Centroidal Voronoi Tessellation of Line Segments and Graphs
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Date
2012
Authors
Journal Title
Journal ISSN
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Publisher
The Eurographics Association and John Wiley and Sons Ltd.
Abstract
Centroidal Voronoi Tessellation (CVT) of points has many applications in geometry processing, including remeshing and segmentation, to name but a few. In this paper, we generalize the CVT concept to graphs via a variational characterization. Given a graph and a 3D polygonal surface, our method optimizes the placement of the vertices of the graph in such a way that the graph segments best approximate the shape of the surface. We formulate the computation of CVT for graphs as a continuous variational problem, and present a simple, approximate method for solving this problem. Our method is robust in the sense that it is independent of degeneracies in the input mesh, such as skinny triangles, T-junctions, small gaps or multiple connected components. We present some applications, to skeleton fitting and to shape segmentation.
Description
@article{10.1111:j.1467-8659.2012.03058.x,
journal = {Computer Graphics Forum},
title = {{Centroidal Voronoi Tessellation of Line Segments and Graphs}},
author = {Lu, Lin and Lévy, Bruno and Wang, Wenping},
year = {2012},
publisher = {The Eurographics Association and John Wiley and Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/j.1467-8659.2012.03058.x}
}