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Implicit Surfaces with Globally Regularised and Compactly Supported Basis Functions

2007

Conference Paper

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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.
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

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

Event Name: 20th Annual Conference on Neural Information Processing Systems (NIPS 2006)
Event Place: Vancouver, BC, Canada

Address: Cambridge, MA, USA
Digital: 0
ISBN: 0-262-19568-2
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

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BibTex

@inproceedings{4191,
  title = {Implicit Surfaces with Globally Regularised and Compactly Supported Basis Functions},
  author = {Walder, C. and Sch{\"o}lkopf, B. and Chapelle, O.},
  journal = {Advances in Neural Information Processing Systems 19: Proceedings of the 2006 Conference},
  booktitle = {Advances in Neural Information Processing Systems 19},
  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},
  month_numeric = {9}
}