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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© 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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