This paper discusses non-parametric regression between Riemannian manifolds. This learning problem arises frequently in many application areas ranging from signal processing, computer vision, over robotics to computer graphics. We present a new algorithmic scheme for the solution of this general learning problem based on regularized empirical risk minimization. The regularization functional takes into account the geometry of input and output manifold, and we show that it implements a prior which is particularly natural. Moreover, we demonstrate that our algorithm performs well in a difficult surface registration problem.
| Author(s): | Steinke, F. and Hein, M. |
| Book Title: | Advances in neural information processing systems 21 |
| Journal: | Advances in neural information processing systems 21 : 22nd Annual Conference on Neural Information Processing Systems 2008 |
| Pages: | 1561-1568 |
| Year: | 2009 |
| Month: | June |
| Day: | 0 |
| Editors: | Koller, D. , D. Schuurmans, Y. Bengio, L. Bottou |
| Publisher: | Curran |
| Bibtex Type: | Conference Paper (inproceedings) |
| Address: | Red Hook, NY, USA |
| Event Name: | Twenty-Second Annual Conference on Neural Information Processing Systems (NIPS 2008) |
| Event Place: | Vancouver, BC, Canada |
| Digital: | 0 |
| Electronic Archiving: | grant_archive |
| ISBN: | 978-1-605-60949-2 |
| Language: | en |
| Organization: | Max-Planck-Gesellschaft |
| School: | Biologische Kybernetik |
| Links: | |
BibTex
@inproceedings{5469,
title = {Non-parametric Regression between Riemannian Manifolds},
journal = {Advances in neural information processing systems 21 : 22nd Annual Conference on Neural Information Processing Systems 2008},
booktitle = {Advances in neural information processing systems 21},
abstract = {This paper discusses non-parametric regression between Riemannian manifolds. This learning problem arises frequently in many application areas ranging from signal processing, computer vision, over robotics to computer graphics. We present a new algorithmic scheme for the solution of this general learning problem based on regularized empirical risk minimization. The regularization functional takes into account the geometry of input and output manifold, and we show that it implements a prior which is particularly natural. Moreover, we demonstrate that our algorithm performs well in a difficult surface registration problem.},
pages = {1561-1568},
editors = {Koller, D. , D. Schuurmans, Y. Bengio, L. Bottou},
publisher = {Curran},
organization = {Max-Planck-Gesellschaft},
school = {Biologische Kybernetik},
address = {Red Hook, NY, USA},
month = jun,
year = {2009},
slug = {5469},
author = {Steinke, F. and Hein, M.},
month_numeric = {6}
}