Optimization Schemes for the Reversible Discrete Volume Polyhedrization Using Marching Cubes Simplification

  • David Coeurjolly
  • Florent Dupont
  • Laurent Jospin
  • Isabelle Sivignon
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4245)


The aim of this article is to present a reversible and topologically correct construction of a polyhedron from a binary object. The proposed algorithm is based on a Marching Cubes (MC) surface, a digital plane segmentation of the binary object surface and an optimization step to simplify the MC surface using the segmentation information.


Linear Constraint Euclidean Plane Discrete Volume Discrete Object Marching Cube 
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.


  1. 1.
    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
  2. 2.
    Debled-Rennesson, I.: Etude et reconnaissance des droites et plans discrets. PhD thesis, Université Louis Pasteur (1995)Google Scholar
  3. 3.
    Sivignon, I., Dupont, F., Chassery, J.M.: Decomposition of a three-dimensional discrete object surface into discrete plane pieces. Algorithmica 38(1), 25–43 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Coeurjolly, D., Guillaume, A., Sivignon, I.: Reversible discrete volume polyhedrization using marching cubes simplification. In: SPIE Vision Geometry XII, San Jose, USA, vol. 5300, pp. 1–11 (2004)Google Scholar
  5. 5.
    Sivignon, I., Dupont, F., Chassery, J.M.: Reversible polygonalization of a 3D planar discrete curve: Application on discrete surfaces. In: International Conference on Discrete Geometry for Computer Imagery, pp. 347–358 (2005)Google Scholar
  6. 6.
    Dexet, M.: Design of a topology based geometrical discrete modeler and reconstruction methods in 2D and 3D. PhD thesis, Laboratoire SIC, Université de Poitiers (2006) (in French)Google Scholar
  7. 7.
    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, Anaheim, CA, July 27–31, 1987, vol. 21(4), pp. 163–170 (1987)Google Scholar
  8. 8.
    Lachaud, J.O.: Topologically defined isosurfaces. In: Miguet, S., Ubéda, S., Montanvert, A. (eds.) DGCI 1996. LNCS, vol. 1176, pp. 245–256. Springer, Heidelberg (1996)Google Scholar
  9. 9.
    Borianne, P., Francon, J.: Reversible polyhedrization of discrete volumes. In: 4th Discrete Geometry for Computer Imagery, Grenoble, France, pp. 157–168 (1994)Google Scholar
  10. 10.
    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
  11. 11.
    Klette, R., Sun, H.J.: Digital planar segment based polyhedrization for surface area estimation. In: Arcelli, C., Cordella, L.P., Sanniti di Baja, G. (eds.) IWVF 2001. LNCS, vol. 2059, pp. 356–366. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  12. 12.
    Lachaud, J.O., Montanvert, A.: Continuous analogs of digital boundaries: A topological approach to iso-surfaces. Graphical Models and Image Processing 62, 129–164 (2000)Google Scholar
  13. 13.
    Klette, R., Rosenfeld, A.: Digital Geometry: Geometric Methods for Digital Picture Analysis. Series in Computer Graphics and Geometric Modelin. Morgan Kaufmann, San Francisco (2004)zbMATHGoogle Scholar
  14. 14.
    Brimkov, V., Coeurjolly, D., Klette, R.: Digital planarity - a review. Technical Report RR-2004-024, Laboratoire LIRIS, Université Claude Bernard Lyon 1 (2004)Google Scholar
  15. 15.
    Coeurjolly, D., Sivignon, I., Dupont, F., Feschet, F., Chassery, J.M.: On digital plane preimage structure. Discrete Applied Mathematics 151(1–3), 78–92 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Andrès, E.: Discrete linear objects in dimension n: the standard model. Graphical models 65(1–3), 92–111 (2003)zbMATHCrossRefGoogle Scholar
  17. 17.
    Coeurjolly, D., Brimkov, V.E.: Computational aspects of digital plane and hyperplane recognition. In: Reulke, R., Eckardt, U., Flach, B., Knauer, U., Polthier, K. (eds.) IWCIA 2006. LNCS, vol. 4040, pp. 291–306. Springer, Heidelberg (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • David Coeurjolly
    • 1
  • Florent Dupont
    • 1
  • Laurent Jospin
    • 1
  • Isabelle Sivignon
    • 1
  1. 1.Laboratoire LIRIS/ UMR CNRS 5205Université Claude Bernard Lyon 1VilleurbanneFrance

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