Advertisement

A Lattice-Based Minimal Gray-Scale Switching Algorithm for Obtaining the Optimal Increasing Filter from the Optimal Filter

  • Edward R. Dougherty
Article
  • 54 Downloads

Abstract

For binary window-based filters, the optimal increasing filter is often derived from the optimal unconstrained (nonincreasing) filter by iteratively switching the filter values at pixels from 0 to 1 or from 1 to 0 so as to make the resulting filter be the optimal increasing filter. This paper gives a corresponding switching algorithm for gray-scale nonlinear filters, and it does so in the context of finite lattices, which makes the algorithm applicable to computational morphology on lattices. The algorithm is minimal in the sense that it involves a minimal search if one wishes to be certain to obtain the optimal increasing filter when beginning with the optimal unconstrained filter.

aperture filter computational morphology optimal filter nonlinear filter 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E.R. Dougherty and R.P. Loce, “Optimal mean-absoluteerror hit-or-miss filters: Morphological representation and estimation of the binary conditional expectation,” Optical Engineering, Vol. 32, No. 4, pp. 815–823, 1993.Google Scholar
  2. 2.
    J. Barrera, E.R. Dougherty, and N.S. Tomita, “Automatic programming of binary morphological machines by design of statistically optimal operators in the context of computational learning theory,” Electronic Imaging, Vol. 6, No. 1, pp. 54–67, 1997.Google Scholar
  3. 3.
    E.J. Coyle and J.-H. Lin, “Stack filters and the mean absolute error criterion,” IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 36, No. 8, pp. 1244–1254, 1988.Google Scholar
  4. 4.
    E.R. Dougherty, “Optimal mean-square N-observation digital morphological filters-Part I: Optimal binary filters,” CVGIP: Image Understanding, Vol. 55, No. 1, pp. 36–54, 1992.Google Scholar
  5. 5.
    A.V. Mathew, E.R. Dougherty, and V. Swarnakar, “Efficient derivation of the optimal mean-square binary morphological filter from the conditional expectation via a switching algorithm for the discrete power-set lattice,” Circuits, Systems, and Signal Processing, Vol. 12, No. 3, pp. 409–430, 1993.Google Scholar
  6. 6.
    N.S.T. Hirata, E.R. Dougherty, and J. Barrera, “A switching algorithm for design of optimal increasing binary filters over large windows,” Pattern Recognition, Vol. 33, pp. 1059–1081, 2000.Google Scholar
  7. 7.
    M. Gabbouj and E.J. Coyle, “Minimum mean absolute error stack filtering with structuring constraints and goals,” IEEE Trans. Acoustics, Speech, and Signal Processing, Vol. 38, No. 6, pp. 955–968, 1990.Google Scholar
  8. 8.
    R.P. Loce and E.R. Dougherty, “Optimal morphological restoration: The morphological filter mean-absolute-error theorem,” Visual Communication and Image Representation, Vol. 3, No. 4, pp. 412–432, 1992.Google Scholar
  9. 9.
    J. Barrera, E.R. Dougherty, and M. Brun, “Hybrid humanmachine binary morphological operator design: An independent constraint approach,” Signal Processing, Vol. 80, No. 8, pp. 1469–1487, 2000.Google Scholar
  10. 10.
    N.R. Harvey and S. Marshall, “The use of genetic algorithms in morphological filter design,” Signal Processing: Image Communication, Vol. 8, No. 1, pp. 55–72, 1996.Google Scholar
  11. 11.
    P. Kraft, N.R. Harvey, and S. Marshall, “Parallel genetic algorithms in the optimization of morphological filters: A general design tool,” Electronic Imaging, Vol. 6, No. 4, pp. 504–516, 1997.Google Scholar
  12. 12.
    P. Kuosmanen and J. Astola, “Optimal stack filters under rank selection and structural constraints,” Signal Processing, Vol. 41, No. 3, pp. 309–338, 1995.Google Scholar
  13. 13.
    L. Yin, “Optimal stack filter design: A structural approach,” IEEE Transactions on Signal Processing, Vol. 43, No. 4, pp. 831–840, 1995.Google Scholar
  14. 14.
    P. Kuosmanen and J. Astola, “Breakdown points, breakdown probabilities, midpoint sensitivity curves, and optimization of stack filters,” Circuits, Systems, and Signal Processing, Vol. 15, No. 2, pp. 165–211, 1996.Google Scholar
  15. 15.
    I.Tabus, D. Petrescu, and M. Gabbouj, “Atraining framework for stack and Boolean filtering-Fast optimal design procedures and robustness case study,” IEEE Transactions on Image Processing, Vol. 5, No. 6, pp. 809–826, 1996.Google Scholar
  16. 16.
    E.R. Dougherty, “Optimal mean-square N-observation digital morphological filters-Part II: Optimal gray-scale filters,” CVGIP:iImage Understanding, Vol. 55, No. 1, pp. 55–72, 1992.Google Scholar
  17. 17.
    E.R. Dougherty and D. Sinha, “Computational mathematical morphology,” Signal Processing, Vol. 38, pp. 21–29, 1994.Google Scholar
  18. 18.
    H. Heijmans and C. Ronse, “The algebraic basis of mathematical morphology, I. Dilations and erosions,” CVGIP: Image Understanding, Vol. 50, No. 3, 1990.Google Scholar
  19. 19.
    G.J.F. Banon and J. Barrera, “Decomposition of mappings between complete lattices by mathematical morphology, Part I. General lattices,” Signal Processing, Vol. 30, 1993.Google Scholar
  20. 20.
    E.R. Dougherty and D. Sinha, “Computational gray-scale morphology on lattices (A Comparator-based image algebra) Part I: Architecture,” Real-Time Imaging, Vol. 1, No. 1, pp. 69–85, 1995.Google Scholar
  21. 21.
    R. Hirata, E.R. Dougherty, and J. Barrera, “Aperture filters,” Signal Processing, Vol. 80, No. 4, pp. 697–721, 2000.Google Scholar
  22. 22.
    R.P. Loce and E.R. Dougherty, Enhancement and Restoration of Digital Documents: Statistical Design of Nonlinear Algorithms, SPIE Press; Bellingham, 1997.Google Scholar
  23. 23.
    E.R. Dougherty and R.P. Loce, “Precision of morphological representation estimators for translation-invariant binary filters: Increasing and nonincreasing,” Signal Processing, Vol. 40, No. 3, pp. 129–154, 1994.Google Scholar
  24. 24.
    E.R. Dougherty and J. Barrera, “Pattern recognition theory in nonlinear signal processing,” Mathematical Imaging and Vision, Vol. 16, No. 3, pp. 181–197, 2002.Google Scholar
  25. 25.
    R.P. Loce and E.R. Dougherty, “Mean-absolute-error representation and optimization of computational-morphological filters,” Computer Vision, Graphics, and Image Processing: Graphical Models and Image Processing, Vol. 57, No. 1, 1995.Google Scholar
  26. 26.
    E.R. Dougherty and J. Barrera, “Computational gray-scale image operators,” in Nonlinear Filters for Image Processing, E. Dougherty and J. Astola (Eds.), SPIE and IEEE Press; Bellingham, 1999, pp. 61–98.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Edward R. Dougherty
    • 1
  1. 1.Department of Electrical EngineeringTexas A & M UniversityUSA

Personalised recommendations