Journal
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
Volume 33, Issue 8, Pages 1502-1517Publisher
IEEE COMPUTER SOC
DOI: 10.1109/TPAMI.2010.221
Keywords
Shape; geometric transformations; triangular meshes; exact geodesic metrics; point patterns
Funding
- Natural Science Foundation of China [60970099]
- National Basic Research Program of China [2011CB302202]
- Hong Kong RGC [ENG.620409]
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In the research of computer vision and machine perception, 3D objects are usually represented by 2-manifold triangular meshes M. In this paper, we present practical and efficient algorithms to construct iso-contours, bisectors, and Voronoi diagrams of point sites on M, based on an exact geodesic metric. Compared to euclidean metric spaces, the Voronoi diagrams on M exhibit many special properties that fail all of the existing euclidean Voronoi algorithms. To provide practical algorithms for constructing geodesicmetric- based Voronoi diagrams on M, this paper studies the analytic structure of iso-contours, bisectors, and Voronoi diagrams on M. After a necessary preprocessing of model M, practical algorithms are proposed for quickly obtaining full information about iso-contours, bisectors, and Voronoi diagrams on 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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