Reconstruction with Voronoi Centered Radial Basis Functions

Samozino, M.; Alexa, M.; Alliez, P.; Yvinec, M.

Reconstruction with Voronoi Centered Radial Basis Functions

Files

051-060.pdf (400.32 KB)

Date

2006

Authors

Samozino, M.
Alexa, M.
Alliez, P.
Yvinec, M.

Publisher

The Eurographics Association

Abstract

We consider the problem of reconstructing a surface from scattered points sampled on a physical shape. The sampled shape is approximated as the zero level set of a function. This function is defined as a linear combination of compactly supported radial basis functions. We depart from previous work by using as centers of basis functions a set of points located on an estimate of the medial axis, instead of the input data points. Those centers are selected among the vertices of the Voronoi diagram of the sample 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 selected subset of Voronoi vertices is filtered using the notion of lambda medial axis, then clustered to fit the allocated budget.

        @inproceedings{:10.2312/SGP/SGP06/051-060
,
booktitle = {Symposium on Geometry Processing
},
editor = {Alla Sheffer and Konrad Polthier
},
title = {{Reconstruction with Voronoi Centered Radial Basis Functions
}},
author = {Samozino, M. and 
Alexa, M. and 
Alliez, P. and 
Yvinec, M.
},
year = {2006
},
publisher = {The Eurographics Association
},
ISSN = {1727-8384
},
ISBN = {3-905673-24-X
},
DOI = {/10.2312/SGP/SGP06/051-060
}
}