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Implicit Surface Modelling as an Eigenvalue Problem


Conference Paper


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.

Author(s): Walder, C. and Chapelle, O. and Schölkopf, B.
Book Title: Proceedings of the 22nd International Conference on Machine Learning
Pages: 937-944
Year: 2005
Day: 0
Editors: L De Raedt and S Wrobel
Publisher: ACM

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

Event Name: ICML 2005
Event Place: Bonn, Germany

Address: New York, NY, USA
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: PDF


  title = {Implicit Surface Modelling as an Eigenvalue Problem},
  author = {Walder, C. and Chapelle, O. and Sch{\"o}lkopf, B.},
  booktitle = {Proceedings of the 22nd International Conference on Machine Learning},
  pages = {937-944},
  editors = {L De Raedt and S Wrobel},
  publisher = {ACM},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {New York, NY, USA},
  year = {2005}