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Construction of Iso-Contours, Bisectors, and Voronoi Diagrams on Triangulated Surfaces

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3 Author(s)
Yong jin Liu ; Dept. of Comput. Sci. & Technol., Tsinghua Univ., Beijing, China ; Zhanqing Chen ; Kai Tang

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 geodesic-metric-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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Pattern Analysis and Machine Intelligence, IEEE Transactions on  (Volume:33 ,  Issue: 8 )