Abstract
Morphological attribute openings and closings and related operators are generalizations of the area opening and closing, and allow filtering of images based on a wide variety of shape or size based criteria. A fast union-find algorithm for the computation of these operators is presented in this paper. The new algorithm has a worst case time complexity of O(N log N) where N is the image size, as opposed to O (N 2 log N) for the existing algorithm. Memory requirements are O(N) for both algorithms.
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References
E. J. Breen and R. Jones. Attribute openings, thinnings and granulometries. Computer Vision and Image Understanding, 64(3):377–389, 1996.
M. Dillencourt, H. Samet, and M. Tamminen. A general approach to connectedcomponent labeling for arbitrary image representations. Journal of the ACM, 39:253–280, 1992.
C. Fiorio and J. Gustedt. Two linear time union-find strategies for image processing. Theoretical Computer Science (A), 154:165–181, 1996.
A. Meijster and J. B. T. M. Roerdink. A disjoint set algorithm for the watershed transform. In Proc. EUSIPC0’98, IX European Signal Processing Conference, pages 1665–1668, Rhodes, Greece, 1998.
A. Meijster and M. H. F. Wilkinson. An efficient algorithm for morphological area operators. Technical Report 99-9-07, Institute for Mathematics and Computing Science, University of Groningen, submitted.
P. Salembier, A. Oliveras, and L. Garrido. Anti-extensive connected operators for image and sequence processing. IEEE Transactions on Image Processing, 7:555–570, 1998.
R. E. Tarjan. Efficiency of a good but not linear set union algorithm. Journal of the. ACM, 22:215–225, 1975.
L. Vincent. Grayscale area openings and closings, their efficient implementation and applications. In Proc. EURASIP Workshop on Mathematical Morphology and its Application to Signal Processing, pages 22–27, Barcelona, Spain, 1993.
L. Vincent. Morphological area openings and closings for grey-scale images. In Y.-L. O, A. Toet, D. Foster, H. J. A. M. Heijmans, and P. Meer, editors, Shape in Picture: Mathematical Description of Shape in Grey-level Images, pages 197–208. NATO, 1993.
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© 2002 Kluwer Academic/Plenum Publishers
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Wilkinson, M.H.F., Roerdink, J.B.T.M. (2002). Fast Morphological Attribute Operations Using Tarjan’s Union-Find Algorithm. In: Goutsias, J., Vincent, L., Bloomberg, D.S. (eds) Mathematical Morphology and its Applications to Image and Signal Processing. Computational Imaging and Vision, vol 18. Springer, Boston, MA. https://doi.org/10.1007/0-306-47025-X_34
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DOI: https://doi.org/10.1007/0-306-47025-X_34
Publisher Name: Springer, Boston, MA
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