Abstract
The foundation of mathematical morphology is based on the kernel representation of nonlinear operators in terms of rudimentary morphological operations. The practical utility of these results requires the representation of nonlinear operators based on a minimal collection of elements of the kernel—minimal basis—in terms of rudimentary morphological operations. A kernel representation of increasing—not necessarily spatially—invariant—operators in terms of spatially—variant morphological erosions and dilations is provided. The existence of a unique minimal basis representation in the Euclidean space of increasing—not necessarily spatially—invariant—upper semi—continuous operators for the hit-or-miss topology in terms of spatially-variant morphological erosions and dilations is established.
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References
G. Matheron, Random Sets and Integral Geometry. J.Wiley and Sons: New York, New York, 1975.
S. Beucher, J.M. Blosseville and F. Lenoir, “Traffic spatial measurements using video image processing,” Proceedings of the SPIE Conference on Intelligent Robots and Computer Vision, vol. 848, pp. 648–655, Cambridge, Massachusetts, Nov. 2–6, 1987.
P.A. Maragos and R.W. Schafer, “Morphological filters - Part I: Their set-theoretic analysis and relations to linear shift-invariant filters,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 35, pp. 1153–1169,1987.
J. Serra, Image Analysis and Mathematical Morphology. Volume 2: Theoretical Advances. Academic Press: New York, New York, 1988.
G.J.F. Banon and J. Barrera, “Minimal representation for translation-invariant set mappings by mathematical morphology,” SIAM Journal of Applied Mathematics, vol. 51, pp. 1782–1798, 1991.
J.G. Verly and R.L. Delanoy, “Adaptive mathematical morphology for range imagery,” IEEE Transactions on Image Processing, vol. 2, pp. 272–275,1993.
G.J.F. Banon and J. Barrera, “Decomposition of mappings between complete lattices by mathematical morphology: Part I. General lattices,” Signal Processing, vol. 30, pp. 299–327, 1993.
Mohammed Charif-Chefchaouni, Morphological Representation of Nonlinear Filters: Theory and Applications. Department of Electrical Engineering and Computer Science, University of Illinois at Chicago, Chicago, Illinois, Sep. 1993.
M. Charif-Chefchaouni and D. Schonfeld, “Spatially-variant morphological skeleton representation,” Proceedings of the SPIE Workshop on Image Algebra and Morphological Image Processing V, vol. 2300, pp. 290–299, San Diego, California, July 25–26, 1994.
M. Charif-Chefchaouni and D. Schonfeld, “Spatially-variant mathematical morphology,” Proceedings of the IEEE International Conference on Image Processing, pp. 555–559, Austin, Texas, Nov. 13–16,1994.
H.J.A.M. Heijmans, Morphological Image Operators. Academic Press: San Diego, California, 1994.
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© 1996 Kluwer Academic Publishers
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Charif-Chefchaouni, M., Schonfeld, D. (1996). Spatially-Variant Mathematical Morphology. In: Maragos, P., Schafer, R.W., Butt, M.A. (eds) Mathematical Morphology and its Applications to Image and Signal Processing. Computational Imaging and Vision, vol 5. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0469-2_7
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DOI: https://doi.org/10.1007/978-1-4613-0469-2_7
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