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Journal of Inforamtion Science and Engineering, Vol.11 No.4, pp.567-593 (December 1995)
An Optimal Design of Fuzzy (m,n) Rank Order
Filtering with Hard Decision Neural Learning*

Rong-Chung Chen and Pao-Ta Yu
Institute of Computer Science and Information Engineering
National Chung Cheng University
Chiayi, Taiwan 621, R.O.C.

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.

Keywords: median filter, rank order filter, threshold decomposition, positive Boolean function, stacking property, the fuzzy(m,n) rank order filter, winner-take-all learning rule

Received August 26, 1994; revised May 19, 1995.
Communicated by Zen Chen.
*This work is supported by National Science Council of the Republic of China NSC83-0408-E-194-001.