ON ROOT STRUCTURES AND CONVERGENCE PROPERTIES OF WEIGHTED MEDIAN FILTERS

A weighted median filter is a nonlinear digital Biter consisting of a window of length 2N + 1 and a weight vector W = (W--N,..., W-0,..., W-N) A root signal of a median type filter is a signal that is invariant to the filter. However, not all weighted median filters possess the convergence property. In this paper, we shall study the root structures and the convergence behavior of a subclass of weighted median filters, called class-1 filters, which is symmetric in its weight vector, We shall introduce an important parameter, called feature value, and show that any one-dimensional unappended signal of length L will converge to a root signal in at most 3[L-2/2(2N + 2 - p)] passes of a class-1 filter with window width 2N + 1 and the feature value p.