Implicit Surface Modelling with a Globally Regularised Basis of Compact Support
2006
Article
ei
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. |
Journal: | Computer Graphics Forum |
Volume: | 25 |
Number (issue): | 3 |
Pages: | 635-644 |
Year: | 2006 |
Month: | September |
Day: | 0 |
Department(s): | Empirical Inference |
Bibtex Type: | Article (article) |
Digital: | 0 |
DOI: | 10.1111/j.1467-8659.2006.00983.x |
Language: | en |
Organization: | Max-Planck-Gesellschaft |
School: | Biologische Kybernetik |
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BibTex @article{3958, title = {Implicit Surface Modelling with a Globally Regularised Basis of Compact Support}, author = {Walder, C. and Sch{\"o}lkopf, B. and Chapelle, O.}, journal = {Computer Graphics Forum}, volume = {25}, number = {3}, pages = {635-644}, organization = {Max-Planck-Gesellschaft}, school = {Biologische Kybernetik}, month = sep, year = {2006}, doi = {10.1111/j.1467-8659.2006.00983.x}, month_numeric = {9} } |