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




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.

Author(s): Steinke, F. and Hein, M. and Peters, J. and Schölkopf, B.
Journal: Computer Graphics Forum
Volume: 27
Number (issue): 2
Pages: 437-448
Year: 2008
Month: April
Day: 0

Department(s): Empirical Inference
Bibtex Type: Article (article)

Digital: 0
DOI: 10.1111/j.1467-8659.2008.01141.x
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: PDF


  title = {Manifold-valued Thin-plate Splines
  with Applications in Computer Graphics},
  author = {Steinke, F. and Hein, M. and Peters, J. and Sch{\"o}lkopf, B.},
  journal = {Computer Graphics Forum},
  volume = {27},
  number = {2},
  pages = {437-448},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  month = apr,
  year = {2008},
  month_numeric = {4}