PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Implicit Surface Modelling as an Eigenvalue Problem
christian wadler, Olivier Chapelle and Bernhard Schölkopf
In: International conference on machine learning, 7-11 august 2005, Bonn.


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.

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EPrint Type:Conference or Workshop Item (Talk)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:1162
Deposited By:Olivier Chapelle
Deposited On:19 November 2005