Fuzzy set theory and the rank order filtering technique are employed to develop a fuzzy (m,n) rank order filter. The representation of this new filter is very simple and compact in contrast to the representation of median-related filters. Based on this simple representation, an efficient neural learning algorithm can be easily proposed to achieve the optimal filter design for image restoration in contrast to conventional learning algorithms use in the research area of stack filters. Our image restoration result is extremely well in comparison with that median filtering.
In order to perform neural learning, several control parameters are given to fuzzify the space bounded by the mth and nth rank order filters. Hence, the fuzzy (m,n) rank order filter can be adjusted by our proposed learning algorithm, and it then converges to an optimal fuzzy (m,n) rank order filter.