Steerable Weighted Median Filters

A filter is steerable if transformed (i.e., rotated, scaled, etc.) versions of its impulse response can be expressed as linear combinations of a fixed set of basis functions. Steerability is important for numerous image processing applications. However, it is a property presently shared only by a specific class of linear filters. On the other hand, several classes of nonlinear filters, such as weighted median filters (WMFs), may offer certain advantages over linear filters such as robustness and edge preserving capabilities. In this paper, the concept of steerability is extended to encompass WMFs. It will be shown that, in general, a steerable WMF design technique needs to be capable of handling negative weights. Although methods that allow the design of WMFs admitting negative weights have already been proposed, such methods do not necessarily produce filters that are steerable, as opposed to the approach presented in this work. Experimental results illustrate the applicability of steerable WMFs in two applications, namely edge detection and orientation analysis.