The Connection between Generalized Soft Morphological Operations and Stack Filters

Abstract
In this paper, explicit formulas for stack filter expressions of generalized soft morphological filters are presented. These formulas make it possible to derive analytical results for their statistical properties. The statistical properties of generalized soft morphological filters are studied and illustrated in this paper. Especially, the output expectations and variances of several generalized soft morphological filters are computed for different noise distributions.

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