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 function, and have presented its design method. The design of the FWM filter can be considered in terms of the design of the weight and the design of the fuzzy Boolean function separately. In the design methods developed to date, 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 filters has been significantly expanded to incorporate nearly all classes of FWM filters by establishing all weights independently and by defining the fuzzy Boolean functions by appropriate functions in addition to the sigmoid-type functions. Thus, a high-performance filter is designed by the filter weight and the fuzzy Boolean function designed for the kinds of added noise for real image processing examples, which change more flexibly as compared with the FWM filters developed in the previous design methods. In addition, a design procedure for realistic cases in which only the images which are targets of processing are known is presented and a design method for an FWM filter, which is effective in practical terms, is presented by showing its performance.