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PDE for Bivariate Amoeba Median Filtering

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Mathematical Morphology and Its Applications to Signal and Image Processing (ISMM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10225))

Abstract

Amoebas are image-adaptive structuring elements for morphological filters that have been introduced by Lerallut et al. in 2005. Iterated amoeba median filtering on grey-scale images has been proven to approximate asymptotically for vanishing structuring element radius a partial differential equation (PDE) which is known in image filtering by the name of self-snakes. This approximation property helps to understand the properties of both, morphological and PDE, image filter classes. Recently, also the PDEs approximated by multivariate median filtering with non-adaptive structuring elements have been studied. Affine equivariant multivariate medians turned out to yield more favourable PDEs than the more popular \(L^1\) median. We continue this work by considering amoeba median filtering of bivariate images using affine equivariant medians. We prove a PDE approximation result for this case. We validate the result by numerical experiments on example functions sampled with high spatial resolution.

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Authors and Affiliations

  1. Institute of Biomedical Image Analysis, Private University for Health Sciences, Medical Informatics and Technology (UMIT), Eduard-Wallnöfer-Zentrum 1, 6060, Hall, Tyrol, Austria

    Martin Welk

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  1. Martin Welk
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Correspondence to Martin Welk .

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Editors and Affiliations

  1. MINES ParisTech, PSL-Research University, Fontainebleau, France

    Jesús Angulo

  2. MINES ParisTech, PSL-Research University , Fontainebleau, France

    Santiago Velasco-Forero

  3. MINES ParisTech, PSL-Research University, Fontainebleau, France

    Fernand Meyer

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Welk, M. (2017). PDE for Bivariate Amoeba Median Filtering. In: Angulo, J., Velasco-Forero, S., Meyer, F. (eds) Mathematical Morphology and Its Applications to Signal and Image Processing. ISMM 2017. Lecture Notes in Computer Science(), vol 10225. Springer, Cham. https://doi.org/10.1007/978-3-319-57240-6_22

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  • DOI: https://doi.org/10.1007/978-3-319-57240-6_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57239-0

  • Online ISBN: 978-3-319-57240-6

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