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Processing Multispectral Images via Mathematical Morphology

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Visualization and Processing of Higher Order Descriptors for Multi-Valued Data

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

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Abstract

In this chapter, we illustrate how to process multispectral and hyperspectral images via mathematical morphology. First, according to the number of channels the data are embeded into a sufficiently high dimensional space. This transformation utilizes a special geometric structure, namely double hypersimplices, for further processing the data. For example, RGB-color images are transformed into points within a specific double hypersimplex. It is explained in detail how to calculate the supremum and infimum of samples of those transformed data to allow for the meaningful definition of morphological operations such as dilation and erosion and in a second step top hats, gradients, and morphological Laplacian. Finally, numerical results are presented to explore the advantages and shortcomings of the new proposed approach.

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Notes

  1. 1.

    https://engineering.purdue.edu/~biehl/MultiSpec/hyperspectral.html.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics, Natural Sciences and Computer Science, Brandenburg University of Technology Cottbus, 03046, Cottbus, Germany

    Andreas Kleefeld

  2. Faculty of Mathematics and Computer Science, Saarland University, 66041, Saarbrücken, Germany

    Bernhard Burgeth

Authors
  1. Andreas Kleefeld
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  2. Bernhard Burgeth
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Corresponding author

Correspondence to Andreas Kleefeld .

Editor information

Editors and Affiliations

  1. Linköping University, Norrköping, Sweden

    Ingrid Hotz

  2. Visualization and Medical Image Analysis, University of Bonn, Bonn, Germany

    Thomas Schultz

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Kleefeld, A., Burgeth, B. (2015). Processing Multispectral Images via Mathematical Morphology. In: Hotz, I., Schultz, T. (eds) Visualization and Processing of Higher Order Descriptors for Multi-Valued Data. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-319-15090-1_7

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