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Implicit Surfaces with Globally Regularised and Compactly Supported Basis Functions

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Walder,  C
Project group: Cognitive Engineering, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Department Human Perception, Cognition and Action, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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

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

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Citation

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.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-CBE5-7
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.