A new approach is proposed for finding optimal cuts in hierarchies of partitions by energy minimization. It rests on the notion of h-increasingness, allows to find best(optimal) cuts in one pass, and to obtain nice ”climbing” scale space operators. The ways to construct h-increasing energies, and to combine them are studied, and illustrated by two examples on color and on textures.


Image Segmentation Optimal Segmentation Partial Partition Colour Image Segmentation Hierarchical Image 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Akcay, H.G., Aksoy, S.: Automatic detection of geospatial objects using multiple hierarchical segmentations. IEEE T. Geoscience and Remote Sensing 46, 2097–2111 (2008)CrossRefGoogle Scholar
  2. 2.
    Angulo, J., Serra, J.: Modeling and segmentation of colour images in polar representations. Image and Vision Computing 25, 475–495 (2007)CrossRefGoogle Scholar
  3. 3.
    Arbelez, P., Cohen, L.: Constrained Image Segmentation from Hierarchical Boundaries. In: CVPR (2008)Google Scholar
  4. 4.
    Cardelino, J., Caselles, V.: Bertalm ´ ıo, M., Randall, G.: A contrario hierarchical image segmentation. In: IEEE ICIP 2009, Cairo, Egypt (2009)Google Scholar
  5. 5.
    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
  6. 6.
    Guigues, L., Cocquerez, J.P., Le Men, H.: Scale-Sets Image Analysis. Int. Journal of Computer Vision 68(3), 289–317 (2006)CrossRefGoogle Scholar
  7. 7.
    Ravi Kiran, B., Serra, J.: Global-local optimizations on hierarchies of segmentations. Special issue on Computer vision applying PR, Pattern Recognition Letters (2013)Google Scholar
  8. 8.
    Mumford, D., Shah, J.: Boundary Detection by Minimizing Functionals. In: Ulmann, S., Richards, W. (eds.) Image Understanding (1988)Google Scholar
  9. 9.
    Ronse, C.: Partial partitions, partial connections and connective segmentation. Journal of Mathematical Imaging and Vision 32, 97–125 (2008)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Salembier, P., Garrido, L.: Binary Partition Tree as an Efficient Representation for Image Processing, Segmentation, and Information Retrieval. IEEE Trans. on Image Processing 9(4), 561–576 (2000)CrossRefGoogle Scholar
  11. 11.
    Serra, J.: Hierarchies and Optima. In: Debled-Rennesson, I., Domenjoud, E., Kerautret, B., Even, P. (eds.) DGCI 2011. LNCS, vol. 6607, pp. 35–46. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  12. 12.
    Soille, P.: Constrained connectivity for hierarchical image partitioning and simplification. IEEE Transactions on PAMI 30, 1132–1145 (2008)CrossRefGoogle Scholar
  13. 13.
    Xu, Y., Géraud, T., Najman, L.: Morphological Filtering in Shape Spaces: Applications using Tree-Based Image Representations. In: ICPR 2012 (2012)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

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

Personalised recommendations