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International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing

ISMM 2017: Mathematical Morphology and Its Applications to Signal and Image Processing pp 296–308Cite as

Matrix-Valued Levelings for Colour Images

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10225))

Abstract

Morphological levelings represent a useful tool for the decomposition of an image into cartoon and texture components. Moreover, they can be used to construct a morphological scale space. However, the classic construction of levelings is limited to the use of grey scale images, since an ordering of pixel values is required.

In this paper we propose an extension of morphological levelings to colour images. To this end, we consider the formulation of colour images as matrix fields and explore techniques based on the Loewner order for formulating morphological levelings in this setting. Using the matrix-valued colours we study realisations of levelings relying on both the completely discrete construction and the formulation using a partial differential equation. Experimental results confirm the potential of our matrix-based approaches for analysing texture in colour images and for extending the range of applications of levelings in a convenient way to colour image processing.

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Author information

Authors and Affiliations

  1. Institute for Mathematics, Brandenburg Technical University, Platz der Deutschen Einheit 1, 03046, Cottbus, Germany

    Michael Breuß & Laurent Hoeltgen

  2. Forschungszentrum Jülich, Institute for Advanced Simulation, Jülich Supercomputing Centre, Wilhelm-Johnen-Straße, 52425, Jülich, Germany

    Andreas Kleefeld

Authors
  1. Michael Breuß
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  2. Laurent Hoeltgen
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  3. Andreas Kleefeld
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Corresponding author

Correspondence to Michael Breuß .

Editor information

Editors and Affiliations

  1. MINES ParisTech, PSL-Research University, Fontainebleau, France

    Jesús Angulo

  2. MINES ParisTech, PSL-Research University , Fontainebleau, France

    Santiago Velasco-Forero

  3. MINES ParisTech, PSL-Research University, Fontainebleau, France

    Fernand Meyer

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Breuß, M., Hoeltgen, L., Kleefeld, A. (2017). Matrix-Valued Levelings for Colour Images. In: Angulo, J., Velasco-Forero, S., Meyer, F. (eds) Mathematical Morphology and Its Applications to Signal and Image Processing. ISMM 2017. Lecture Notes in Computer Science(), vol 10225. Springer, Cham. https://doi.org/10.1007/978-3-319-57240-6_24

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  • DOI: https://doi.org/10.1007/978-3-319-57240-6_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57239-0

  • Online ISBN: 978-3-319-57240-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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