How the Delaunay Triangulation Can Be used For Representing Stereo Data

This article proposes a coherent method of interpolating 3D data obtained for example by stereo, with a polyhedral surface by means of the Delaunay Triangulation. We first give some theoretical properties concerning the approximations of sampled objects we obtain when the sampling rate increases, based on the study of their skeleton using some tools of Mathematical Morphology. Then, we present the algorithms and their complexity analysis which yield both a surface representation of objects and a volume representation of free space which may be useful in Robotics. This goal is achieved by means of a simple visibility criterion. The method is intrinsically discontinuity preserving and can be used for the integration of multiple viewpoints.

[1]  Demetri Terzopoulos,et al.  Multilevel computational processes for visual surface reconstruction , 1983, Comput. Vis. Graph. Image Process..

[2]  V. Klee.  On the complexity ofd- dimensional Voronoi diagrams , 1979 .

[3]  Jean-Daniel Boissonnat,et al.  Geometric structures for three-dimensional shape representation , 1984, TOGS.

[4]  F. Hermeline,et al.  Triangulation automatique d'un polyèdre en dimension $N$ , 1982 .

[5]  Takao Asano,et al.  A new point-location algorithm and its practical efficiency: comparison with existing algorithms , 1984, TOGS.

[6]  Adrian Bowyer,et al.  Computing Dirichlet Tessellations , 1981, Comput. J..

[7]  Chris L. Jackins,et al.  Oct-trees and their use in representing three-dimensional objects , 1980 .

[8]  Olivier D. Faugeras,et al.  Building, Registrating, and Fusing Noisy Visual Maps , 1988, Int. J. Robotics Res..

[9]  Takeo Kanade,et al.  Incremental Acquisition of a Three-Dimensional Scene Model from Images , 1982, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[10]  Jean-Daniel Boissonnat,et al.  The hierarchical representation of objects: the Delaunay tree , 1986, SCG '86.

[11]  Jake K. Aggarwal,et al.  Volume/surface octrees for the representation of three-dimensional objects , 1986, Comput. Vis. Graph. Image Process..

[12]  D. T. Lee,et al.  Generalized delaunay triangulation for planar graphs , 1986, Discret. Comput. Geom..

[13]  Olivier D. Faugeras,et al.  Representing stereo data with the Delaunay triangulation , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[14]  N. Ayache,et al.  Trinocular Stereovision: Recent Results , 1987, IJCAI.

[15]  Olivier D. Faugeras,et al.  Building visual maps by combining noisy stereo measurements , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[16]  W. Eric L. Grimson,et al.  An implementation of a computational theory of visual surface interpolation , 1983, Comput. Vis. Graph. Image Process..

[17]  Olivier D. Faugeras,et al.  Maintaining representations of the environment of a mobile robot , 1988, IEEE Trans. Robotics Autom..

[18]  G. Matheron.  Random Sets and Integral Geometry , 1976 .

[19]  Raimund Seidel,et al.  Voronoi diagrams and arrangements , 1985, SCG '85.

[20]  W E Grimson,et al.  A computational theory of visual surface interpolation. , 1982, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[21]  Jean Serra,et al.  Image Analysis and Mathematical Morphology , 1983 .

[22]  D. F. Watson.  Computing the n-Dimensional Delaunay Tesselation with Application to Voronoi Polytopes , 1981, Comput. J..

[23]  Hanan Samet,et al.  The Quadtree and Related Hierarchical Data Structures , 1984, CSUR.