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 c onvergence 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 f ilter with window width 2N + 1 and the feature value p.