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  Implicit Surface Modelling with a Globally Regularised Basis of Compact Support

Walder, C., Schölkopf, B., & Chapelle, O. (2006). Implicit Surface Modelling with a Globally Regularised Basis of Compact Support. Computer Graphics Forum, 25(3), 635-644. doi:10.1111/j.1467-8659.2006.00983.x.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-D02F-2 Version Permalink: http://hdl.handle.net/21.11116/0000-0003-1D9E-C
Genre: Journal Article

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 Creators:
Walder, C1, 2, 3, Author              
Schölkopf, B3, 4, Author              
Chapelle, O3, 4, Author              
Affiliations:
1Department Human Perception, Cognition and Action, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497797              
2Project group: Cognitive Engineering, Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_2528702              
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 globally smooth analytic function that represents a surface implicitly by way of its zero set, given sample points with surface normal vectors. The contributions of the paper include a novel means of regularising multi-scale compactly supported basis functions that leads to the desirable interpolation properties previously only associated with fully supported bases. We also provide a regularisation framework for simpler and more direct treatment of surface normals, along with a corresponding generalisation of the representer theorem lying at the core of kernel-based machine learning methods. We demonstrate the techniques on 3D problems of up to 14 million data points, as well as 4D time series data and four-dimensional interpolation between three-dimensional shapes.

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 Dates: 2006-09
 Publication Status: Published in print
 Pages: -
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 Rev. Method: -
 Identifiers: DOI: 10.1111/j.1467-8659.2006.00983.x
BibTex Citekey: 3958
 Degree: -

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Title: Computer Graphics Forum
  Other : Computer Graphics Forum : journal of the European Association for Computer Graphics
  Abbreviation : Comput. Graph. Forum
Source Genre: Journal
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Publ. Info: Oxford : Blackwell-Wiley
Pages: - Volume / Issue: 25 (3) Sequence Number: - Start / End Page: 635 - 644 Identifier: ISSN: 0167-7055
CoNE: https://pure.mpg.de/cone/journals/resource/954925483671