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Watersheding Hierarchies

Conference paper
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Part of the Lecture Notes in Computer Science book series (LNCS, volume 11564)

Abstract

The computation of hierarchies of partitions from the watershed transform is a well-established segmentation technique in mathematical morphology. In this article, we introduce the watersheding operator, which maps any hierarchy into a hierarchical watershed. The hierarchical watersheds are the only hierarchies that remain unchanged under the action of this operator. After defining the watersheding operator, we present its main properties, namely its relation with extinction values and sequences of minima of weighted graphs. Finally, we discuss practical applications of the watersheding operator.

References

  1. 1.
    Arbelaez, P., Maire, M., Fowlkes, C., Malik, J.: Contour detection and hierarchical image segmentation. PAMI 33(5), 898–916 (2011)CrossRefGoogle Scholar
  2. 2.
    Beucher, S., Meyer, F.: The morphological approach to segmentation: the watershed transformation. Opt. Eng. New York-Marcel Dekker Inc. 34, 433–481 (1992)Google Scholar
  3. 3.
    Couprie, C., Grady, L., Najman, L., Talbot, H.: Power watersheds: a new image segmentation framework extending graph cuts, random walker and optimal spanning forest. In: ICCV, pp. 731–738. IEEE (2009)Google Scholar
  4. 4.
    Cousty, J., Bertrand, G., Najman, L., Couprie, M.: Watershed cuts: minimum spanning forests and the drop of water principle. PAMI 31(8), 1362–1374 (2009)CrossRefGoogle 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).  https://doi.org/10.1007/978-3-642-21569-8_24CrossRefzbMATHGoogle Scholar
  6. 6.
    Cousty, J., Najman, L., Kenmochi, Y., Guimarães, S.: Hierarchical segmentations with graphs: quasi-flat zones, minimum spanning trees, and saliency maps. JMIV 60(4), 479–502 (2018)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Cousty, J., Najman, L., Perret, B.: Constructive links between some morphological hierarchies on edge-weighted graphs. In: Hendriks, C.L.L., Borgefors, G., Strand, R. (eds.) ISMM 2013. LNCS, vol. 7883, pp. 86–97. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-38294-9_8CrossRefGoogle Scholar
  8. 8.
    Dollár, P., Zitnick, C.L.: Structured forests for fast edge detection. In: ICCV, pp. 1841–1848. IEEE (2013)Google Scholar
  9. 9.
    Santana Maia, D., de Albuquerque Araujo, A., Cousty, J., Najman, L., Perret, B., Talbot, H.: Evaluation of combinations of watershed hierarchies. In: Angulo, J., Velasco-Forero, S., Meyer, F. (eds.) ISMM 2017. LNCS, vol. 10225, pp. 133–145. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-57240-6_11CrossRefGoogle Scholar
  10. 10.
    Maia, D.S., Cousty, J., Najman, L., Perret, B.: Proofs of the properties presented in the article “Watersheding hierarchies”. Research report, April 2019Google Scholar
  11. 11.
    Maia, D.S., Cousty, J., Najman, L., Perret, B.: Recognizing hierarchical watersheds. In: Couprie, M., Cousty, J., Kenmochi, Y., Mustafa, N. (eds.) DGCI 2019. LNCS, vol. 11414, pp. 300–313. Springer, Cham (2019).  https://doi.org/10.1007/978-3-030-14085-4_24CrossRefGoogle Scholar
  12. 12.
    Maninis, K.-K., Pont-Tuset, J., Arbeláez, P., Van Gool, L.: Convolutional oriented boundaries: from image segmentation to high-level tasks. PAMI 40(4), 819–833 (2018)CrossRefGoogle Scholar
  13. 13.
    Meyer, F., Maragos, P.: Morphological scale-space representation with levelings. In: Nielsen, M., Johansen, P., Olsen, O.F., Weickert, J. (eds.) Scale-Space 1999. LNCS, vol. 1682, pp. 187–198. Springer, Heidelberg (1999).  https://doi.org/10.1007/3-540-48236-9_17CrossRefGoogle Scholar
  14. 14.
    Meyer, F., Vachier, C., Oliveras, A., Salembier, P.: Morphological tools for segmentation: connected filters and watersheds. Annales des télécommunications 52, 367–379 (1997). SpringerGoogle Scholar
  15. 15.
    Nagao, M., Matsuyama, T., Ikeda, Y.: Region extraction and shape analysis in aerial photographs. CGIP 10(3), 195–223 (1979)Google Scholar
  16. 16.
    Najman, L.: On the equivalence between hierarchical segmentations and ultrametric watersheds. JMIV 40(3), 231–247 (2011)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Najman, L., Cousty, J., Perret, B.: Playing with kruskal: algorithms for morphological trees in edge-weighted graphs. In: Hendriks, C.L.L., Borgefors, G., Strand, R. (eds.) ISMM 2013. LNCS, vol. 7883, pp. 135–146. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-38294-9_12CrossRefGoogle Scholar
  18. 18.
    Najman, L., Schmitt, M.: Geodesic saliency of watershed contours and hierarchical segmentation. PAMI 18(12), 1163–1173 (1996)CrossRefGoogle Scholar
  19. 19.
    Perret, B., Cousty, J., Guimaraes, S.J.F., Maia, D.S.: Evaluation of hierarchical watersheds. TIP 27(4), 1676–1688 (2018)MathSciNetzbMATHGoogle Scholar
  20. 20.
    Salembier, P., Garrido, L.: Binary partition tree as an efficient representation for image processing, segmentation, and information retrieval. TIP 9(4), 561–576 (2000)Google Scholar
  21. 21.
    Salembier, P., Oliveras, A., Garrido, L.: Antiextensive connected operators for image and sequence processing. TIP 7(4), 555–570 (1998)Google Scholar
  22. 22.
    Vachier, C., Meyer, F.: Extinction value: a new measurement of persistence. In: Workshop on nonlinear signal and image processing, pp. 254–257 (1995)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Université Paris-Est, LIGM (UMR 8049), CNRS, ENPC, ESIEE Paris, UPEMNoisy-le-GrandFrance

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