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.
Invited at the LIP of the ENS Lyon during spring 1996.
This research has been done while the author was member of the LIP, ENS-Lyon.
Chapter PDF
References
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.
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.
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.
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.
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.
Arie Kaufman. Volume Visualization. IEEE Computer Society Press Tutorial, 1991.
E. Keppel. Approximation of complex surfaces by triangulation of contour lines. IBM J. Res. Develop. 19, pages 2–11, January 1975.
Marc Levoy. Display of surfaces from volume data. IEEE Computer Graphics and Applications, pages 29–37, May 1988.
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.
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.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Boumghar, F., Miguet, S., Nicod, JM. (1996). Complexity of discrete surfaces in the Dividing-cubes algorithm. In: Miguet, S., Montanvert, A., Ubéda, S. (eds) Discrete Geometry for Computer Imagery. DGCI 1996. Lecture Notes in Computer Science, vol 1176. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62005-2_23
Download citation
DOI: https://doi.org/10.1007/3-540-62005-2_23
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-62005-1
Online ISBN: 978-3-540-49595-6
eBook Packages: Springer Book Archive