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Conference Paper

Implicit Surface Modelling as an Eigenvalue Problem

MPS-Authors
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Walder,  C
Department Human Perception, Cognition and Action, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;
Project group: Cognitive Engineering, Max Planck Institute for Biological Cybernetics, Max Planck Society;

/persons/resource/persons83855

Chapelle,  O
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

/persons/resource/persons84193

Schölkopf,  B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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https://dl.acm.org/citation.cfm?doid=1102351.1102469
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Citation

Walder, C., Chapelle, O., & Schölkopf, B. (2005). Implicit Surface Modelling as an Eigenvalue Problem. In S. Dzeroski, L. De Raedt, & S. Wrobel (Eds.), ICML '05: 22nd international conference on Machine learning (pp. 936-939). New York, NY, USA: ACM Press.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-D6DB-8
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.