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Mathematical Morphology - Theory and Applications

Editor-in-Chief: Passat, Nicolas / Talbot, Hugues

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2353-3390
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Quantile Filtering of Colour Images via Symmetric Matrices

Martin Welk
  • Corresponding author
  • University for Health Sciences, Medical Informatics and Technology (UMIT), Hall/Tyrol, Austria
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Andreas Kleefeld
  • Corresponding author
  • Brandenburg University of Technology Cottbus–Senftenberg, Cottbus, Germany
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Michael Breuß
  • Corresponding author
  • Brandenburg University of Technology Cottbus–Senftenberg, Cottbus, Germany
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2016-04-19 | DOI: https://doi.org/10.1515/mathm-2016-0008

Abstract

Quantile filters, or rank-order filters, are local image filters which assign quantiles of intensities of the input image within neighbourhoods as output image values. Combining a multivariate quantile definition developed in matrix-valued morphology with a recently introduced mapping between the RGB colour space and the space of symmetric 2 × 2 matrices, we state a class of colour image quantile filters, along with a class of morphological gradient filters derived from these.We consider variants of these filters based on three matrix norms – the nuclear, Frobenius, and spectral norm – and study their differences. We investigate the properties of the quantile and gradient filters and their links to dilation and erosion operators. Using amoeba structuring elements,we devise image-adaptive versions of our quantile and gradient filters. Experiments are presented to demonstrate the favourable properties of the filters, and compare them to existing approaches in colour morphology.

Keywords: quantile; rank-order filter; colour image; matrix field; amoebas

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About the article

Received: 2015-07-29

Accepted: 2016-02-18

Published Online: 2016-04-19


Citation Information: Mathematical Morphology - Theory and Applications, Volume 1, Issue 1, ISSN (Online) 2353-3390, DOI: https://doi.org/10.1515/mathm-2016-0008.

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© 2016 Martin Welk et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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