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Deterministic and statistical properties of two-dimensional FIR-median hybrid filters

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Abstract

In this paper, we present a new class of two-dimensional FIR-median hybrid (FMH) filters, which we call separable FMH filters, for image noise smoothing. In a separable FMH filter, a one-dimensional FMH filter is applied to the rows and the columns of an image successively. The deterministic properties of separable and cross window FMH filters are discussed. Under certain assumptions, it is proved that a root of a separable FMH filter is a root of the corresponding cross window FMH filter. The noise attenuating properties of a separable FMH filter are studied and compared with those of the separable median filter, the two-dimensional median filter with a square window, and the cross window FMH filter.

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References

  1. G. R. Arce and M. P. Mcloughlin, Theoretical analysis of the max/median filter,IEEE Trans. on Acoustics, Speech, and Signal Processing, vol. ASSP-35, no. 1, pp. 60–69, Jan. 1987.

    Google Scholar 

  2. J. Astola, P. Heinonen, and Y. Neuvo, On root structures of median and median-type filters,IEEE Trans. on Acoustics, Speech, and Signal Processing, vol. ASSP-35, no. 8, pp. 1199–1201, Aug. 1987.

    Google Scholar 

  3. J. P. Fitch, E. J. Coyle, and N. C. Gallagher, Jr., Root properties and convergence rates of median filters,IEEE Trans. on Acoustics, Speech, and Signal Processing, vol. ASSP-33, no. 1, pp. 230–240, Feb. 1985.

    Google Scholar 

  4. N. C. Gallagher, Jr., and G. L. Wise, A theoretical analysis of the properties of median filters,IEEE Trans. on Acoustics, Speech, and Signal Processing, vol. ASSP-29, no. 6, pp. 1136–1141, Dec. 1981.

    Google Scholar 

  5. P. Heinonen and Y. Neuvo, FIR-median hybrid filters,IEEE Trans. on Acoustics, Speech, and Signal Processing, vol. ASSP-35, no. 6, pp. 832–838, June 1987.

    Google Scholar 

  6. B. I. Justusson, Median filtering: Statistical properties, inTopics in Applied Physics, Two-Dimensional Digital Signal Processing II, T. S. Huang, ed., Springer, Berlin, 1981, pp. 161–196.

    Google Scholar 

  7. G. Liao, T. A. Nodes, and N. C. Gallagher, Jr., Output distributions of two-dimensional median filters,IEEE Trans. on Acoustics, Speech, and Signal Processing, vol. ASSP-33, no. 4, pp. 1280–1295, Oct. 1985.

    Google Scholar 

  8. M. P. Mcloughlin and G. R. Arce, Deterministic properties of the recursive separable median filter,IEEE Trans. on Acoustics, Speech, and Signal Processing, vol. ASSP-35, no. 1, pp. 98–106, Jan. 1987.

    Google Scholar 

  9. P. M. Narendra, A separable median filter for image noise smoothing,IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. PAMI-3, no. 1, pp. 20–29, Jan. 1981.

    Google Scholar 

  10. J. Neejarvi and Y. Neuvo, Sinusoidal and pulse responses of FIR-median hybrid filters,IEEE Trans. on Circuits and Systems, vol. 37, no. 12, pp. 1552–1556, Dec. 1990.

    Google Scholar 

  11. A. Nieminen, P. Heinonen, and Y. Neuvo, A new class of detail-preserving filters for image processing,IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. PAMI-9, no. 1, pp. 74–90, Jan. 1987.

    Google Scholar 

  12. T. A. Nodes and N. C. Gallagher, Jr., Median filters: Some modifications and their properties,IEEE Trans. on Acoustics, Speech, and Signal Processing, vol. ASSP-30, no. 5, pp. 739–746, Oct. 1982.

    Google Scholar 

  13. T. A. Nodes and N. C. Gallagher, Two-dimensional root structures and convergence properties of the separable median filter,IEEE Trans. on Acoustics, Speech, and Signal Processing, vol. ASSP-31, no. 6, pp. 1350–1365, Dec. 1983.

    Google Scholar 

  14. S. G. Tyan, Median filtering: Deterministic properties, inTopics in Applied Physics, Two-Dimensional Digital Signal Processing II, T. S. Huang, ed., Springer, Berlin, 1981, pp. 197–217.

    Google Scholar 

  15. Q. Wang and Y. Neuvo, On two-dimensional root structures of separable and cross median filters,Proc. of 1991 Int. Symp. on Circuits andSystems, Singapore, 11–14 June 1991, pp. 104–107.

  16. Q. Wang and Y. Neuvo, Application of median-type filtering to image segmentation in electrophoresis,Proc. of SPIE/SPSE Conference on Biomedical Image Processing II, San Jose, CA, February 24–March 1, 1991, pp. 47–58.

  17. Q. Wang and Y. Neuvo, Separable FIR-median hybrid filters for image processing,Proc. of 1991 Int. Conf. on Digital Signal Processing, Florence, Italy, Sept. 4–6, 1991.

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Authors and Affiliations

  1. Signal Processing Laboratory, Tampere University of Technology, P.O. Box 553, SF-33101, Tampere, Finland

    Qiaofei Wang & Yrjö Neuvo

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  1. Qiaofei Wang
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  2. Yrjö Neuvo
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Wang, Q., Neuvo, Y. Deterministic and statistical properties of two-dimensional FIR-median hybrid filters. Circuits Systems and Signal Process 14, 1–16 (1995). https://doi.org/10.1007/BF01183745

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  • DOI: https://doi.org/10.1007/BF01183745

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