Implicit Surfaces with Globally Regularised and Compactly Supported Basis Functions
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.
Cite
Text
Walder et al. "Implicit Surfaces with Globally Regularised and Compactly Supported Basis Functions." Neural Information Processing Systems, 2006.Markdown
[Walder et al. "Implicit Surfaces with Globally Regularised and Compactly Supported Basis Functions." Neural Information Processing Systems, 2006.](https://mlanthology.org/neurips/2006/walder2006neurips-implicit/)BibTeX
@inproceedings{walder2006neurips-implicit,
title = {{Implicit Surfaces with Globally Regularised and Compactly Supported Basis Functions}},
author = {Walder, Christian and Chapelle, Olivier and Schölkopf, Bernhard},
booktitle = {Neural Information Processing Systems},
year = {2006},
pages = {273-280},
url = {https://mlanthology.org/neurips/2006/walder2006neurips-implicit/}
}