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International Workshop on Graph-Based Representations in Pattern Recognition

GbRPR 2013: Graph-Based Representations in Pattern Recognition pp 91–100Cite as

Adjunctions on the Lattice of Dendrograms

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 7877))

Abstract

Dendrograms are used in hierarchical classification. They also are useful structures in image processing, for segmentation or filtering purposes. The structure of a hierarchy is univocally expressed by a ultrametric ecart. The hierarchies form a complete lattice on which two adjunctions will be defined.

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References

  1. Benzécri, J.P.: L’analyse des données 1. La taxinomie, ch. 3, pp. 119–153. Dunod (1973)

    Google Scholar 

  2. Heijmans, H.: Connected morphological operators for binary images. Computer Vision and Image Understanding 73(1), 99–120 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  3. Matheron, G.: Filters and lattices. In: Serra, J. (ed.) Mathematical Morphology Volume II: theoretical advances. Academic Press, London (1988)

    Google Scholar 

  4. Meyer, F.: An overview of morphological segmentation. International Journal of Pattern Recognition and Artificial Intelligence 17(7), 1089–1118 (2001)

    Article  Google Scholar 

  5. Ronse, C.: Partial partitions, partial connections and connective segmentation. J. Math. Imaging Vis. 32(2), 97–125 (2008)

    Article  MathSciNet  Google Scholar 

  6. Ronse, C.: Reconstructing masks from markers in non-distributive lattices. Appl. Algebra Eng. Commun. Comput. 19, 51–85 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. Ronse, C.: Adjunctions on the lattices of partitions and of partial partitions. Appl. Algebra Eng., Commun. Comput. 21(5), 343–396 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Salembier, P., Garrido, L.: Connected operators based on region-tree pruning. In: Goutsias, J., Vincent, L., Bloomberg, D.S. (eds.) Mathematical Morphology and its Applications to Image and Signal Processing, vol. 18, pp. 169–178. Springer, US (2002)

    Google Scholar 

  9. Serra, J. (ed.): Image Analysis and Mathematical Morphology. II: Theoretical Advances. Academic Press, London (1988)

    Google Scholar 

  10. Serra, J.: Morphological operators for the segmentation of colour images. In: Bilodeau, M.S.M., Meyer, F. (eds.) Space, structure, and randomness. Contributions in honor of Georges Matheron in the fields of geostatistics, random sets, and mathematical morphology. Lecture Notes in Statistics, vol. 183, pp. 223–255, xviii, 395 p. Springer, New York (2005)

    Google Scholar 

  11. Serra, J.: A lattice approach to image segmentation. J. Math. Imaging Vis. 24, 83–130 (2006)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. CMM-Centre de Morphologie Mathématique, Mathématiques et Systèmes, MINES ParisTech, France

    Fernand Meyer

Authors
  1. Fernand Meyer
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Editor information

Editors and Affiliations

  1. Dept. of Pattern Recognition and Image Processing, Vienna University of Technology, Favoritenstr. 9-11, 186-3, 1040, Vienna, Austria

    Walter G. Kropatsch , Nicole M. Artner  & Yll Haxhimusa ,  & 

  2. Department of Computer Science, University of Münster, Einsteinstr. 62, 48149, Münster, Germany

    Xiaoyi Jiang

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Meyer, F. (2013). Adjunctions on the Lattice of Dendrograms. In: Kropatsch, W.G., Artner, N.M., Haxhimusa, Y., Jiang, X. (eds) Graph-Based Representations in Pattern Recognition. GbRPR 2013. Lecture Notes in Computer Science, vol 7877. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38221-5_10

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  • DOI: https://doi.org/10.1007/978-3-642-38221-5_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38220-8

  • Online ISBN: 978-3-642-38221-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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