Abstract
An object of interest is digitized if we acquire its 3-dimensional digital images by using techniques such as computerized tomographic imaging. For recognition or shape analysis of such digitized objects, we need the study of 3-dimensional digital geometry and topology. In this paper, we focus on one of the simplest geometric objects such as planes and study their geometric and topological properties which are expressed by using an algebraic method.
Chapter PDF
Similar content being viewed by others
Keywords
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
Imiya, A., Eckhardt, U.: The Euler Characteristics of Discrete Objects and Discrete Quasi-Objects. Computer Vision and Image Understanding 75 3 (1999) 307–318 249, 258
Borgefors, G., Nyström, I., di Baja, G. S.: Computing skeletons in three dimensions. Pattern Recognition 32 (1999) 1225–1236 249
Andres, E.: Le Plan Discret. In Proceedings of 3e Colloque Géométrie discète en imagerie: fondements et applications. Strasbourg (1993) 45–61 249
Françon, J.: Sur la topologie d’un plan arithmétique. Theoretical Computer Science 156 (1996) 159–176 249, 256, 258, 259
Reveillès, J. P.: Combinatorial Pieces in Digital Lines and Planes. In Vision Geometry III. Proceedings of SPIE, Vol. 2573 (1995) 23–34 249, 250, 256
Françon, J., Schramm, J. M., Tajine, M.: Recognizing arithmetic straight lines and planes. In Discrete Geometry for Computer Imagery. LNCS 1176 Springer-Verlag, Berlin, Heidelberg (1996) 141–150 249, 256
Debled-Renesson, I.: Etude et reconnaissance des droites et plans discrets. PhD thesis, University of Louis Pasteur (1995) 249, 256
Kenmochi, Y.: Discrete Combinatorial Polyhedra: Theory and Application. Doctoral thesis, Chiba University (1998) 249, 251, 252
Kenmochi, Y., Imiya, A.: On Combinatorial Properties of Discrete Planar Surfaces. In Proceedings of International Conference on Free Boundary Problems: Theory and Applications. Vol. 2. Gakkotosho, Tokyo (2000) 255–272. 249, 253
Aleksandrov, P. S.: Combinatorial Topology. Vol. 1. Graylock Press, Rochester, New York (1956) 249, 250
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kenmochi, Y., Imiya, A. (2000). Naive Planes as Discrete Combinatorial Surfaces. In: Borgefors, G., Nyström, I., di Baja, G.S. (eds) Discrete Geometry for Computer Imagery. DGCI 2000. Lecture Notes in Computer Science, vol 1953. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44438-6_21
Download citation
DOI: https://doi.org/10.1007/3-540-44438-6_21
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41396-7
Online ISBN: 978-3-540-44438-1
eBook Packages: Springer Book Archive