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Construction of Iso-Contours, Bisectors, and Voronoi Diagrams on Triangulated Surfaces
August 2011 (vol. 33 no. 8)
pp. 1502-1517
ASCII Text
x 
 
Yong-Jin Liu, Zhan-Qing Chen, Kai Tang, "Construction of Iso-Contours, Bisectors, and Voronoi Diagrams on Triangulated Surfaces," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 33, no. 8, pp. 1502-1517, August, 2011.
 
 
BibTex
x
 
@article{ 10.1109/TPAMI.2010.221,
author = {Yong-Jin Liu and Zhan-Qing Chen and Kai Tang},
title = {Construction of Iso-Contours, Bisectors, and Voronoi Diagrams on Triangulated Surfaces},
journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence},
volume = {33},
number = {8},
issn = {0162-8828},
year = {2011},
pages = {1502-1517},
doi = {http://doi.ieeecomputersociety.org/10.1109/TPAMI.2010.221},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
TI - Construction of Iso-Contours, Bisectors, and Voronoi Diagrams on Triangulated Surfaces
IS - 8
SN - 0162-8828
SP1502
EP1517
EPD - 1502-1517
A1 - Yong-Jin Liu,
A1 - Zhan-Qing Chen,
A1 - Kai Tang,
PY - 2011
KW - Shape
KW - geometric transformations
KW - triangular meshes
KW - exact geodesic metrics
KW - point patterns.
VL - 33
JA - IEEE Transactions on Pattern Analysis and Machine Intelligence
ER -
 
Yong-Jin Liu, Tsinghua University, Beijing
Zhan-Qing Chen, Hong Kong University of Science and Technology, Hong Kong
Kai Tang, Hong Kong University of Science and Technology, Hong Kong
In the research of computer vision and machine perception, 3D objects are usually represented by 2-manifold triangular meshes {\cal M}. In this paper, we present practical and efficient algorithms to construct iso-contours, bisectors, and Voronoi diagrams of point sites on {\cal M}, based on an exact geodesic metric. Compared to euclidean metric spaces, the Voronoi diagrams on {\cal M} exhibit many special properties that fail all of the existing euclidean Voronoi algorithms. To provide practical algorithms for constructing geodesic-metric-based Voronoi diagrams on {\cal M}, this paper studies the analytic structure of iso-contours, bisectors, and Voronoi diagrams on {\cal M}. After a necessary preprocessing of model {\cal M}, practical algorithms are proposed for quickly obtaining full information about iso--contours, bisectors, and Voronoi diagrams on {\cal M}. The complexity of the construction algorithms is also analyzed. Finally, three interesting applications—surface sampling and reconstruction, 3D skeleton extraction, and point pattern analysis—are presented that show the potential power of the proposed algorithms in pattern analysis.

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Index Terms:
Shape, geometric transformations, triangular meshes, exact geodesic metrics, point patterns.
Citation:
Yong-Jin Liu, Zhan-Qing Chen, Kai Tang, "Construction of Iso-Contours, Bisectors, and Voronoi Diagrams on Triangulated Surfaces," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 33, no. 8, pp. 1502-1517, Aug. 2011, doi:10.1109/TPAMI.2010.221
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