In this paper a hyperconnectivity class that tries to address the leakage problem typical of connected filters is used. It shows similarities with the theory of viscous lattices. A novel algorithm to perform attribute filtering of viscous-hyperconnected components is proposed. First, the max-tree of the image eroded by a structuring element is built: it represents the hierarchy of the cores of the hyperconnected components. Then, a processing phase takes place and the node attributes are updated consistently with the pixels of the actual hyperconnected components. Any state-of-the-art algorithm can be used to build the max-tree of the component cores. An issue arises: edges of components are not always correctly preserved. Implementation and performance are presented. A possible solution is put forward and it will be treated in future work.


Hyperconnected components Max-tree Attribute filtering 


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  1. 1.
    Bender, M.A., Farach-Colton, M.: The lca problem revisited. In: Gonnet, G.H., Viola, A. (eds.) LATIN 2000. LNCS, vol. 1776, pp. 88–94. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  2. 2.
    Braga-Neto, U., Goutsias, J.: A theoretical tour of connectivity in image processing and analysis. J. Math. Imaging Vis. 19(1), 5–31 (2003), http://dx.doi.org/10.1023/A:1024476403183 CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Breen, E.J., Jones, R.: Attribute openings, thinnings and granulometries. Comp. Vis. Image Understand. 64(3), 377–389 (1996)CrossRefGoogle Scholar
  4. 4.
    Ouzounis, G.K., Wilkinson, M.H.F.: Mask-based second generation connectivity and attribute filters. IEEE Transactions on Pattern Analysis and Machine Intelligence 29(6), 990–1004 (2007)CrossRefGoogle Scholar
  5. 5.
    Ouzounis, G.K., Wilkinson, M.H.F.: Hyperconnected attribute filters based on k-flat zones. IEEE Transactions on Pattern Analysis and Machine Intelligence 33(2), 224–239 (2011)CrossRefGoogle Scholar
  6. 6.
    Perret, B.: Inf-structuring functions: A unifying theory of connections and connected operators. J. Math. Imaging Vis. 51(1), 171–194 (2015)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Perret, B., Cousty, J., Tankyevych, O., Talbot, H., Passat, N.: Directed connected operators: Asymmetric hierarchies for image filtering and segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence (2014)Google Scholar
  8. 8.
    Perret, B., Lefevre, S., Collet, C., Slezak, E.: Hyperconnections and hierarchical representations for grayscale and multiband image processing. IEEE Transactions on Image Processing 21(1), 14–27 (2012)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Salembier, P., Oliveras, A., Garrido, L.: Anti-extensive connected operators for image and sequence processing. IEEE Transactions on Image Processing 7, 555–570 (1998)CrossRefGoogle Scholar
  10. 10.
    Salembier, P., Serra, J.: Flat zones filtering, connected operators, and filters by reconstruction. IEEE Transactions on Image Processing 4, 1153–1160 (1995)CrossRefGoogle Scholar
  11. 11.
    Santillán, I., Herrera-Navarro, A.M., Mendiola-Santibáñez, J.D., Terol-Villalobos, I.R.: Morphological connected filtering on viscous lattices. J. Math. Imaging Vis. 36(3), 254–269 (2010), http://dx.doi.org/10.1007/s10851-009-0184-8 CrossRefGoogle Scholar
  12. 12.
    Serra, J.: Image Analysis and Mathematical Morphology. II: Theoretical Advances. Academic Press, London (1988)Google Scholar
  13. 13.
    Serra, J.: Viscous lattices. In: Proc. Int. Symp. Math. Morphology (ISMM 2002), pp. 79–90 (2002)Google Scholar
  14. 14.
    Serra, J.: Connectivity on complete lattices. J. Math. Imag. Vis. 9(3), 231–251 (1998), http://dx.doi.org/10.1023/A:1008324520475 CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Sofou, A., Tzafestas, C., Maragos, P.: Segmentation of soilsection images using connected operators. In: Int. Conf. Image Proc. 2001, pp. 1087–1090 (2001)Google Scholar
  16. 16.
    Terol-Villalobos, I.R., Vargas-Vzquez, D.: Openings and closings with reconstruction criteria: A study of a class of lower and upper levelings. J. Electronic Imaging 14(1), 013006 (2005), http://dblp.uni-trier.de/db/journals/jei/jei14.html#Terol-VillalobosV05
  17. 17.
    Tzafestas, C.S., Maragos, P.: Shape connectivity: Multiscale analysis and application to generalized granulometries. J. Math. Imag. Vis. 17, 109–129 (2002)CrossRefMATHMathSciNetGoogle Scholar
  18. 18.
    Urbach, E.R., Wilkinson, M.H.F.: Efficient 2-D gray-scale morphological transformations with arbitrary flat structuring elements. IEEE Transactions on Image Processing 17, 1–8 (2008)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Wilkinson, M.H.F.: Connected filtering by reconstruction: Basis and new advances. In: 15th IEEE International Conference on Image Processing, ICIP 2008, pp. 2180–2183 (October 2008)Google Scholar
  20. 20.
    Wilkinson, M.H.F.: Attribute-space connectivity and connected filters. Image Vision Comput. 25(4), 426–435 (2007), http://dx.doi.org/10.1016/j.imavis.2006.04.015 CrossRefGoogle Scholar
  21. 21.
    Wilkinson, M.H.F.: An axiomatic approach to hyperconnectivity. In: Wilkinson, M.H.F., Roerdink, J.B.T.M. (eds.) ISMM 2009. LNCS, vol. 5720, pp. 35–46. Springer, Heidelberg (2009), http://dx.doi.org/10.1007/978-3-642-03613-2_4 CrossRefGoogle Scholar
  22. 22.
    Wilkinson, M.H.F.: Hyperconnectivity, attribute-space connectivity and path openings: Theoretical relationships. In: Wilkinson, M.H.F., Roerdink, J.B.T.M. (eds.) ISMM 2009. LNCS, vol. 5720, pp. 47–58. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  23. 23.
    Wilkinson, M.H.F.: Hyperconnections and openings on complete lattices. In: Soille, P., Pesaresi, M., Ouzounis, G.K. (eds.) ISMM 2011. LNCS, vol. 6671, pp. 73–84. Springer, Heidelberg (2011), http://dx.doi.org/10.1007/978-3-642-21569-8_7 CrossRefGoogle Scholar

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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute for Mathematics and Computing ScienceUniversity of GroningenGroningenThe Netherlands

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