@incollection{KleefeldBreussWelketal., author = {Kleefeld, Andreas and Breuß, Michael and Welk, Martin and Burgeth, Bernhard}, title = {Adaptive Filters for Color Images: Median Filtering and Its Extensions}, series = {Computational Color Imaging}, booktitle = {Computational Color Imaging}, editor = {Tr{\´e}meau, Alain and Schettini, Raimondo and Tominaga, Shoji}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-319-15978-2}, doi = {10.1007/978-3-319-15979-9_15}, pages = {149 -- 158}, abstract = {In this paper we are concerned with robust structure-preserving denoising filters for color images. We build on a recently proposed transformation from the RGB color space to the space of symmetric 2×2 matrices that has already been used to transfer morphological dilation and erosion concepts from matrix-valued data to color images. We investigate the applicability of this framework to the construction of color-valued median filters. Additionally, we introduce spatial adaptivity into our approach by morphological amoebas that offer excellent capabilities for structure-preserving filtering. Furthermore, we define color-valued amoeba M-smoothers as a generalization of the median-based concepts. Our experiments confirm that all these methods work well with color images. They demonstrate the potential of our approach to define color processing tools based on matrix field techniques.}, language = {en} } @incollection{WelkKleefeldBreuss, author = {Welk, Martin and Kleefeld, Andreas and Breuß, Michael}, title = {Non-adaptive and Amoeba Quantile Filters for Colour Images}, series = {Mathematical Morphology and Its Applications to Signal and Image Processing}, booktitle = {Mathematical Morphology and Its Applications to Signal and Image Processing}, editor = {Benediktsson, J{\´o}n Atli and Chanussot, Jocelyn and Najman, Laurent and Talbot, Hugues}, publisher = {Springer International Publishing}, address = {Berlin}, isbn = {978-3-319-18719-8}, doi = {10.1007/978-3-319-18720-4_34}, pages = {398 -- 409}, 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. Using amoeba structuring elements, we devise image-adaptive versions of both filter classes. Experiments demonstrate the favourable properties of the filters.}, language = {en} } @inproceedings{KhanianBreussDavari, author = {Khanian, Maryam and Breuß, Michael and Davari, Ali}, title = {An improved stopping criterion for anisotropic diffusion}, series = {Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014 (ICNAAM-2014), Rhodes, Greece, 22-28 September 2014}, booktitle = {Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014 (ICNAAM-2014), Rhodes, Greece, 22-28 September 2014}, editor = {Simos, Theodore E. and Tsitouras, Charalambos}, publisher = {AIP Publishing}, address = {Melville, New York}, isbn = {978-0-7354-1287-3}, doi = {10.1063/1.4919928}, language = {en} }