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Some examples of algorithms analysis in computational geometry by means of mathematical morphological techniques

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Geometry and Robotics (GeoRob 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 391))

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Abstract

In this paper we show how the notion of convergence of a sequence of closed sets and that of random closed sets can be given a precise definition by means of mathematical morphological tools. Then we use these two notions on the one hand to analyze how the Delaunay triangulation enables us to get a good approximation of the skeleton of an object and on the other hand to estimate the performances of bucketing techniques in the average case.

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References

  1. T. Asano, M. Edahiro, H. Imai, and M. Iri. Computational Geometry, chapter Practical Use of Bucketing Techniques in Computational Geometry. Elsevier Science Publishers B.V. (North Holland), 1985.

    Google Scholar 

  2. J.D. Boissonnat, O.D. Faugeras, and E. Le Bras-Mehlman. Representing Stereo Data with the Delaunay Triangulation. Technical Report 788, INRIA, February 1988.

    Google Scholar 

  3. L. Calabi and J.A. Riley. The Skeletons of Stable plane Sets. Technical Report AF 19 (628-5711), Parke Math. Lab. Inc., December 1967.

    Google Scholar 

  4. G. Choquet. Theory of capacities. Ann. Inst. Fourier, V:131–295, 1953–54.

    Google Scholar 

  5. T. Lozano-Pérez and M.A. Wesley. An algorithm for planning collision free paths among polyhedral obstacles. Comm. ACM, 22:560–570, 1979.

    Google Scholar 

  6. G. Matheron. Image Analysis and Mathematical Morphology, Volume 2: Theoretical Advances, chapter Filters and Lattices. Academic Press, 1988.

    Google Scholar 

  7. G. Matheron. Random Sets and Integral Geometry. Wiley, 1975.

    Google Scholar 

  8. G. Matheron. Théorie des ensembles aléatoires. Les cahiers du Centre de Morphologie Mathématique, Ecole des Mines de Paris, 1969.

    Google Scholar 

  9. F.P. Preparata and M.I. Shamos. Computational Geometry: an Introduction. Springer Verlag, 1985.

    Google Scholar 

  10. F. Prêteux and M. Schmitt. Analyse et synthèse de fonctions booléennes: théorèmes de caractérisation et démonstrations. Technical Report 34/87/MM, CGMM, Ecole des Mines, 1987.

    Google Scholar 

  11. L.A. Santalo. Integral Geometry and Geometric Probability. Addison Wesley, 1976.

    Google Scholar 

  12. J. Serra. Eléments de théorie pour l'optique morphologique. Thèse d'Etat, Université de Paris VI, 1986.

    Google Scholar 

  13. J. Serra. Image Analysis and Mathematical Morphology. Academic Press, 1982.

    Google Scholar 

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Authors and Affiliations

  1. INRIA Sophia-Antipolis, 2004, route des Lucioles, 06565, Valbonne Cedex, France

    Michel Schmitt

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  1. Michel Schmitt
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J. -D. Boissonnat J. -P. Laumond

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© 1989 Springer-Verlag Berlin Heidelberg

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Schmitt, M. (1989). Some examples of algorithms analysis in computational geometry by means of mathematical morphological techniques. In: Boissonnat, J.D., Laumond, J.P. (eds) Geometry and Robotics. GeoRob 1988. Lecture Notes in Computer Science, vol 391. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51683-2_33

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  • DOI: https://doi.org/10.1007/3-540-51683-2_33

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51683-5

  • Online ISBN: 978-3-540-46748-9

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