Abstract
In digital topology, a 1 in a binary image is said to be simple if its deletion from the image “preserves topology”. Two (closely related) sets of necessary and sufficient conditions for a 1 in a 2-, 3- or 4-dimensional binary image to be simple are established. The 4-dimensional cases of these results may be regarded as the principal contribution of this paper. A different discrete characterization of simple 1's in 2-, 3-and 4-dimensional binary images, discovered by A. W. Roscoe and the author, is also presented (without proof).
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References
M. A. Armstrong, Basic Topology, Springer-Verlag, New York, 1983.
S. S. Cairns, Introductory Topology, Ronald Press, New York, 1968.
T. Y. Kong, On topology preservation in 2-D and 3-D thinning, International Journal of Pattern Recognition and Artificial Intelligence 9, 1995, 813–844.
T. Y. Kong and A. W. Roscoe, Characterizations of simply-connected finite polyhedra in 3-space, Bulletin of the London Mathematical Society 17, 1985, 575–578.
T. Y. Kong and A. W. Roscoe, Simple Points in 4-Dimensional (and Higher-Dimensional) Binary Images. Paper in preparation.
G. Malandain and G. Bertrand, Fast characterization of 3D simple points, Proceedings, 11th IAPR International Conference on Pattern Recognition, Volume 111, The Hagues, The Netherlands, 1992, 232–235.
A. Rosenfeld, Connectivity in digital pictures, J. ACM 17, 1970, 146–160.
P. K. Saha, B. Chanda and D. D. Majumder, Principles and Algorithms for 2D and 3D Shrinking, Technical Report TR/KBCS/2/91, N. C. K. B. C. S. Library, Indian Statistical Institute, Calcutta, India, 1991.
Y. F. Tsao and K. S. Fu, A 3D parallel skeletonwise thim-drig algorithm, Proceedings, IEEE Computer Society Conference on Pattern Recognition and Image Processing, 1982, 678–683.
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© 1997 Springer-Verlag Berlin Heidelberg
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Yung Kong, T. (1997). Topology-preserving deletion of 1's from 2-, 3- and 4-dimensional binary images. In: Ahronovitz, E., Fiorio, C. (eds) Discrete Geometry for Computer Imagery. DGCI 1997. Lecture Notes in Computer Science, vol 1347. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0024826
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DOI: https://doi.org/10.1007/BFb0024826
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