Generalized fuzzy weighted median filter and its design method

Since weighted median filters effective in recovering images belong to the class of stack filters, the authors have proposed a fuzzy weighted median ( FWM) filter, which is a weighted median filter defined by a fuzzy Boolean f unction, and have presented its design method. The design of the FWM filter can be considered in terms of the design of die weight and the design of t he fuzzy Boolean function separately. In the design methods developed to da te, the fuzzy Boolean functions are sigmoid-type functions and the weights are S-type functions with only the distance from the processing point as a variable, which are approximated and require derivations of four parameters , which is an easy task. Such methods, however, are restricted to the class of designable FWM filters. In this paper, the class of designable FWM filt ers has been significantly expanded to incorporate nearly all classes of FW M filters by establishing all weights independently and by defining the fuz zy Boolean functions by appropriate functions in addition to the sigmoid-ty pe functions. Thus, a high-performance filter is designed by the filter wei ght and the fuzzy Boolean function designed for the kinds of added noise fo r real image processing examples, which change more flexibly as compared wi th the FWM filters developed in the previous design methods. In addition, a design procedure for realistic cases in which only the images which are ta rgets of processing are known is presented and a design method for an FWM f ilter, which is effective in practical terms, is presented by showing its p erformance. (C) 2000 Scripta Technica, Electron Comm Jpn Pt 3, 84(2): 95-10 6, 2001.