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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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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