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A Unified Approach to the Processing of Hyperspectral Images

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Book cover 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))

Abstract

Since vector fields, such as RGB-color, multispectral or hyperspectral images, possess only limited algebraic and ordering structures they do not lend themselves easily to image processing methods. However, for fields of symmetric matrices a sufficiently elaborate calculus, that includes, for example, suitable notions of multiplication, supremum/infimum and concatenation with real functions, is available. In this article a vector field is coded as a matrix field, which is then processed by means of the matrix valued counterparts of image processing methods. An approximate decoding step transforms a processed matrix field back into a vector field. Here we focus on proposing suitable notions of a pseudo-supremum/infimum of two vectors/colors and a PDE-based dilation/erosion process of color images as a proof-of-concept. In principle there is no restriction on the dimension of the vectors considered. Experiments, mainly on RGB-images for presentation reasons, will reveal the merits and the shortcomings of the proposed methods.

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Author information

Authors and Affiliations

  1. Saarland University, 66123, Saarbrücken, Germany

    Bernhard Burgeth

  2. Trier University of Applied Sciences, Environmental Campus Birkenfeld, 55761, Birkenfeld, Germany

    Stephan Didas

  3. Forschungszentrum Jülich GmbH, Jülich Supercomputing Centre, 52425, Jülich, Germany

    Andreas Kleefeld

Authors
  1. Bernhard Burgeth
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  2. Stephan Didas
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  3. Andreas Kleefeld
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Corresponding author

Correspondence to Bernhard Burgeth .

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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Burgeth, B., Didas, S., Kleefeld, A. (2019). A Unified Approach to the Processing of Hyperspectral Images. 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_16

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  • DOI: https://doi.org/10.1007/978-3-030-20867-7_16

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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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