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Weighted order statistics filters-their classification, some properties, and conversion algorithm

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2 Author(s)
Pao-Ta Yu ; Inst. of Comput. Sci. & Inf. Eng., Nat. Chung Cheng Univ., Chiayi, Taiwan ; Wei-Hsiang Liao

Stack filters that are based on threshold logic with nonnegative weights and threshold value are called weighted order statistics (WOS) filters and are classified into four different types: type-0 (trivial), type-1 (decreasing), type-2 (increasing), and type-3 (mixed). A significant property of the threshold logic is that it only needs (n+1) tuples to represent its function representation if the input of this function has it variables. This associative representation is very useful in neural computing, nonlinear filtering, etc. The authors propose a significant classification of threshold logic such that the behaviors of WOS filters can be understood easily based on this classification. In the paper, all type-0, type-1, and type-2 WOS filters are shown to possess the convergence property. However, type-3 WOS filters do not necessarily possess the convergence property. Hence, the authors investigate the convergence behaviors of some type-3 WOS filters including symmetric weighted median filters and the type-3 filters proposed in Wendt [1990]. Finally, an efficient algorithm to determine whether a positive Boolean function corresponds to a weighted median filter is proposed. The authors use the property “all threshold logics are regular” to make the algorithm tractable

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Signal Processing, IEEE Transactions on  (Volume:42 ,  Issue: 10 )