Abstract
We consider the problem of morphologically sampling binary images and binary morphological image operators, as proposed by Heijmans and Toet. In the deterministic case, we obtain some new results, including approximation of continuous space erosions by discrete erosions and discretization of composite operators. These results are then applied to the case of a random closed set. We show convergence of a morphologically sampled random closed set, and its associated capacity functional, in the limit as the sampling grid size goes to zero. Similar results are obtained for the case of a morphologically transformed random closed set, and for a large class of morphological operators.
This work has been supported by the Office of Naval Research, Mathematical, Computer, and Information Sciences Division, under ONR Grant N00014–90–1345.
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© 1996 Kluwer Academic Publishers
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Sivakumar, K., Goutsias, J. (1996). Morphological Sampling of Random Closed Sets. 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_10
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DOI: https://doi.org/10.1007/978-1-4613-0469-2_10
Publisher Name: Springer, Boston, MA
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