Manifold-valued Thin-Plate Splines with Applications in Computer Graphics
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Date
2008
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and Blackwell Publishing Ltd
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.
Description
@article{10.1111:j.1467-8659.2008.01141.x,
journal = {Computer Graphics Forum},
title = {{Manifold-valued Thin-Plate Splines with Applications in Computer Graphics}},
author = {Steinke, Florian and Hein, Matthias and Peters, Jan and Schoelkopf, Bernhard},
year = {2008},
publisher = {The Eurographics Association and Blackwell Publishing Ltd},
ISSN = {1467-8659},
DOI = {10.1111/j.1467-8659.2008.01141.x}
}