## Developments in generalized ranked-order filters

JOSA A, Vol. 15, Issue 5, pp. 1084-1099 (1998)

http://dx.doi.org/10.1364/JOSAA.15.001084

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### Abstract

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

**OCIS Codes**

(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

**Citation**

John Bart Wilburn, "Developments in generalized ranked-order filters," J. Opt. Soc. Am. A **15**, 1084-1099 (1998)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-5-1084

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### References

- B. R. Frieden, Probability, Statistical Optics and Data Testing (Springer-Verlag, Berlin, 1983), pp. 254–259.
- B. I. Justasson, “Median filtering: statistical properties,” in Two-Dimensional Signal Processing II: Transforms and Median Filters, T. S. Huang, ed. (Springer-Verlag, Berlin, 1982), pp. 161–196.
- D. Eberly, H. G. Longbotham, and J. Aragon, “Complete classifications of roots to 1-dimensional median and ranked-order filters,” IEEE Trans. Acoust. Speech Signal Process. 39, 197–200 (1991).
- S. G. Tyan, “Median filtering: deterministic properties,” in Two-Dimensional Signal Processing II: Transforms and Median Filters, T. S. Huang, ed. (Springer-Verlag, Berlin, 1982), pp. 197–218.
- H. G. Longbotham, “Theory of order statistic filters and their relationship to FIR filters,” IEEE Trans. Acoust. Speech Signal Process. 37, 275–287 (1989).
- H. A. David, Order Statistics, 2nd ed. (Wiley, New York, 1981).
- A. Bovick, T. S. Huang, and D. Muson, “A generalization of median filtering using linear combinations of order statistics,” IEEE Trans. Acoust. Speech Signal Process. 31, 1342–1350 (1983).
- J. R. Shoenfeld, Mathematical Logic (Addison-Wesley, Reading, Mass., 1967), Chaps. 6 and 7.
- J. R. Shoenfeld, Mathematical Logic (Addison-Wesley, Reading, Mass., 1967), pp. 282–292.
- G. R. Arce and R. E. Foster, “Detail preserving ranked-order based filters for image processing,” IEEE Trans. Acoust. Speech Signal Process. 37, 83–98 (1989).
- B. Chellas, Modal Logic: An Introduction (Cambridge U. Press, Cambridge, UK, 1980).

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