph. Forum
Source Genre: Journal
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Publ. Info: Oxford : Blackwell-Wiley
Pages: - Volume / Issue: 27 (2) Sequence Number: - Start / End Page: 437 - 448 Identifier: ISSN: 0167-7055
CoNE: https://pure.mpg.de/cone/journals/resource/954925483671