Implicit Surface Modelling as an Eigenvalue Problem
Abstract
We discuss the problem of fitting an implicit shape model to a set of points sampled from a co-dimension one manifold of arbitrary topology. The method solves a non-convex optimisation problem in the embedding function that defines the implicit by way of its zero level set. By assuming that the solution is a mixture of radial basis functions of varying widths we attain the globally optimal solution by way of an equivalent eigenvalue problem, without using or constructing as an intermediate step the normal vectors of the manifold at each data point. We demonstrate the system on two and three dimensional data, with examples of missing data interpolation and set operations on the resultant shapes.
Cite
Text
Walder et al. "Implicit Surface Modelling as an Eigenvalue Problem." International Conference on Machine Learning, 2005. doi:10.1145/1102351.1102469Markdown
[Walder et al. "Implicit Surface Modelling as an Eigenvalue Problem." International Conference on Machine Learning, 2005.](https://mlanthology.org/icml/2005/walder2005icml-implicit/) doi:10.1145/1102351.1102469BibTeX
@inproceedings{walder2005icml-implicit,
title = {{Implicit Surface Modelling as an Eigenvalue Problem}},
author = {Walder, Christian and Chapelle, Olivier and Schölkopf, Bernhard},
booktitle = {International Conference on Machine Learning},
year = {2005},
pages = {936-939},
doi = {10.1145/1102351.1102469},
url = {https://mlanthology.org/icml/2005/walder2005icml-implicit/}
}