# Voronoi Centered Radial Basis Functions

1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : This thesis considers the problem of reconstructing a surface from scattered points sampled on a physical shape. Our contribution is the development of a surface reconstruction method based on the Radial Basis Functions (RBF) approach which uses Voronoi tools in
order to filter noise, reconstruct using different level of details and obtain a smaller final representation.
Recent improvements in automated shape acquisition have stimulated a profusion of surface reconstruction techniques over the past few years for computer graphics and reverse engineering applications. Data collected from scanning processes of physical objects are often provided as large point sets scattered on the surface object. Functional based approaches where the surface is reconstructed as the zero-set of a function are standard. And the RBF approach has shown successful at reconstructing surfaces from point sets scattered on surfaces of arbitrary topology. The implicit function is defined as a linear combination of compactly supported radial basis functions. We reduce the number of basis functions to obtain a more compact representation and to reduce the evaluation cost. Reducing the number of basis function is equivalent to reduce the number of points (centers) where the functions are centered. Our aim consist in selecting a "little" set of relevant centers. To reduce the number of centers while maintaining decent fitting accuracy, we relax the one-to-one correspondence between the centers and the data points. We depart from previous work by using as centers of basis functions a set of points located on an estimate of the medial axis. Those centers are selected among the vertices of the Voronoi diagram of the data points. Being a Voronoi vertex, each center is associated with a maximal empty ball. We use the radius of this ball to adapt the support of each radial basis function. Our method can fit a user-defined budget of centers: the user can define the number of centers, i.e. the size of the representation and our algorithm will adapt the level of detail to this number using ltering and clustering or greedy selection.
Keywords :
Document type :
Theses
Domain :

https://tel.archives-ouvertes.fr/tel-00178274
Contributor : Marie Samozino <>
Submitted on : Wednesday, October 10, 2007 - 3:41:39 PM
Last modification on : Saturday, January 27, 2018 - 1:30:50 AM
Long-term archiving on: : Friday, April 9, 2010 - 4:55:21 PM

### Identifiers

• HAL Id : tel-00178274, version 1

### Citation

Marie Samozino. Voronoi Centered Radial Basis Functions. Mathematics [math]. Université Nice Sophia Antipolis, 2007. English. ⟨tel-00178274⟩

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