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3D Discrete Normal Vectors

  • Pierre Tellier
  • Isabelle Debled-Rennesson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1568)

Abstract

Precise knowledge of normal vectors to discrete objects is mandatory in rendering algorithms. This article introduces a new method for the calculation of normal vectors to a digital object. This technique relies on discrete geometry theories : the recognition of discrete straight lines and tangential lines in dimension 2. Results obtained with synthetic and real objects from medical imagery are presented and commented.

Keywords

Normal Vector Tangent Line Integer Point Regular Case Medical Imagery 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    E. Andres. Cercles discrets et rotations discrètes. Thèse. Université Louis Pasteur, Strasbourg, 1992.Google Scholar
  2. 2.
    I. Debled-Rennesson. Etude et reconnaissance des droites et plans discrets. Thèse. Université Louis Pasteur, Strasbourg, 1995.Google Scholar
  3. 3.
    I. Debled-Rennesson, and J.P. ReveillÈes. A linear algorithm for segmentation of digital curves. In International Journal of Pattern Recognition and Artificial Intelligence, volume 9, pages 635–662, 1995.CrossRefGoogle Scholar
  4. 4.
    J. FranÇon. Arithmetic planes and combinatorial manifolds. In Proceedings of the 5th International Workshop Discrete Geometry for computer Imagery, pages 209–217, Clermont-Ferrand (France), September 1995.Google Scholar
  5. 5.
    J. FranÇon. Discrete combinatorial surfaces. In CVGIP, pages 20–26, 1995.Google Scholar
  6. 6.
    J. FranÇon. Sur la topologie d’un plan arithmétique. In Theoretical Computer Science, volume 156, pages 159–176, 1996.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    H. Freeman. Boundary encoding and processing. In Picture Processing and Psychopictorics, pages 241–266. New York Academic, 1970.Google Scholar
  8. 8.
    Y. Kirschhoffer. Estimation de normale dans un espace discret 3d. analyse comparative de méthodes, Juin 1997. Rapport de DEA, U.L.P., Strasbourg.Google Scholar
  9. 9.
    S. Lefschetz. Applications of algebraic topology. In Springer Berlin, 1975.Google Scholar
  10. 10.
    L. Papier and J. FranÇon. Evaluation de la normale au bord d’un objet discret 3d. In, Revue internationale de CFAO et d’Informatique graphique, à paraître.Google Scholar
  11. 11.
    J.P. ReveillÈes. Géométrie discrète, calculs en nombre entiers et algorithmique. Thèse d’ état. Université Louis Pasteur, Strasbourg, 1991.Google Scholar
  12. 12.
    J.P. ReveillÈes. Structure des droites discrètes. In Journés mathématique et informatique, Marseille-Luminy, Octobre 1989.Google Scholar
  13. 13.
    G. Thurmer and A. Wuthrich. Normal computation for discrete surface in 3d space. In Eurographics, 1997.Google Scholar
  14. 14.
    A. Vialard. Chemins euclidiens: un modèle de représentation des contours discrets. Thèse. Université Bordeaux I, Bordeaux, 1996.Google Scholar
  15. 15.
    R. Yagel, D. Cohen, and A. Kaufman. Normal estimation in 3d discrete space. In The visual computer, volume 8, pages 278–291, 1992.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Pierre Tellier
    • 1
  • Isabelle Debled-Rennesson
    • 1
  1. 1.Laboratoire des Sciences de l’Image d’Informatique et de TélédétectionLSIIT UPRES-A ULP-CNRS 7005ILLKIRCH

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