Implicit Surfaces with Globally Regularised and Compactly Supported Basis Functions
Christian Walder, Bernhard Schölkopf, Olivier Chapelle · The MIT Press eBooks · 2007
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.