Abstract: In this paper, we investigate the morphological bounds on order- statistics (median) filters (and their repeated iterations). Conditions are derived for morphological openings and closing to serve as bounds (lower and upper, respectively) on order- statistics (median) filters (and their repeated iterations). Under various assumptions, morphological open-closings (open- close-openings) and close-openings (close-open-closings) are also shown to serve as (tighter) bounds (lower and upper, respectively) on iterations of order-statistics (median) filters. Conditions for the convergence of iterations of order-statistics (median) filters are proposed. Criteria for the morphological characterization of roots of order-statistics (median) filters are also proposed.!24
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