Abstract
In the present paper, we propose a topological characterization of digital surfaces. We introduce simple local conditions on the neighborhood of a voxel. If each voxel of a 26-connected digital set satisfies them, we prove a Jordan theorem and ensure that this set is strong 6-separating in ℤ3. Thus, we consider it as a digital surface.
Chapter PDF
Similar content being viewed by others
References
Rosenfeld, A.: Arcs and curves in digital pictures. Journal of the ACM 20(1), 81–87 (1973)
Malgouyres, R.: There is no local characterization of separating and thin objects in z 3. Theoretical Computer Science 163(1&2), 303–308 (1996)
Morgenthaler, D.G., Rosenfeld, A.: Surfaces in three-dimensional digital images. Information and Control 51(3), 227–247 (1981)
Reveillès, J.P.: Géométrie discrète, calcul en nombres entiers et algorithmique. Thèse d’Etat, Université Louis Pasteur, Strasbourg (1991)
Bertrand, G., Malgouyres, R.: Some topological properties of discrete surfaces. In: Miguet, S., Ubéda, S., Montanvert, A. (eds.) DGCI 1996. LNCS, vol. 1176, pp. 325–336. Springer, Heidelberg (1996)
Malgouyres, R., Bertrand, G.: A new local property of strong n-surfaces. Pattern Recognition Letters 20(4), 417–428 (1999)
Malgouyres, R.: A definition of surfaces of z 3: a new 3d discrete jordan theorem. Theoretical Computer Science 186(1-2), 1–41 (1997)
Couprie, M., Bertrand, G.: Simplicity surfaces: a new definition of surfaces in z 3. In: SPIE Vision Geometry V, vol. 3454, pp. 40–51 (1998)
Ciria, J.C., Domínguez, E., Francés, A.R.: Separation theorems for simplicity 26-surfaces. In: Braquelaire, A., Lachaud, J.-O., Vialard, A. (eds.) DGCI 2002. LNCS, vol. 2301, pp. 45–56. Springer, Heidelberg (2002)
Bertrand, G.: On p-simple points. Compte-Rendus de l’Académie des Sciences, Série 1, Mathématique 321(8), 1077–1084 (1995)
Kong, T.Y.: A digital fundamental group. Computers & Graphics 13(2), 159–166 (1989)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Malgouyres, R., Toutant, JL. (2009). Characterization of Simple Closed Surfaces in ℤ3: A New Proposition with a Graph-Theoretical Approach. In: Brlek, S., Reutenauer, C., Provençal, X. (eds) Discrete Geometry for Computer Imagery. DGCI 2009. Lecture Notes in Computer Science, vol 5810. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04397-0_25
Download citation
DOI: https://doi.org/10.1007/978-3-642-04397-0_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04396-3
Online ISBN: 978-3-642-04397-0
eBook Packages: Computer ScienceComputer Science (R0)