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

Content Provider	IEEE Xplore Digital Library
Author	Pao-Ta Yu Wei-Hsiang Liao
Copyright Year	1991
Abstract	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.<>
Sponsorship	IEEE Signal Processing Society
Starting Page	2678
Ending Page	2691
Page Count	14
File Size	1333771
File Format	PDF
ISSN	1053587X
Volume Number	42
Issue Number	10
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1994-10-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Statistics Filters Convergence Boolean functions Councils Filtering Upper bound Computer science Logic functions
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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