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Hierarchical Laplacian and Its Spectrum in Ultrametric Image Processing

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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

The Laplacian of an image is one of the simplest and useful image processing tools which highlights regions of rapid intensity change and therefore it is applied for edge detection and contrast enhancement. This paper deals with the definition of the Laplacian operator on ultrametric spaces as well as its spectral representation in terms of the corresponding eigenfunctions and eigenvalues. The theory reviewed here provides the computational framework to process images or signals defined on a hierarchical representation associated to an ultrametric space. In particular, image regularization by ultrametric heat kernel filtering and image enhancement by hierarchical Laplacian are illustrated.

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Authors and Affiliations

  1. CMM-Centre de Morphologie Mathématique, MINES ParisTech, PSL-Research University, Paris, France

    Jesús Angulo

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  1. Jesús Angulo
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Correspondence to Jesús Angulo .

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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Angulo, J. (2019). Hierarchical Laplacian and Its Spectrum in Ultrametric Image Processing. 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_3

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  • DOI: https://doi.org/10.1007/978-3-030-20867-7_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-20866-0

  • Online ISBN: 978-3-030-20867-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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