Implicit Surface Modelling with a Globally Regularised Basis of Compact Support
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We consider the problem of constructing a globally smooth analytic function that represents a surface implicitly by way of its zero set, given sample points with surface normal vectors. The contributions of the paper include a novel means of regularising multi-scale compactly supported basis functions that leads to the desirable interpolation properties previously only associated with fully supported bases. We also provide a regularisation framework for simpler and more direct treatment of surface normals, along with a corresponding generalisation of the representer theorem lying at the core of kernel-based machine learning methods. We demonstrate the techniques on 3D problems of up to 14 million data points, as well as 4D time series data and four-dimensional interpolation between three-dimensional shapes.
| Author(s): | Walder, C. and Schölkopf, B. and Chapelle, O. |
| Links: | |
| Journal: | Computer Graphics Forum |
| Volume: | 25 |
| Number (issue): | 3 |
| Pages: | 635-644 |
| Year: | 2006 |
| Month: | September |
| Day: | 0 |
| BibTeX Type: | Article (article) |
| DOI: | 10.1111/j.1467-8659.2006.00983.x |
| Digital: | 0 |
| Electronic Archiving: | grant_archive |
| Language: | en |
| Organization: | Max-Planck-Gesellschaft |
| School: | Biologische Kybernetik |
BibTeX
@article{3958,
title = {Implicit Surface Modelling with a Globally Regularised Basis of Compact Support},
journal = {Computer Graphics Forum},
abstract = {We consider the problem of constructing a globally smooth analytic function that represents a surface implicitly by way of its zero set, given sample points with surface normal vectors. The contributions of the paper include a novel means of regularising multi-scale compactly supported basis functions that leads to the desirable interpolation properties previously only associated with fully supported bases. We also provide a regularisation framework for simpler and more direct treatment of surface normals, along with a corresponding generalisation of the representer theorem lying at the core of kernel-based machine learning methods. We demonstrate the techniques on 3D problems of up to 14 million data points, as well as 4D time series data and four-dimensional interpolation between three-dimensional shapes.},
volume = {25},
number = {3},
pages = {635-644},
organization = {Max-Planck-Gesellschaft},
school = {Biologische Kybernetik},
month = sep,
year = {2006},
author = {Walder, C. and Sch{\"o}lkopf, B. and Chapelle, O.},
doi = {10.1111/j.1467-8659.2006.00983.x},
month_numeric = {9}
}