Abstract
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.
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Arbelaez, P., Maire, M., Fowlkes, C., Malik, J.: Contour Detection and Hierarchical Image Segmentation. IEEE PAMI 33 (2011)
Ballester, C., Caselles, V., Igual, L., Garrido, L.: Level lines selection with variational models for segmentation and encoding. JMIV 27, 5–27 (2007)
Cardelino, J., Caselles, V., Bertalmío, M., Randall, G.: A contrario hierarchical image segmentation. In: IEEE ICIP 2009, Cairo, Egypt (2009)
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)
Guigues, L.: Modèles multi-échelles pour la segmentation d’images.Thèse doctorale Université de Cergy-Pontoise (Décembre 2003)
Najman, L., Schmitt, M.: Geodesic Saliency of Watershed Contours and Hierarchical Segmentation. IEEE Trans. PAMI (1996)
Najman, L.: On the Equivalence Between Hierarchical Segmentations and Ultrametric Watersheds. JMIV 40(3), 231–247 (2011)
Ronse, C.: Partial partitions, partial connections and connective segmentation. JMIV 32, 97–125 (2008)
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)
Serra, J.: Hierarchies and optima. In: Domenjoud, E. (ed.) DGCI 2011. LNCS, vol. 6607, pp. 35–46. Springer, Heidelberg (2011)
Serra, J., Kiran, B.R.: Climbing the pyramids. Techn. report ESIEE (March 2012)
Soille, P.: Constrained connectivity for hierarchical image partitioning and simplification. IEEE PAMI 30, 1132–1145 (2008)
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)
Zanoguera, F., Marcotegui, B., Meyer, F.: A toolbox for interactive segmentation based on nested partitions. In: Proc. of ICIP 1999, Kobe, Japan (1999)
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Serra, J., Kiran, B.R., Cousty, J. (2012). Hierarchies and Climbing Energies. In: Alvarez, L., Mejail, M., Gomez, L., Jacobo, J. (eds) Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications. CIARP 2012. Lecture Notes in Computer Science, vol 7441. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33275-3_101
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DOI: https://doi.org/10.1007/978-3-642-33275-3_101
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