Abstract
The connection between morphological and stack filters is used in the analysis of the statistical properties of morphological filters. Closed-form expressions for the output distributions of morphological filters are given, and their statistical symmetry properties are analyzed. Asytotically tight bounds on the expectations of two-dimensional morphological filters, and asymptotic formulas for the variances of one-dimensional morphological filters are derived. These results form the basis for analyzing general asymptotic properties of morphological filters.
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Koskinen, L., Astola, J. Asymptotic behavior of morphological filters. J Math Imaging Vis 2, 117–135 (1992). https://doi.org/10.1007/BF00118585
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DOI: https://doi.org/10.1007/BF00118585