In evaluating a hierarchy of segmentations H of an image by ground truth G, which can be partitions of the space or sets, we look for the optimal partition in H that “fits” G best. Two energies on partial partitions express the proximity from H to G, and G to H. They derive from a local version of the Hausdorff distance. Then the problem amounts to finding the cut of the hierarchy which minimizes the said energy. This cuts provide global similarity measures of precision and recall. This allows to contrast two input hierarchies with respect to the G, and also to describe how to compose energies from different ground truths. Results are demonstrated over the Berkeley database.


Distance Function Ground Truth Partial Partition Minimum Span Forest Global Consistency Error 
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  1. 1.
    Martin, D.R.: An Empirical Approach to Grouping and Segmentation, PhD Thesis, EECS Department, University of California, Berkeley, Number = UCB/CSD-03-1268 (2003)Google Scholar
  2. 2.
    Arbeláez, P.: Une approche mtrique pour la segmentation d’images, Phd thesis, Univ.of Paris Dauphine (November 2005)Google Scholar
  3. 3.
    Arbeláez, P., Cohen, L.: Constrained Image Segmentation from Hierarchical Boundaries. In: CVPR (2008)Google Scholar
  4. 4.
    Arbeláez, P., Maire, M., Fowlkes, C., Malik, J.: Contour Detection and Hierarchical Image Segmentation. IEEE PAMI 33 (2011)Google Scholar
  5. 5.
    Pont-Tuset, J., Marques, F.: Supervised Assessment of Segmentation Hierarchies. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part IV. LNCS, vol. 7575, pp. 814–827. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  6. 6.
    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
  7. 7.
    Serra, J., Kiran, B.R.: Climbing the pyramids CoRR abs/1204.5383 (2012)Google Scholar
  8. 8.
    Serra, J., Kiran, B.R., Cousty, J.: Hierarchies and climbing energies. In: Alvarez, L., Mejail, M., Gomez, L., Jacobo, J. (eds.) CIARP 2012. LNCS, vol. 7441, pp. 821–828. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  9. 9.
    Pont-Tuset, J., Marqués, F.: Upper-bound assessment of the spatial accuracy of hierarchical region-based image representations. In: IEEE International Conference on Acoustics, Speech, and Signal Processing (2012)Google Scholar
  10. 10.
    Movahedi, V., Elder, J.H.: Design and perceptual validation of performance measures for salient object segmentation. In: 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), pp. 49–56 (2010)Google Scholar
  11. 11.
    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
  12. 12.
    Gorelick, L., Schmidt, F.R., Boykov, Y., Delong, A., Ward, A.: Segmentation with non-linear regional constraints via line-search cuts. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part I. LNCS, vol. 7572, pp. 583–597. Springer, Heidelberg (2012)CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

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

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