In recent works, a new notion of component-graph has been introduced to extend the data structure of component-tree –and the induced antiextensive filtering methodologies– from grey-level images to multivalued ones. In this article, we briefly recall the main structural key-points of component-graphs, and we present the initial algorithmic results that open the way to the actual development of component-graph-based antiextensive filtering procedures.


Component-graph component-tree multivalued images partially ordered sets connected operators antiextensive filtering 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aho, A.V., Garey, M.R., Ullman, J.D.: The transitive reduction of a directed graph. SIAM J. Comput. 1(2), 131–137 (1972)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Angulo, J.: Geometric algebra colour image representations and derived total orderings for morphological operators–Part I: Colour quaternions. J. Vis. Commun. Image R. 21(1), 33–48 (2010)CrossRefGoogle Scholar
  3. 3.
    Aptoula, E., Lefèvre, S.: A comparative study on multivariate mathematical morphology. Pattern Recogn. 40(11), 2914–2929 (2007)zbMATHCrossRefGoogle Scholar
  4. 4.
    Berger, C., Géraud, T., Levillain, R., Widynski, N., Baillard, A., Bertin, E.: Effective component tree computation with application to pattern recognition in astronomical imaging. In: ICIP, pp. 41–44 (2007)Google Scholar
  5. 5.
    Carlinet, E.: Extending the tree of shapes on colors. Master’s thesis, ENS Cachan (2012)Google Scholar
  6. 6.
    Cousty, J., Bertrand, G., Najman, L., Couprie, M.: Watershed cuts: Thinnings, shortest path forests, and topological watersheds. IEEE Trans. Pattern Anal. Mach. Intell. 32(5), 925–939 (2010)CrossRefGoogle Scholar
  7. 7.
    Goutsias, J., Heijmans, H.J.A.M., Sivakumar, K.: Morphological operators for image sequences. Comp. Vis. Imag. Under. 62(3), 326–346 (1995)CrossRefGoogle Scholar
  8. 8.
    Heijmans, H.: Theoretical aspects of gray level morphology. IEEE Trans. Pattern Anal. Mach. Intell. 13(6), 568–592 (1991)CrossRefGoogle Scholar
  9. 9.
    Jones, R.: Connected filtering and segmentation using component trees. Comp. Vis. Imag. Under. 75(3), 215–228 (1999)CrossRefGoogle Scholar
  10. 10.
    Monasse, P., Guichard, F.: Scale-space from a level lines tree. J. Vis. Commun. Image R. 11(2), 224–236 (2000)CrossRefGoogle Scholar
  11. 11.
    Naegel, B., Passat, N.: Component-trees and multi-value images: A comparative study. In: Wilkinson, M.H.F., Roerdink, J.B.T.M. (eds.) ISMM 2009. LNCS, vol. 5720, pp. 261–271. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  12. 12.
    Najman, L., Couprie, M.: Building the component tree in quasi-linear time. IEEE Trans. Image Proc. 15(11), 3531–3539 (2006)CrossRefGoogle Scholar
  13. 13.
    Passat, N., Naegel, B.: An extension of component-trees to partial orders. In: ICIP, pp. 3981–3984 (2009)Google Scholar
  14. 14.
    Passat, N., Naegel, B.: Component-trees and multivalued images: Structural properties. Technical report, INRIA-00611714 (2012),
  15. 15.
    Ronse, C., Agnus, V.: Morphology on label images: Flat-type operators and connections. J. Math. Imaging Vis. 22(2), 283–307 (2005)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Salembier, P., Garrido, L.: Binary partition tree as an efficient representation for image processing, segmentation and information retrieval. IEEE Trans. Image Proc. 9(4), 561–576 (2000)CrossRefGoogle Scholar
  17. 17.
    Salembier, P., Oliveras, A., Garrido, L.: Anti-extensive connected operators for image and sequence processing. IEEE Trans. Image Proc. 7(4), 555–570 (1998)CrossRefGoogle Scholar
  18. 18.
    Soille, P.: Constrained connectivity for hierarchical image partitioning and simplification. IEEE Trans. Pattern Anal. Mach. Intell. 30(7), 1132–1145 (2008)CrossRefGoogle Scholar
  19. 19.
    Urbach, E.R., Roerdink, J.B.T.M., Wilkinson, M.H.F.: Connected shape-size pattern spectra for rotation and scale-invariant classification of gray-scale images. IEEE Trans. Pattern Anal. Mach. Intell. 29(2), 272–285 (2007)CrossRefGoogle Scholar
  20. 20.
    Velasco-Forero, S., Angulo, J.: Supervised ordering in ℝp: Application to morphological processing of hyperspectral images. IEEE Trans. Image Proc. 20(11), 3301–3308 (2011)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Wilkinson, M.H.F., Gao, H., Hesselink, W.H., Jonker, J.-E., Meijster, A.: Concurrent computation of attribute filters on shared memory parallel machines. IEEE Trans. Pattern Anal. Mach. Intell. 30(10), 1800–1813 (2008)CrossRefGoogle Scholar
  22. 22.
    Xu, Y., Géraud, T., Najman, L.: Morphological filtering in shape spaces: Applications using tree-based image representations. In: ICPR, pp. 485–488 (2012)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Benoît Naegel
    • 1
  • Nicolas Passat
    • 2
  1. 1.ICube, UMR CNRSUniversité de StrasbourgFrance
  2. 2.CReSTIC, EA 3804Université de ReimsFrance

Personalised recommendations