Hierarchies and Climbing Energies

  • Jean Serra
  • Bangalore Ravi Kiran
  • Jean Cousty
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7441)


A new approach is proposed for finding the ”best cut” in a hierarchy of partitions by energy minimization. Said energy must be ”climbing” i.e. it must be hierarchically and scale increasing. It encompasses separable energies [5], [9] and those which composed under supremum [14], [12]. It opens the door to multivariate data processing by providing laws of combination by extrema and by products of composition.


Shape Descriptor Compression Rate Separable Energy Binary Energy Partial Partition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Arbelaez, P., Maire, M., Fowlkes, C., Malik, J.: Contour Detection and Hierarchical Image Segmentation. IEEE PAMI 33 (2011)Google Scholar
  2. 2.
    Ballester, C., Caselles, V., Igual, L., Garrido, L.: Level lines selection with variational models for segmentation and encoding. JMIV 27, 5–27 (2007)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Cardelino, J., Caselles, V., Bertalmío, M., Randall, G.: A contrario hierarchical image segmentation. In: IEEE ICIP 2009, Cairo, Egypt (2009)Google Scholar
  4. 4.
    Cousty, J., Najman, L.: Incremental Algorithm for Hierarchical Minimum Spanning Forests and Saliency of Watershed Cuts. In: Soille, P., Pesaresi, M., Ouzounis, G.K. (eds.) ISMM 2011. LNCS, vol. 6671, pp. 272–283. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  5. 5.
    Guigues, L.: Modèles multi-échelles pour la segmentation d’images.Thèse doctorale Université de Cergy-Pontoise (Décembre 2003)Google Scholar
  6. 6.
    Najman, L., Schmitt, M.: Geodesic Saliency of Watershed Contours and Hierarchical Segmentation. IEEE Trans. PAMI (1996)Google Scholar
  7. 7.
    Najman, L.: On the Equivalence Between Hierarchical Segmentations and Ultrametric Watersheds. JMIV 40(3), 231–247 (2011)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Ronse, C.: Partial partitions, partial connections and connective segmentation. JMIV 32, 97–125 (2008)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Salembier, Ph., Garrido, L.: Binary Partition Tree as an Efficient Representation for Image Processing, Segmentation, and Information Retrieval. IEEE TIP 9(4), 561–576 (2000)Google Scholar
  10. 10.
    Serra, J.: Hierarchies and optima. In: Domenjoud, E. (ed.) DGCI 2011. LNCS, vol. 6607, pp. 35–46. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  11. 11.
    Serra, J., Kiran, B.R.: Climbing the pyramids. Techn. report ESIEE (March 2012)Google Scholar
  12. 12.
    Soille, P.: Constrained connectivity for hierarchical image partitioning and simplification. IEEE PAMI 30, 1132–1145 (2008)CrossRefGoogle Scholar
  13. 13.
    Soille, P., Grazzini, J.: Constrained Connectivity and Transition Regions. In: Wilkinson, M.H.F., Roerdink, J.B.T.M. (eds.) ISMM 2009. LNCS, vol. 5720, pp. 59–69. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  14. 14.
    Zanoguera, F., Marcotegui, B., Meyer, F.: A toolbox for interactive segmentation based on nested partitions. In: Proc. of ICIP 1999, Kobe, Japan (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jean Serra
    • 1
  • Bangalore Ravi Kiran
    • 1
  • Jean Cousty
    • 1
  1. 1.Laboratoire d’Informatique Gaspard-Monge, A3SI, ESIEEUniversité Paris-EstFrance

Personalised recommendations