MORPHOLOGICAL REPRESENTATION OF ORDER-STATISTICS FILTERS

In this correspondence, we propose a comprehensive theory for the morp hological bounds on order-statistics filters (and their repeated itera tions). Conditions are derived for morphological openings and closings to serve as bounds (lower and upper, respectively) on order-statistic s filters (and their repeated iterations). Under various assumptions, morphological open-closings and close-openings are also shown to serve as (tighter) bounds (lower and upper, respectively) on iterations of order-statistics filters. Simulations of the application of the result s presented to image restoration are finally provided.