SOME ROOT PROPERTIES OF RECURSIVE WEIGHTED MEDIAN FILTERS

Abstract

The weights of weighted median and recursive weighted median filters have close relationship with the root signal characteristics of these filters. In this paper, we find a set of conditions on weights under which a recursive weighted median filter preserves monotone or locally monotone sequence and that under which any input sequence converges to a locally monotone sequence after a finite number of passes. We also find a set of conditions on weights under which the output of a recursive weighted median filter is the same as that of a recursive median filter.