Implicit Surfaces with Globally Regularised and Compactly Supported Basis Functions

Part of Advances in Neural Information Processing Systems 19 (NIPS 2006)

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Christian Walder, Olivier Chapelle, Bernhard Schölkopf


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.