Name
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. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1111/j.1467-8659.2008.01141.x | COMPUTER GRAPHICS FORUM |
Keywords | Field | DocType |
thin plate spline,computer graphic | Spline (mathematics),Mathematical optimization,Thin plate spline,Box spline,Spline interpolation,Algebra,Computer science,Interpolation,Theoretical computer science,Energy functional,Polyharmonic spline,Manifold | Journal |
Volume | Issue | ISSN |
27 | 2 | 0167-7055 |
Citations | PageRank | References |
2 | 0.41 | 8 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Florian Steinke | 1 | 269 | 19.19 |
| Matthias Hein | 2 | 663 | 62.80 |
| Jan Peters | 3 | 3553 | 264.28 |
| Bernhard Schölkopf | 4 | 23120 | 3091.82 |