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Complexity of discrete surfaces in the Dividing-cubes algorithm

  • Fatima Boumghar
  • Serge Miguet
  • Jean-Marc Nicod
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1176)

Abstract

The main result of this paper is to exhibit a complexity model for discrete surfaces obtained by regular subdivisions of cells. We use it for estimating the number of points that will be generated by the Dividing-Cubes algorithm to represent the surface of 3D medical objects. Under the assumption that surfaces have uniform orientations in the space, and can be locally compared to planes, we show that their average number of points is a quadratic function of the subdivision factors. We give analytical expressions for the coefficients of the quadratic form.

Keywords

Polygon Mesh Discrete Surface IEEE Computer Graphic Regular Subdivision Distribute Memory Machine 
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.
    Fatima Boumghar and Serge Miguet. Subdivision optimale dans l'algorithme des dividing-cubes, application à l'imagerie médicale 3D. In 3èmes Journées de l'Association Française d'Informatique Graphique (in french), pages 185–192. GAMSAU, Ecole d'architecture, Luminy, November 1995.Google Scholar
  2. 2.
    Fatima Boumghar, Serge Miguet, and Jean-Marc Nicod. Optimal subdivision and complexity of discrete surfaces in the dividing-cubes algorithm. Reseach report, Laboratoire de l'Informatique du Parallélisme, 46 Allée d'Italie 69364 Lyon Cedex 07, 1996. To appear in Sept.96.Google Scholar
  3. 3.
    Harvey E. Cline, C. R. Crawford, Wiliam E. Lorensen, S. Ludke, and B. C. Teeter. Two algorithms for the three-dimensional reconstruction of tomograms. Medical Physics, 15(3):320–327, may–june 1988.Google Scholar
  4. 4.
    D. Magid D.R. Ney, E.K. Fishman and R.A. Drebin. Volumetric rendering of computer tomography data: Principles and techniques. IEEE Computer Graphics and Applications, pages 24–32, March 1990.Google Scholar
  5. 5.
    H. Fuchs, Z. M. Kedem, and S. P. Uselton. Optimal surface reconstruction from planar contours. Comm. of the ACM 20, 10:693–702, Octobre 1977.Google Scholar
  6. 6.
    Arie Kaufman. Volume Visualization. IEEE Computer Society Press Tutorial, 1991.Google Scholar
  7. 7.
    E. Keppel. Approximation of complex surfaces by triangulation of contour lines. IBM J. Res. Develop. 19, pages 2–11, January 1975.Google Scholar
  8. 8.
    Marc Levoy. Display of surfaces from volume data. IEEE Computer Graphics and Applications, pages 29–37, May 1988.Google Scholar
  9. 9.
    William E. Lorensen and Harvey E. Cline. Marching cubes: A high resolution 3D surface construction algorithm. ACM Computer Graphics, 21(4):163–169, July 1987.Google Scholar
  10. 10.
    Serge Miguet. Un Environnement Parallèle pour l'Imagerie 3D. Mémoire d'habilitation à diriger des recherches (in french), Ecole Normale Supérieure de Lyon, December 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Fatima Boumghar
    • 1
  • Serge Miguet
    • 2
  • Jean-Marc Nicod
    • 3
  1. 1.LASIE-AlgerU.S.T.H.B. Bab-EzzouarAlgerAlgeria
  2. 2.Laboratoire ERIC Bât. LUniversité Lyon-2BronFrance
  3. 3.Ecole Normale Supérieure de LyonLIP, URA CNRS 1398Lyon Cedex 7France

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