M. Charifchefchaouni et D. Schonfeld, MORPHOLOGICAL REPRESENTATION OF ORDER-STATISTICS FILTERS, IEEE transactions on image processing, 4(6), 1995, pp. 838-845
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.