PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Implicit Surfaces with Globally Regularised and Compactly Supported Basis Functions
Christian Walder, Bernhard Schölkopf and Olivier Chapelle
In: 20th Annual Conference on Neural Information Processing Systems, 4-9 Dec 2006, Vancouver / Whistler, Canada.


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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EPrint Type:Conference or Workshop Item (Poster)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:3116
Deposited By:Bernhard Schölkopf
Deposited On:21 December 2007