<title>Nonlinear image filtering with structural approach</title>

Abstract

In this paper, we develop a theory to design weighted order statistic filters with structural approach and discuss their applications in image filtering. By introducing a set of parameters, called M_is, the statistical properties of weighted order statistic filters are analyzed. A theorem is presented to show that any symmetric weighted order statistic filter will drive the input to a root or oscillate in a cycle of period 2. This result was proven to hold only for some weighted order statistic filters. A condition is provided to guarantee the convergence of weighted order statistic filters.