Abstract
We recall the definition of simple points which uses the digital fundamental group introduced by T. Y. Kong in [Kon89]. Then, we prove that a not less restrictive de.nition can be given. Indeed, we prove that there is no need of considering the fundamental group of the complement of an object in order to characterize its simple points. In order to prove this result, we do not use the fact that “the number of holes of X is equal to the number of holes in X” which is not su.cient for our purpose but we use the linking number de.ned in [FM00]. In so doing, we formalize the proofs of several results stated without proof in the literature (Bertrand, Kong, Morgenthaler).
Chapter PDF
Similar content being viewed by others
References
G. Bertrand. Simple points, topological numbers and geodesic neighborhoods in cubics grids. Patterns Recognition Letters, 15:1003–1011, 1994. 29
G. Bertrand and G. Malandain. A new characterization of three-dimensional simple points. Pattern Recognition Letters, 15:169–175, February 1994. 32, 33
S. Fourey and R. Malgouyres. A digital linking number for discrete curves. In Proceedings of the 7th International Workshop on Combinatorial Image Analysis (IWCIA’00), pages 59–77. University of Caen, July 2000. 27, 28, 30
T. Y. Kong. Polyhedral analogs of locally finite topological spaces. In R. M. Shortt, editor, General Topology and Applications: Proceedings of the 188 Northeast Conference, Middletown, CT (USA), volume 123 of Lecture Notes in Pure and Applied Mathematics, pages 153–164, 1988. 29
T. Y. Kong. A digital fundamental group. Computer Graphics, 13:159–166, 1989. 27, 29, 31
T. Y. Kong and Azriel Rosenfeld. Digital topology: introduction and survey. Computer Vision, Graphics and Image Processing, 48:357–393, 1989. 27
D. G. Morgenthaler. Three-dimensional simple points: serial erosion, parallel thinning,and skeletonization. Technical Report TR-1005, Computer vision laboratory, Computer science center, University of Maryland, February 1981. 27, 28
Dale Rolfsen. Knots and Links. Mathematics Lecture Series. University of British Columbia. 30
Y. F. Tsao and K. S. Fu. A 3d parallel skeletonwise thinning algorithm. In Proceeddings, IEEE PRIP Conference, pages 678–683, 1982. 31
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
Fourey, S., Malgouyres, R. (2000). A Concise Characterization of 3D Simple Points. 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_3
Download citation
DOI: https://doi.org/10.1007/3-540-44438-6_3
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