Second-Order Connected Attribute Filters Using Max-Trees

  • Georgios K. Ouzounis
  • Michael H. F. Wilkinson
Part of the Computational Imaging and Vision book series (CIVI, volume 30)


The work presented in this paper introduces a novel method for second-order connected attribute filtering using Max-Trees. The proposed scheme is generated in a recursive manner from two images, the original and a modified copy by an either extensive or an anti-extensive operator. The tree structure is shaped by the component hierarchy of the modified image while the node attributes are based on the connected components of the original image. Attribute filtering of second-order connected sets proceeds as in conventional Max-Trees with no further computational overhead.


second-order connectivity Max-Tree attribute filters clustering partitioning 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    U. Braga-Neto and J. Goutsias. Connectivity on complete lattices: New results. Comp. Vis. Image Understand., 85:22–53, 2002.Google Scholar
  2. [2]
    U. Braga-Neto and J. Goutsias. A multiscale approach to connectivity. Comp. Vis. Image Understand., 89:70–107, 2003.CrossRefGoogle Scholar
  3. [3]
    E. J. Breen and R. Jones. Attribute openings, thinnings and granulometries. Comp. Vis. Image Understand., 64(3):377–389, 1996.Google Scholar
  4. [4]
    P. Maragos and R. D. Ziff. Threshold superposition in morphological image analysis systems. IEEE Trans. Pattern Anal. Mach. Intell., 12(5), 1990.Google Scholar
  5. [5]
    A. Meijster and M. H. F. Wilkinson. A comparison of algorithms for connected set openings and closings. IEEE Trans. Pattern Anal. Mach. Intell., 24(4):484–494, 2002.CrossRefGoogle Scholar
  6. [6]
    C. Ronse. Openings: Main properties, and how to construct them. Technical report, Université Louis Pasteur, Strasbourg, 1990.Google Scholar
  7. [7]
    P. Salembier, A. Oliveras, and L. Garrido. Anti-extensive connected operators for image and sequence processing. IEEE Trans. Image Proc., 7:555–570, 1998.CrossRefGoogle Scholar
  8. [8]
    J. Serra. Connectivity on complete lattices. Mathematical Imaging and Vision, 9:231–251, 1998.CrossRefGoogle Scholar
  9. [9]
    C. S. Tzafestas and P. Maragos. Shape connectivity: Multiscale analysis and application to generalized granulometries. J. Math. Imag. Vis., 17:109–129, 2002.CrossRefGoogle Scholar
  10. [10]
    E. R. Urbach and M. H. F Wilkinson. Shape-only granulometries and grey-scale shape filters. In Proc. Int. Symp. Math. Morphology (ISMM) 2002, pages 305–314, 2002.Google Scholar
  11. [11]
    M. H. F. Wilkinson. Attribute-space connected filters. In Proc. Int. Symp. Math. Morphology (ISMM) 2005, 18–20 Apr 2005. These proceedings, pp. 85–94.Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  • Georgios K. Ouzounis
    • 1
  • Michael H. F. Wilkinson
    • 1
  1. 1.Institute of Mathematics and Computing ScienceUniversity of GroningenGroningen

Personalised recommendations