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Multiscale Connected Operators

  • Ulisses Braga-NetoEmail author
Article

Abstract

Among the major developments in Mathematical Morphology in the last two decades are the interrelated subjects of connectivity classes and connected operators. Braga-Neto and Goutsias have proposed an extension of the theory of connectivity classes to a multiscale setting, whereby one can assign connectivity to an object observed at different scales. In this paper, we study connected operators in the context of multiscale connectivity. We propose the notion of a σ-connected operator, that is, an operator connected at scale σ. We devote some attention to the study of binary σ-grain operators. In particular, we show that families of σ-grain openings and σ-grain closings, indexed by the connectivity scale parameter, are granulometries and anti-granulometries, respectively. We demonstrate the use of multiscale connected operators with image analysis applications. The first is the scale-space representation of grayscale images using multiscale levelings, where the role of scale is played by the connectivity scale. Then we discuss the application of multiscale connected openings in granulometric analysis, where both size and connectivity information are summarized. Finally, we describe an application of multiscale connected operators to an automatic target recognition problem.

Keywords

connectivity connectivity classes connected operators multiscale connectivity grain operators flattenings levelings image analysis scale-space granulometry pattern spectrum granulometric analysis automatic target recognition 

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References

  1. 1.
    S. Batman and E. Dougherty, “Size distributions for multivariate morphological granulometries: Texture classification and statistical properties”Optical Engineering, Vol. 36, pp. 1518–1529, 1997.Google Scholar
  2. 2.
    G. Birkhoff,Lattice Theory, 3rd edition, Vol. 25, American Mathematical Society, Providence, Rhode Island,1967.Google Scholar
  3. 3.
    U.M. Braga-Neto and J. Goutsias, “Constructing multiscale connectivities” to appear inComputer Vision and Image Understanding, 2005.Google Scholar
  4. 4.
    U.M. Braga-Neto, M. Choudhary, and J. Goutsias, “Automatic target detection and tracking on forward-looking infrared image sequences using morphological connected operators”Journal of Electronic Imaging, Vol. 13, No. 4, pp. 802–813, 2004.Google Scholar
  5. 5.
    U.M. Braga-Neto and J. Goutsias, “Multiresolution connectivity: An axiomatic approach” in Mathematical Morphology and its Applications to Image and Signal Processing, J. Goutsias, L. Vincent, and D.S. Bloomberg (Eds.), Kluwer: Boston, Massachusetts, 2000, pp. 159–168.Google Scholar
  6. 6.
    U.M. Braga-Neto and J. Goutsias, “Connectivity on complete lattices: New results”Computer Vision and Image Understanding, Vol. 85, No. 1, pp. 22–53, 2002.Google Scholar
  7. 7.
    U.M. Braga-Neto and J. Goutsias, “A multiscale approach to connectivity”Computer Vision and Image Understanding, Vol. 89, No. 1, pp. 70–107,2003.Google Scholar
  8. 8.
    U.M. Braga-Neto and J. Goutsias, “A theoretical tour of connectivity in image processing and analysis”Journal of Mathematical Imaging and Vision, Vol. 19, No. 1, pp. 5–31, 2003.Google Scholar
  9. 9.
    J. Crespo and R.W. Schafer, “Locality and adjacency stability constraints for morphological connected operators”Journal of Mathematical Imaging and Vision, Vol. 7, pp. 85–102, 1997.Google Scholar
  10. 10.
    J. Crespo, J. Serra, and R.W. Schafer, “Theoretical aspects of morphological filters by reconstruction”Signal Processing, Vol. 47, No. 2, pp. 201–225, 1995.Google Scholar
  11. 11.
    H.J.A.M. Heijmans, “Connected morphological operators for binary images”Computer Vision and Image Understanding, Vol. 73, pp. 99–120, 1999.Google Scholar
  12. 12.
    H.J.A.M. Heijmans,Morphological Image Operators, Academic Press: Boston, MA, 1994.Google Scholar
  13. 13.
    R. Jones, “Connected filtering and segmentation using component trees”Computer Vision and Image Understanding, Vol. 75, pp. 215–228, 1999.Google Scholar
  14. 14.
