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Optima on Hierarchies of Partitions

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 7883))

Abstract

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.

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References

  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)

    Article  Google Scholar 

  2. Angulo, J., Serra, J.: Modeling and segmentation of colour images in polar representations. Image and Vision Computing 25, 475–495 (2007)

    Article  Google Scholar 

  3. Arbelez, P., Cohen, L.: Constrained Image Segmentation from Hierarchical Boundaries. In: CVPR (2008)

    Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  6. Guigues, L., Cocquerez, J.P., Le Men, H.: Scale-Sets Image Analysis. Int. Journal of Computer Vision 68(3), 289–317 (2006)

    Article  Google Scholar 

  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. Mumford, D., Shah, J.: Boundary Detection by Minimizing Functionals. In: Ulmann, S., Richards, W. (eds.) Image Understanding (1988)

    Google Scholar 

  9. Ronse, C.: Partial partitions, partial connections and connective segmentation. Journal of Mathematical Imaging and Vision 32, 97–125 (2008)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Chapter  Google Scholar 

  12. Soille, P.: Constrained connectivity for hierarchical image partitioning and simplification. IEEE Transactions on PAMI 30, 1132–1145 (2008)

    Article  Google Scholar 

  13. Xu, Y., Géraud, T., Najman, L.: Morphological Filtering in Shape Spaces: Applications using Tree-Based Image Representations. In: ICPR 2012 (2012)

    Google Scholar 

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© 2013 Springer-Verlag Berlin Heidelberg

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Serra, J., Kiran, B.R. (2013). Optima on Hierarchies of Partitions. In: Hendriks, C.L.L., Borgefors, G., Strand, R. (eds) Mathematical Morphology and Its Applications to Signal and Image Processing. ISMM 2013. Lecture Notes in Computer Science, vol 7883. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38294-9_13

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  • DOI: https://doi.org/10.1007/978-3-642-38294-9_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38293-2

  • Online ISBN: 978-3-642-38294-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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