A general formulation of ranked-order filters is developed in two parts: part 1, signal-to-noise-ratio analysis and part 2, construction and analysis of a ranked-order-filter function based on a mathematical logic approach. The filter function is analyzed to define the structure of filter roots far one-dimensional (1-D) and two-dimensional (2-D) window filters as data patterns that are invariant of the filter. The 1-D and 2-D code/ window filters defined for roots of repeated patterns of binary data are defined and analyzed. The analysis concludes with an application of the coded window filter to a computer-generated 2-D noisy image containing a binary pattern and an application for feature extraction by a 2-D filter constrained by a predicate function to select only fixed-point root data structures. # 1998 Optical Society of America [S0740-3232(98)01705-0] OCIS codes: 100.5010, 100.3010, 100.2980, 100.2000.
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