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Implicit Surface Modelling with a Globally Regularised Basis of Compact Support

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons84294

Walder,  C
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Department Human Perception, Cognition and Action, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84193

Schölkopf,  B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons83855

Chapelle,  O
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

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.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-D02F-2
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.