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The Morphological Equivalents of Relativistic and Alpha-Scale-Spaces

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Scale Space and Variational Methods in Computer Vision (SSVM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9087))

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Abstract

The relations between linear system theory and mathematical morphology are mainly understood on a pure convolution / dilation level. A formal connection on the level of differential or pseudo-differential equations is still missing. In our paper we close this gap. We establish the sought relation by means of infinitesimal generators, exploring essential properties of the slope and a modified Cramér transform. As an application of our general theory, we derive the morphological counterparts of relativistic scale-spaces and of \(\alpha \)-scale-spaces for \(\alpha \in [\frac{1}{2}, \infty )\). Our findings are illustrated by experiments.

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Authors and Affiliations

  1. Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Campus E1.7, 66041, Saarbrücken, Germany

    Martin Schmidt & Joachim Weickert

Authors
  1. Martin Schmidt
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  2. Joachim Weickert
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Correspondence to Martin Schmidt .

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Editors and Affiliations

  1. University of Bordeaux, Talence, France

    Jean-François Aujol

  2. ENS Cachan, Cachan, France

    Mila Nikolova

  3. University of Bordeaux, Talence, France

    Nicolas Papadakis

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Schmidt, M., Weickert, J. (2015). The Morphological Equivalents of Relativistic and Alpha-Scale-Spaces. In: Aujol, JF., Nikolova, M., Papadakis, N. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2015. Lecture Notes in Computer Science(), vol 9087. Springer, Cham. https://doi.org/10.1007/978-3-319-18461-6_3

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  • DOI: https://doi.org/10.1007/978-3-319-18461-6_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-18460-9

  • Online ISBN: 978-3-319-18461-6

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