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

—In the research of computer vision and machine perception, three-dimensional 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 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 extracti...

• Type: Journal
• Year: 2011
• Where: PAMI
• Authors: Yong-Jin Liu, Zhanqing Chen, Kai Tang
• Keywords: Computer Networks, Construction Algorithms, PAMI 2011, Reconstruction 3d, Triangular Meshes