Abstract
The shape description of the surface of three-dimensional discrete objects is widely used for displaying these objects, or measuring some useful parameters. Elementary components of discrete surfaces, called surfels, contain some geometric information, but at a scale that is too small with respect to the scale at which we actually want to describe objects. We present here a fast computational technique to compute the normal vector field of a discrete object at a given scale. Its time cost is proportional to the number of surfels at and little dependent on the scale. We prove that our algorithm converges toward the right value in the case of a plane surface. We also give some experimental results on families of curved surfaces.
Chapter PDF
Similar content being viewed by others
Index terms
Bibliography
E. Artzy, G. Frieder, G. T. Herman. The Theory, Design, Implementation and Evaluation of a Three-Dimensional Surface Detection Algorithm. CVGIP 15, 1–24 (1981).
R. Deriche. Recursively Implementing the Gaussian and its Derivatives. Rapport de Recherche de l'INRIA No 1893, Avril 1993.
G. T. Herman, H. T. Liu. Three-Dimensional Display of Human Organs from Computed Tomograms. Computer Graphics and Image Processing 9. 1–21, 1979.
G.T. Herman. Discrete Multidimensional Jordan Surfaces. CVGIP: Graphical Models and Image Processing. Vol. 54 No 6, November, pp 507–515, 1992.
F. Mokhtarian, A. Mackworth. Scale-Based Description and Recognition of Planar Curves and Two-Dimensional Shapes. IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI-8 No 1 January 1986, pp. 665–668.
A. Rosenfeld, T. Y. Yung Kong, A. Y. Wu. Digital Surfaces. CVGIP 53, No 4, July, pp 305–312, 1991
G. Sapiro, A. Tannenbaum. Area and Length Preserving Geometric Invariant Scale-Spaces. IEEE Transactions on Pattern Analysis and Machine Intelligence Vol. 17 No 1 January 1995, pp. 67–72.
J.P. Thirion. New Feature Points based on Geometric Invariants for 3D Image Registration. Rapport de Recherche de l'INRIA N∘ 1901, Mai 1993.
J.K. Udupa. Multidimensional Digital Boundaries in CVGIP: Graphical Models and Image Processing. Vol. 56 N∘ 4. July 1994, pp. 311–323.
T. J. Fan, G. Medioni, R. Nevata. Recognising 3D Objects Using Surface Descriptions. IEEE Transactions on Pattern Analysis and Machine Intelligence Vol. 11 No 11 November 1989, pp. 1140–1157.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lenoir, A., Malgouyres, R., Revenu, M. (1996). Fast computation of the normal vector field of the surface of a 3-D discrete object. 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_9
Download citation
DOI: https://doi.org/10.1007/3-540-62005-2_9
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