    J.J. Koenderink, “The structure of images”Biological Cybernetics, Vol. 50, pp. 363–370, 1984.Google Scholar
  15. 15.
    M. Kunt, A. Ikonomopoulos, and M. Kocher, “Second generation image coding techniques”Proceedings of the IEEE, Vol. 73, pp. 549–574, 1985.Google Scholar
  16. 16.
    P. Maragos, “Pattern spectrum and multiscale shape representation”IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 11, pp. 701–716, 1989.Google Scholar
  17. 17.
    F. Meyer, “From connected operators to levelings” in Mathematical Morphology and its Applications to Image and Signal Processing, H.J.A.M. Heijmans and J.B.T.M. Roerdink (Eds.),Kluwer: Dordrecht, 1998, pp. 191–198.Google Scholar
  18. 18.
    F. Meyer, “The levelings.” InMathematical Morphology and its Applications to Image and Signal Processing, H.J.A.M. Heijmans and J.B.T.M. Roerdink (Eds.), Kluwer: Dordrecht, 1998, pp. 199–206.Google Scholar
  19. 19.
    F. Meyer and P. Maragos, “Morphological scale-space representation with levelings” inScale-Space’99 Symposium, M. Nielsen et al. (Eds.), Springer-Verlag: Berlin Heidelberg, 1999, pp. 187–198.Google Scholar
  20. 20.
    C. Ronse, “Set-theoretic algebraic approaches to connectivity in continuous or digital spaces”Journal of Mathematical Imaging and Vision, Vol. 8, pp. 41–58, 1998.Google Scholar
  21. 21.
    C. Ronse and J. Serra, “Geodesy and connectivity in lattices”Fundamenta Informaticae, Vol. 46, pp. 349–395, 2001.Google Scholar
  22. 22.
    A. Rosenfeld and A.C. Kak,Digital Picture Processing, 2nd edition. Academic Press: Orlando, Florida, 1982.Google Scholar
  23. 23.
    P. Salembier, A. Oliveras, and L. Garrido, “Antiextensive connected operators for image and sequence processing”IEEE Transactions on Image Processing, Vol. 7, pp. 555–570, 1998.Google Scholar
  24. 24.
    P. Salembier and M. Pardàs, “Hierarchical morphological segmentation for image sequence coding”IEEE Transactions on Image Processing, Vol. 3, pp. 639–651, 1994.Google Scholar
  25. 25.
    P. Salembier and J. Serra, “Flat zones filtering, connected operators, and filters by reconstruction”IEEE Transactions on Image Processing, Vol. 4, pp. 1153–1160, 1995.Google Scholar
  26. 26.
    P. Salembier and H. Sanson, “Robust motion estimation using connected operators” inProceedings of the IEEE International Conference on Image Processing, Vol. 1. Santa Barbara, California, 1997, pp. 77–80.Google Scholar
  27. 27.
    J. Serra (Ed.).Image Analysis and Mathematical Morphology. Vol. 2 Theoretical Advances, Academic Press: London, England, 1988.Google Scholar
  28. 28.
    J. Serra, “Connectivity on complete lattices”Journal of Mathematical Imaging and Vision, Vol. 9, pp. 231–251, 1998.Google Scholar
  29. 29.
    J. Serra, “Connections for sets and functions”Fundamenta Informaticae, Vol. 41, pp. 147–186, 2000.Google Scholar
  30. 30.
    J. Serra and P. Salembier, “Connected operators and pyramids” inProceedings of the SPIE Conference on Image Algebra and Morphological Image Processing IV, Vol. 2030, San Diego, California, 1993, pp. 65–76.Google Scholar
  31. 31.
    V. Vilaplana and F. Marques, “Face segmentation using connected operators” in Mathematical Morphology and its Applications to Image and Signal Processing, H.J.A.M. Heijmans and J.B.T.M. Roerdink (Eds.), Kluwer: Boston, Massachusetts, 1998, pp. 207–214.Google Scholar
  32. 32.
    L. Vincent, “Morphological area openings and closings for grayscale images” inProceedings of NATO Shape in Picture Workshop, Driebergen: The Netherlands, 1993, pp. 22–27.Google Scholar
  33. 33.
    L. Vincent, “Morphological grayscale reconstruction in image analysis: Applications and efficient algorithms”IEEE Transactions on Image Processing, Vol. 2, pp. 176–201, 1993.Google Scholar
  34. 34.
    A.P. Witkin, “Scale-space filtering” inProceedings of 7th International Joint Conference on Artificial Intelligence, Karlsruhe, West Germany, 1983, pp. 1019–1022.Google Scholar

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© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Virology and Experimental Therapy LaboratoryAggeu Magalhães Research Center-CPqAM/FIOCRUZBrazil

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