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Introducing Multivariate Connected Openings and Closings

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Mathematical Morphology and Its Applications to Signal and Image Processing (ISMM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 11564))

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Abstract

Component trees provide a high-level, hierarchical, and contrast invariant representation of images, suitable for many image processing tasks. Yet their definition is ill-formed on multivariate data, e.g., color images, multi-modality images, multi-band images, and so on. Common workarounds such as marginal processing, or imposing a total order on data are not satisfactory and yield many problems, such as artifacts, loss of invariances, etc. In this paper, inspired by the way the Multivariate Tree of Shapes (MToS) has been defined, we propose a definition for a Multivariate min-tree or max-tree. We do not impose an arbitrary total ordering on values; we only use the inclusion relationship between components. As a straightforward consequence, we thus have a new class of multivariate connected openings and closings.

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Notes

  1. 1.

    Einige Kreise, from Vasily Kandinsky, 2016 (Solomon R. Guggenheim Museum, New York, ©2018 Artists Rights Society, New York/ADAGP, Paris).

  2. 2.

    Some extra illustrations can be found on https://publications.lrde.epita.fr/carlinet.19.ismm.

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Author information

Authors and Affiliations

  1. EPITA Research and Development Laboratory (LRDE), 14-16 rue Voltaire, 94270, Le Kremlin-Bicêtre, France

    Edwin Carlinet & Thierry Géraud

Authors
  1. Edwin Carlinet
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  2. Thierry Géraud
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Corresponding author

Correspondence to Edwin Carlinet .

Editor information

Editors and Affiliations

  1. Universität des Saarlandes, Saarbrücken, Germany

    Bernhard Burgeth

  2. Forschungszentrum Jülich GmbH, Jülich, Germany

    Andreas Kleefeld

  3. Université de Strasbourg, Illkirch Cedex, France

    Benoît Naegel

  4. Université de Reims Champagne-Ardenne, Reims Cedex 2, France

    Nicolas Passat

  5. Université Paris-Est, Noisy le Grand Cedex, France

    Benjamin Perret

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Carlinet, E., Géraud, T. (2019). Introducing Multivariate Connected Openings and Closings. In: Burgeth, B., Kleefeld, A., Naegel, B., Passat, N., Perret, B. (eds) Mathematical Morphology and Its Applications to Signal and Image Processing. ISMM 2019. Lecture Notes in Computer Science(), vol 11564. Springer, Cham. https://doi.org/10.1007/978-3-030-20867-7_17

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  • DOI: https://doi.org/10.1007/978-3-030-20867-7_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-20866-0

  • Online ISBN: 978-3-030-20867-7

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