Empirical Inference
Conference Paper
2007
Implicit Surfaces with Globally Regularised and Compactly Supported Basis Functions
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Empirical Inference
Empirical Inference
We consider the problem of constructing a function whose zero set is to represent a surface, given sample points with surface normal vectors. The contributions include a novel means of regularising multi-scale compactly supported basis functions that leads to the desirable properties previously only associated with fully supported bases, and show equivalence to a Gaussian process with modified covariance function. We also provide a regularisation framework for simpler and more direct treatment of surface normals, along with a corresponding generalisation of the representer theorem. We demonstrate the techniques on 3D problems of up to 14 million data points, as well as 4D time series data.
| Author(s): | Walder, C. and Schölkopf, B. and Chapelle, O. |
| Links: | |
| Book Title: | Advances in Neural Information Processing Systems 19 |
| Journal: | Advances in Neural Information Processing Systems 19: Proceedings of the 2006 Conference |
| Pages: | 273-280 |
| Year: | 2007 |
| Month: | September |
| Day: | 0 |
| Editors: | B Sch{\"o}lkopf and J Platt and T Hofmann |
| Publisher: | MIT Press |
| BibTeX Type: | Conference Paper (inproceedings) |
| Address: | Cambridge, MA, USA |
| Event Name: | 20th Annual Conference on Neural Information Processing Systems (NIPS 2006) |
| Event Place: | Vancouver, BC, Canada |
| Digital: | 0 |
| Electronic Archiving: | grant_archive |
| ISBN: | 0-262-19568-2 |
| Language: | en |
| Organization: | Max-Planck-Gesellschaft |
| School: | Biologische Kybernetik |
BibTeX
@inproceedings{4191,
title = {Implicit Surfaces with Globally Regularised and Compactly Supported Basis Functions},
journal = {Advances in Neural Information Processing Systems 19: Proceedings of the 2006 Conference},
booktitle = {Advances in Neural Information Processing Systems 19},
abstract = {We consider the problem of constructing a function whose zero set is to represent a surface, given sample points with surface normal vectors. The contributions include a novel means of regularising multi-scale compactly supported basis functions that leads to the desirable properties previously only associated with fully supported bases, and show equivalence to a Gaussian process with modified
covariance function. We also provide a regularisation framework for simpler and more direct treatment of surface normals, along with a corresponding generalisation of the representer theorem. We demonstrate the techniques on 3D
problems of up to 14 million data points, as well as 4D time series data.},
pages = {273-280},
editors = {B Sch{\"o}lkopf and J Platt and T Hofmann},
publisher = {MIT Press},
organization = {Max-Planck-Gesellschaft},
school = {Biologische Kybernetik},
address = {Cambridge, MA, USA},
month = sep,
year = {2007},
author = {Walder, C. and Sch{\"o}lkopf, B. and Chapelle, O.},
month_numeric = {9}
}