Abstract
In this paper we introduce a new thinning algorithm, called MB, which is optimized with respect to the total number of elementary Boolean operators needed to perform it. We first emphasize the sound foundations of the algorithm, which is built by expressing into the Boolean language the three following constraints: (1) homotopy, (2) median axis and (3) isotropy. The MB algorithm benefits from both novel algorithmic ideas and systematic logic minimization. By hunting down any redundancy in the expressions of topological/geometrical features, we achieve a procedure that is: firstly, dramatically low-cost, as it is completely computed in 18 Boolean binary operators per iteration, and secondly, fully parallel, or one-single-pass, which guarantees that the number of iterations equals half the biggest object thickness.
Chapter PDF
Similar content being viewed by others
Keywords
References
C. Arcelli. A condition for digital points removal. Signal Processing, 1-4:283â285, 1979.
H. Blum. A tranformation for extracting new descriptors of shape. In Proc. Symposium Models for the perception of speech and visual form, pages 362â380. W. Wathen-Dunned.M.I.T. Press Cambridge MA, 1967.
Rafael Cardoner and Federico Thomas. Residuals + Directional Gaps = Skeletons. Pattern Recognition Letters, 18:343â353, 1997.
Ching-Sung Chen and Wen-Hsiang Tsai. A new Fast One-Pass Thinning Algorithm and its Parallel Harware Implementation. Pattern Recognition Letters, 11:471â477, 1990.
Zicheng Guo and Richard W. Hall. Fast Fully Parallel Thinning Algorithms. Computer Vision, Graphics and Image Processing, 55-3:317â328, 1992.
Richard W. Hall. Optimal Small Operator Supports for Fully Parallel Thinning algorithms. IEEE Transactions on pattern analysis and machine intelligence, 15-8:828â833, 1993.
C.J. Hilditch. Linear skeletons from square cupboards. Machine Intelligence, 4:403â420, 1969.
Ben-Kwei Jang and Roland T. Chin. Analysis of thinning algorithms using math-ematical morphology. IEEE Transactions on pattern analysis and machine intelligence, 12-6:514â551, 1990.
T.Y. Kong and A. Rosenfeld. Digital Topology: Introduction and Survey. Computer Vision, Graphics and Image Processing, 48:357â393, 1989.
Louisa Lam, Seong-Whan Lee, and Ching Y. Suen. Thinning methodologies: A Comprehensive Survey. IEEE Transactions on pattern analysis and machine Intelligence, 14:869â885, 1992.
Louisa Lam and Chin Y. Suen. An Evaluation of Parallel Thinning Algorithms for Character Recognition. IEEE Transactions on pattern analysis and machine intelligence, 17-9:914â919, 1995.
Jan Olszewski. A flexible thinning algorithm allowing parallel, sequential and distributed application. ACM Transactions on Mathematical Software, 18-1:35â45, 1992.
F. Paillet, D. Mercier, and T.M. Bernard. Making the most of 15k lambda2 silicon area for a digital retina PE. In T.M. Bernard, editor, Proc. SPIE, Vol. 3410, Advanced Focal Plane Arrays and Electronic Cameras, pages 158â167, ZĂŒrich, Switzerland, May 1998.
Christian Ronse. A topological characterization of thinning. Theoretical Computer Science, 43:31â41, 1986.
Christian Ronse. Minimal test patterns for connectivity preservation in parallel thinning algorithms for binary digital images. Discrete Applied Mathematics, 21:67â79, 1988.
D. Rutovitz. Pattern Recognition. J.R. Statist. Soc., 129:504â530, 1966.
C.E. Shannon. The synthesis of two-terminal switching circuits. Bell Systems Tech. J., 1949.
Alan Stewart. A one-pass thinning algorithm with interference guards. Pattern Recognition Letters, 15:825â832, 1994.
S. Suzuki and K. Abe. Binary picture thinning by an iterative parallel two-subcycle operation. Pattern Recognition, 10-3:297â307, 1987.
Luc Vincent. Algorithmes morphologiques Ă base de file dâattente et de lacets. Extension aux graphes. PhD thesis, Ecole Nationale SupĂ©rieure des Mines de Paris, May 1990.
Rei-Yao Wu and Wen-Hsiang Tsai. A new One-Pass Parallel Thinning Algorithm for binary images. Pattern Recognition Letters, 13:715â723, 1992.
S. Yokoi, J.I. Toriwaki, and T. Fukumura. Topological properties in digitized binary pictures. Sytems, Computers, Controls, 4-6:32â39, 1973.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Manzanera, A., Bernard, T.M., PrĂȘteux, F., Longuet, B. (1999). Ultra-Fast Skeleton Based on an Isotropic Fully Parallel Algorithm. In: Bertrand, G., Couprie, M., Perroton, L. (eds) Discrete Geometry for Computer Imagery. DGCI 1999. Lecture Notes in Computer Science, vol 1568. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49126-0_24
Download citation
DOI: https://doi.org/10.1007/3-540-49126-0_24
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65685-2
Online ISBN: 978-3-540-49126-2
eBook Packages: Springer Book Archive