Skip to main content
SpringerLink
Log in

Finding of optimal binary morphological erosion filter via greedy and branch & bound searching

  • Published:
Journal of Mathematical Imaging and Vision Aims and scope Submit manuscript

Abstract

In this paper, an effective and efficient algorithm for finding the optimal morphological erosion filter on binary images is proposed. The design of morphological erosion filter is based on statistical method by minimizing mean square error. Traditionally, finding optimal morphological erosion filters requires searching through a large number of structuring-element combinations which is a long search and time consuming procedure. In the proposed method, the problem of finding the optimal solution is reduced to the problem of searching a minimal path on the error code graph (ECG). Since the graph satisfies some greedy criteria, only few nodes need to be traversed and examined. Experiments are conducted to illustrate the validity of our proposed method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. C.R. Baugh, “Bounds on the number of pseudothreshold function”, IEEE Trans. Comput., Vol. C 20, pp. 1602–1605, 1971.

    Google Scholar 

  2. E.R. Dougherty, “Optimal mean-square N-observation digital morphological filters. Part I: Optimal binary filters”, CVGIP: Image Understanding, Vol. 55, pp. 36–54, 1992.

    Google Scholar 

  3. E.R. Dougherty and C.R. Giardina, Morphological Methods in Image and Signal Processing, Prentice-Hall: Englewood Cliffs, NJ, 1988.

    Google Scholar 

  4. E.R. Dougherty and R.M. Haralick, “The hole spectrum-model-based optimalization of morphological filters”, Proc. SPIE, Vol. 1568, pp. 224–232, 1991.

    Google Scholar 

  5. E.R. Dougherty, A. Mathew, and V. Swarnaker, “A conditional-expectation-based implementation of the optimal mean-square binary morphological filter”, Proc. SPIE, Vol. 1451, pp. 137–147, 1991.

    Google Scholar 

  6. M. Gabbouj, E.J. Coyle, and N.C. Gallagher, “An overview of median and stack filtering”, Circuit System Signal Process, Vol. 11, No. 1 pp. 7–45, 1992.

    Google Scholar 

  7. H.J. Heijmans, “Theoretical aspects of gray-level morphology”, IEEE Trans. Pattern Anal. Machine Intell., Vol. 13, 1991.

  8. H.J. Heijmans and C. Ronse, “The algebraic basis of mathematical morphological—I: Dilations and erosions”, J. Comput. Vision, Graphic, Image Process., Vol. 50, 1990.

  9. D. Kleitman and G. Markowsky, “On dedekind's problem: The number of isotone boolean function—II”, Trans. Amer. Math. Inst., Vol. 213, 1975.

  10. R.P. Loce and E.R. Dougherty, “Using structuring-element libraries to design suboptimal morphological filters”, Proc. SPIE, Vol. 1568, pp. 233–246, 1991.

    Google Scholar 

  11. R.P. Loce and E.R. Dougherty, “Optimal morphological restoration: The morphological filter mean-absolute-error theorem”, J. Visual Comm. Image Representation, Vol. 3, pp. 412–432, 1992.

    Google Scholar 

  12. P. Maragos, “A representation theory for morphological image and signal processing”, IEEE Trans. Pattern Anal. Machine Intell., Vol. 11, No. 6, pp. 586–599, 1989.

    Google Scholar 

  13. P. Maragos and R.S. Schafer, “Morphological filters. I. Their settheoretic analysis and relations to linear shift-invariant filters”, IEEE Trans. Acoust. Speech Signal Process., Vol. ASSP 35, pp. 1153–1169, 1987.

    Google Scholar 

  14. G. Matheron, Random Sets, and Integral Geometry, Wiley: New York, 1975.

    Google Scholar 

  15. 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 discrete power-set lattice”, Circuit Systems Signal Processing, Vol. 12, pp. 409–430, 1993.

    Google Scholar 

  16. S. Muroga, Threshold Logic and Its Applications, Wiley: New York, 1971.

    Google Scholar 

  17. J. Serra, Image Analysis and Mathematical Morphology, Vol. 1, Academic Press: New York, 1988.

    Google Scholar 

  18. J. Serra, Image Analysis and Mathematical Morphology, Vol. 2, Academic Press: New York, 1988.

    Google Scholar 

  19. P.D. Wendt, E.J. Coyle, and N.C. Gallagher, “Stack filters”, IEEE Trans. Acoust. Speech Signal Process., Vol. ASSP 34, pp. 898–911, 1986.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computer Science and Information Engineering, National Central University, 32054, Chung-Li, Taiwan, R.O.C.

    Chin-Chuan Han & Kuo-Chin Fan

Authors
  1. Chin-Chuan Han
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kuo-Chin Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work is supported by National Science Council of Taiwan under grant NSC 83-0404-E-008-022.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Han, CC., Fan, KC. Finding of optimal binary morphological erosion filter via greedy and branch & bound searching. J Math Imaging Vis 6, 335–353 (1996). https://doi.org/10.1007/BF00123351

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00123351

Keywords

Search

Navigation