The output distribution of fuzzy weighted median filters
Yuge Nie, Kenneth E. Barner · 2003
Fuzzy weighted median (FWM) filters are developed by utilizing concepts of fuzzy ordering in the weighted median (WM) filters framework and have great advantages over their crisp counterparts. In this paper, two important properties of fuzzy ordering - the element invariant property and order invariant property - are investigated, which shall serve as the theoretical justification of FWM filters. Based on these two properties, we derive the analytical expressions for the output distribution of FWM filters, which provide systematic methods to study the statistical properties of FWM filters.