Centroidal Voronoi Tessellation of Line Segments and Graphs

Centroidal Voronoi Tessellation (CVT) of points has many applications in geometry processing, including re‐meshing 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 opti...

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Bibliographic Details
Published in:Computer graphics forum Vol. 31; no. 2pt4; pp. 775 - 784
Main Authors: Lu, Lin, Lévy, Bruno, Wang, Wenping
Format: Journal Article
Language:English
Published: Oxford, UK Blackwell Publishing Ltd 01.05.2012
Subjects:
Algorithms
and systems
Approximation
Computer graphics
Computer Graphics [I.3.5]: Computational Geometry and Object Modeling-Geometric algorithms
Computer Graphics [I.3.5]: Computational Geometry and Object Modeling—Geometric algorithms, languages, and systems; Algorithms
Computer science
Geometry
Graphs
languages
Names
Segmentation
Segments
Studies
Tessellation
Three dimensional
Triangles
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary:Centroidal Voronoi Tessellation (CVT) of points has many applications in geometry processing, including re‐meshing 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.
Bibliography:ark:/67375/WNG-FPZJF3N1-1
ArticleID:CGF3058
istex:233DE16AFBDDDA3EA253643E479D3A6B676A41FA
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0167-7055
1467-8659
DOI:10.1111/j.1467-8659.2012.03058.x