Abstract
W-operators are discrete set operators that are both translation invariant and locally defined within a finite window W. A particularly interesting property of W-operators is that they have a sup-decomposition in terms of a family sup-generating operators, that are parameterized by the operator basis. The sup-decomposition has a parallel structure that usually is not efficient for computation in conventional sequential machines. In this paper, we formalize the problem of transforming sup-decompositions into purely sequential decompositions (when they exist). The techniques were developed for general W-operators, specialized for increasing W-operators and applied on operators built by alternating compositions of dilations and erosions.
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References
G. J. F. Banon and J. Barrera. Minimal Representations for Translation-Invariant Set Mappings by Mathematical Morphology. SIAM J. Appl. Math. 51(6):1782–1798, December 1991.
J. Barrera and G. P. Salas. Set Operations on Collections of Closed Intervals and their Applications to the Automatic Programming of Morphological Machines. Journal of Electronic Imaging, 5(3):335–352, July 1996.
G. Birkhoff. Lattice Theory. American Mathematical Society, Providence, Rhode Island, 1967.
R. F. Hashimoto and J. Barrera. Finding Solutions for the Dilation Factorization Equation. Technical Report RT-MAC-9914, Departamento de Ciência da Computação, IMEUSP, November, 1999.
H. J. A. M. Heijmans. Morphological Image Operators. Academic Press, 1994.
R. Jones. The Transformation of the Basis Representation into Cascaded Representation. In Mathematical Morphology and its Applications to Signal Processing, pages 239–244. Barcelona, Spain, 1993.
J. Serra. Image Analysis and Mathematical Morphology. Academic Press, 1982.
J. Serra and L. Vincent. An Overview of Morphological Filtering. Circuits Systems Signal. Process, 11(1):47–108, 1992.
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© 2002 Kluwer Academic/Plenum Publishers
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Hashimoto, R.F., Barrera, J., Dougherty, E.R. (2002). From the Sup-Decomposition to A Sequential Decomposition. 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_3
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DOI: https://doi.org/10.1007/0-306-47025-X_3
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-7923-7862-4
Online ISBN: 978-0-306-47025-7
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