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 for 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 coded 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
(100.2000) Image processing : Digital image processing
(100.2980) Image processing : Image enhancement
(100.3010) Image processing : Image reconstruction techniques
(100.5010) Image processing : Pattern recognition
John Bart Wilburn, "Developments in generalized ranked-order filters," J. Opt. Soc. Am. A 15, 1084-1099 (1998)