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Unification of Nonlinear Filtering in the Context of Binary Logical Calculus, Part II: Gray-Scale Filters

  • Edward R. Dougherty

Abstract

This second part of a two-part study concerning the logical structure of nonlinear filters treats gray-scale filters. The algebraic framework of threshold decomposition is dedscribed in terms of the appropriate underlying commuting diagram, along with the manner in which generalized stack filters fall out of the framework when it is interpreted in the context of logical calculus. Relationships between representations for morphological and generalized stack filters are expressed in cellular logic.

Key words

nonlinear filter morphological filter stack filter image algebra representation cellular logic 

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References

  1. 1.
    P.D. Wendt, E.J. Coyle, and N.C. Gallagher,“Stack filters,” IEEE Trans. Acoust., Speech,Signal Process., vol. 34, 1986.Google Scholar
  2. 2.
    J. Serra, “Anamorphoses and function lattices,” in Mathematical Morphology in Image Processing, E. Dougherty, ed., Marcel Dekker: New York, 1992.Google Scholar
  3. 3.
    J.H. Lin and E.J. Coyle, “Minimum mean absolute error estimation over the class of generalized stack filters,” IEEE Trans. Acoust., Speech, Signal Process., vol. 38, 1990.Google Scholar
  4. 4.
    J. Serra, Image Analysis and Mathematical Morphology,vol. 2, Academic Press: New York, 1988.Google Scholar
  5. 5.
    P. Maragos and R. Schafer, “Morphological filters-part II: their relations to median, order-statistic, and stack filters,” IEEE Trans. Acoust., Speech, Signal Process., vol. 35, 1987.Google Scholar
  6. 6.
    J. Serra, Image Analysis and Mathematical Morphology,Academic Press: New York, 1982.Google Scholar
  7. 7.
    E. Shih and O. Mitchell, “Threshold decomposition of gray-scale morphology into binary morphology,” IEEE Trans. Patt. Anal. Mach. Intell., vol. 11, 1989.Google Scholar
  8. 8.
    S. Sternberg, “Grayscale morphology,” Comput. Vis.,Graph., Image Process., vol. 35, 1986.Google Scholar
  9. 9.
    H. Heijmans, “Theoretical aspects of gray-level morphology,” IEEE Trans. Patt. Anal. Mach. Intell., vol. 13, 1991.Google Scholar
  10. 10.
    E.R. Dougherty and C.R. Giardina, “Morphology on umbra matrices, Internat. J. Patt. Recog. Art. Intell., vol. 2, 1988.Google Scholar
  11. 11.
    C.R. Giardina and E.R. Dougherty, Morphological Methods in Image and Signal Processing, Prentice-Hall: Englewood Cliffs, NJ, 1988.Google Scholar
  12. 12.
    P. Maragos and R. Schafer “Morphological filters-part 1: their set-theoretic analysis and relations to linear shift-invariant filters,” IEEE Trans. Acoust., Speech,Signal Process., vol. 35, 1987.Google Scholar
  13. 13.
    E.R. Dougherty, “Euclidean gray-scale granulometries: representation and umbra inducement,” J. Math. Imag. Vis., vol 1, 1992.Google Scholar

Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Edward R. Dougherty
    • 1
  1. 1.Center for Imaging ScienceRochester Institute of TechnologyRochesterFrance

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