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Complexity of discrete surfaces in the Dividing-cubes algorithm

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Part of the book series:Lecture Notes in Computer Science ((LNCS,volume 1176))

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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.

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References

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Author information

Authors and Affiliations

  1. LASIE-Alger, U.S.T.H.B. Bab-Ezzouar, 16011, Alger, Algeria

    Fatima Boumghar

  2. Laboratoire ERIC Bât. L, Université Lyon-2, 5 av. Pierre Mendès-France, 69676, Bron, France

    Serge Miguet

  3. Ecole Normale Supérieure de Lyon, LIP, URA CNRS 1398, 46 allée d'Italie, 69364, Lyon Cedex 7, France

    Jean-Marc Nicod

Authors
  1. Fatima Boumghar

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  2. Serge Miguet

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  3. Jean-Marc Nicod

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Editor information

Serge Miguet Annick Montanvert Stéphane Ubéda

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© 1996 Springer-Verlag Berlin Heidelberg

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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

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