PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Manifold-valued Thin-plate Splines with Applications in Computer Graphics
F. Steinke, M. Hein, J. Peters and B. Schölkopf
Computer Graphics Forum Volume 27, Number 2, pp. 437-448, 2008.

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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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Brain Computer Interfaces
Theory & Algorithms
ID Code:4328
Deposited By:Bernhard Schölkopf
Deposited On:13 March 2009