Reversible Polygonalization of a 3D Planar Discrete Curve: Application on Discrete Surfaces

  • Isabelle Sivignon
  • Florent Dupont
  • Jean-Marc Chassery
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3429)

Abstract

Reversible polyhedral modelling of discrete objects is an important issue to handle those objects. We propose a new algorithm to compute a polygonal face from a discrete planar face (a set of voxels belonging to a discrete plane). This transformation is reversible, i.e. the digitization of this polygon is exactly the discrete face. We show how a set of polygons modelling exactly a discrete surface can be computed thanks to this algorithm.

Keywords

Dual Space Discrete Point Polygonal Line Discrete Object Discrete Surface 
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.
  2. 2.
    Lorensen, W.E., Cline, H.E.: Marching cubes: a high resolution 3D surface construction algorithm. In: Stone, M.C. (ed.) SIGGRAPH 1987 Conference Proceedings, Computer Graphics, vol. 21(4), pp. 163–170 (1987)Google Scholar
  3. 3.
    Kenmochi, Y., Imiya, A., Ezquerra, N.F.: Polyhedra generation from lattice points. In: Miguet, S., Montanvert, A., Ubéda, S. (eds.) DGCI 1996. LNCS, vol. 1176, pp. 127–138. Springer, Heidelberg (1996)Google Scholar
  4. 4.
    Borianne, P., Françon, J.: Reversible polyhedrization of discrete volumes. In: Discrete Geometry for Computer Imagery, Grenoble, France, pp. 157–167 (1994)Google Scholar
  5. 5.
    Françon, J., Papier, L.: Polyhedrization of the boundary of a voxel object. In: Bertrand, G., Couprie, M., Perroton, L. (eds.) DGCI 1999. LNCS, vol. 1568, pp. 425–434. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  6. 6.
    Burguet, J., Malgouyres, R.: Strong thinning and polyhedrization of the surface of a voxel object. In: Nyström, I., Sanniti di Baja, G., Borgefors, G. (eds.) DGCI 2000. LNCS, vol. 1953, pp. 222–234. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  7. 7.
    Yu, L., Klette, R.: An approximative calculation of relative convex hulls for surface area estimation of 3D digital objects. In: Kasturi, R., Laurendeau, D., Suen, C. (eds.) IAPR International Conference on Pattern Recognition, Québec, Canada, vol. 1, pp. 131–134. IEEE Computer Society, Los Alamitos (2002)Google Scholar
  8. 8.
    Andrès, É.: Defining discrete objects for polygonalization: The standard model. In: Braquelaire, A., Lachaud, J.-O., Vialard, A. (eds.) DGCI 2002. LNCS, vol. 2301, pp. 313–325. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  9. 9.
    Françon, J.: Discrete combinatorial surfaces. GMOD 51(1), 20–26 (1995)Google Scholar
  10. 10.
    Françon, J.: Sur la topologie d’un plan arithmétique. Theoretical Computer Science 156, 159–176 (1996)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Sivignon, I., Dupont, F., Chassery, J.-M.: Discrete surfaces segmentation into discrete planes. In: Klette, R., Žunić, J. (eds.) IWCIA 2004. LNCS, vol. 3322, pp. 458–473. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  12. 12.
    Sivignon, I., Breton, R., Dupont, F., Andrès, E.: Discrete analytical curve reconstruction without patches. Image and Vision Computing 23, 191–202 (2005)CrossRefGoogle Scholar
  13. 13.
    Hough, P.: Method and means for recognizing complex patterns. United States Patent, n°3 069, 654 (1962)Google Scholar
  14. 14.
    Maître, H.: Un panorama de la transformation de Hough. Traitement du Signal 2, 305–317 (1985)Google Scholar
  15. 15.
    McIlroy, M.D.: A note on discrete representation of lines. AT&T Technical Journal 64, 481–490 (1985)Google Scholar
  16. 16.
    Lindenbaum, M., Bruckstein, A.: On recursive, \(\mathcal{O}(n)\) partitioning of a digitized curve into digital straight segments. IEEE Trans. on Pattern Anal. and Mach. Intell. 15, 949–953 (1993)CrossRefGoogle Scholar
  17. 17.
    Vittone, J., Chassery, J.-M.: Recognition of digital naive planes and polyhedrization. In: Nyström, I., Sanniti di Baja, G., Borgefors, G. (eds.) DGCI 2000. LNCS, vol. 1953, pp. 296–307. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  18. 18.
    Reveillès, J.P.: The geometry of the intersection of voxel spaces. In: Fourey, S., Herman, G.T., Kong, T.Y. (eds.) International Workshop on Combinatorial Image Analysis. Electronic Notes in Theoretical Computer Science, vol. 46, Elsevier, Philadeplhie (2001)Google Scholar
  19. 19.
    Andrès, E., Sibata, C., Acharya, R., Shin, K.: New methods in oblique slice generation. In: SPIE Medical Imaging. Proceedings of SPIE, vol. 2707, pp. 580–589 (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Isabelle Sivignon
    • 1
  • Florent Dupont
    • 2
  • Jean-Marc Chassery
    • 1
  1. 1.Laboratoire LISDomaine universitaire GrenobleSt Martin d’HèresFrance
  2. 2.Laboratoire LIRISUniversité Claude Bernard Lyon 1VilleurbanneFrance

Personalised recommendations