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  Implicit Surfaces with Globally Regularised and Compactly Supported Basis Functions

Walder, C., Schölkopf, B., & Chapelle, O. (2007). Implicit Surfaces with Globally Regularised and Compactly Supported Basis Functions. In B. Schölkopf, J. Platt, & T. Hoffman (Eds.), Advances in Neural Information Processing Systems 19 (pp. 273-280). Cambridge, MA, USA: MIT Press.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0013-CBE5-7 Version Permalink: https://hdl.handle.net/21.11116/0000-0003-1DBF-7
Genre: Conference Paper

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 Creators:
Walder, C1, 2, 3, Author           
Schölkopf, B3, 4, Author           
Chapelle, O3, 4, Author           
Affiliations:
1Project group: Cognitive Engineering, Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_2528702              
2Department Human Perception, Cognition and Action, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497797              
3Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              
4Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              

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 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.

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 Dates: 2007-09
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: BibTex Citekey: 4191
 Degree: -

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Title: Twentieth Annual Conference on Neural Information Processing Systems (NIPS 2006)
Place of Event: Vancouver, BC, Canada
Start-/End Date: 2006-12-04 - 2006-12-07

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Title: Advances in Neural Information Processing Systems 19
Source Genre: Proceedings
 Creator(s):
Schölkopf, B1, Editor           
Platt, JC, Editor
Hoffman, T, Editor
Affiliations:
1 Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795            
Publ. Info: Cambridge, MA, USA : MIT Press
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 273 - 280 Identifier: ISBN: 0-262-19568-2