TY - CHAP A1 - Kleefeld, Andreas A1 - Breuß, Michael A1 - Welk, Martin A1 - Burgeth, Bernhard ED - Trémeau, Alain ED - Schettini, Raimondo ED - Tominaga, Shoji T1 - Adaptive Filters for Color Images: Median Filtering and Its Extensions T2 - Computational Color Imaging N2 - 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. KW - Matrix field KW - Color image KW - Median filter KW - M-smoother KW - Amoeba filter Y1 - 2015 UR - http://link.springer.com/chapter/10.1007/978-3-319-15979-9_15# SN - 978-3-319-15978-2 U6 - https://doi.org/10.1007/978-3-319-15979-9_15 SP - 149 EP - 158 PB - Springer CY - Berlin ER - TY - CHAP A1 - Sharifi Boroujerdi, Ali A1 - Breuß, Michael A1 - Burgeth, Bernhard A1 - Kleefeld, Andreas ED - Aujol, Jean-François ED - Nikolova, Mila ED - Papadakis, Nicolas T1 - PDE-Based Color Morphology Using Matrix Fields T2 - Scale Space and Variational Methods in Computer Vision, 5th International Conference, SSVM 2015, Lège-Cap Ferret, France, May 31 - June 4, 2015, Proceedings N2 - In this work, we propose a novel way for performing operations of mathematical morphology on color images. To this end, we convert pixelwise the rgb-values into symmetric 2x2 matrices. The new color space can be interpreted geometrically as a biconal color space structure. Motivated by the formulation of the fundamental morphological operations dilation and erosion in terms of partial differential equations (PDEs), we show how to define finite difference schemes making use of the matrix field formulation. The computation of a pseudo supremum and a pseudo infimum of three color matrices is a crucial step for setting up advanced PDE-based methods. We show that this can be achieved for our goal by an algebraic technique. We investigate our approach by dedicated experiments and confirm useful properties of the new PDE-based color morphology operations. KW - PDE-based morphology KW - Matrix fields KW - Color morphology KW - Finite difference schemes KW - FCT scheme KW - Pseudo supremum KW - Pseudo infimum Y1 - 2015 SN - 978-3-319-18460-9 U6 - https://doi.org/10.1007/978-3-319-18461-6_37 SP - 461 EP - 473 PB - Springer CY - Berlin ER - TY - CHAP A1 - Welk, Martin A1 - Kleefeld, Andreas A1 - Breuß, Michael ED - Benediktsson, Jón Atli ED - Chanussot, Jocelyn ED - Najman, Laurent ED - Talbot, Hugues T1 - Non-adaptive and Amoeba Quantile Filters for Colour Images T2 - Mathematical Morphology and Its Applications to Signal and Image Processing N2 - 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. KW - Quantile KW - Rank-order filter KW - Color image KW - Matrix field KW - Amoebas Y1 - 2015 SN - 978-3-319-18719-8 SN - 978-3-319-18720-4 U6 - https://doi.org/10.1007/978-3-319-18720-4_34 SP - 398 EP - 409 PB - Springer International Publishing CY - Berlin ER - TY - CHAP A1 - Breuß, Michael A1 - Quèau, Yvain A1 - Bähr, Martin A1 - Durou, Jean-Denis T1 - Highly Efficient Surface Normal Integration T2 - Proceedings of the Conference Algoritmy 2016, 20th Conference on Scientific Computing, Vysoké Tatry - Podbanské, Slovakia, March 14 - 18 KW - surface normal integration KW - Poisson integration KW - Krylov subspace methods KW - fast marching methods Y1 - 2016 UR - http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/409 SN - 978-80-227-4544-4 SP - 204 EP - 213 PB - Publishing House of Slovak University of Technology in Bratislava CY - Bratislava ER - TY - CHAP A1 - Hoeltgen, Laurent A1 - Breuß, Michael ED - Handlovičová, A. ED - Ševčovič, D. T1 - Efficient Co-Domain Quantisation for PDE-Based Image Compression T2 - Proceedings of the Conference Algoritmy 2016, 20th Conference on Scientific Computing, Vysoké Tatry - Podbanské, Slovakia, March 14 - 18 KW - Laplace interpolation KW - inpainting KW - compression KW - quantisation KW - clustering KW - partial differential equations Y1 - 2016 UR - http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/408 SN - 978-80-227-4544-4 SP - 194 EP - 203 PB - Publishing House of Slovak University of Technology in Bratislava CY - Bratislava ER - TY - CHAP A1 - Bähr, Martin A1 - Breuß, Michael ED - Gall, Juergen ED - Gehler, Peter ED - Leibe, Bastian T1 - An Improved Eikonal Method for Surface Normal Integration T2 - Pattern Recognition, 37th German Conference, GCPR 2015, Aachen, Germany, October 7-10, 2015, Proceedings Y1 - 2015 UR - http://link.springer.com/chapter/10.1007%2F978-3-319-24947-6_22 SN - 978-3-319-24946-9 U6 - https://doi.org/10.1007/978-3-319-24947-6_22 SP - 274 EP - 284 PB - Springer International Publishing CY - Berlin ER - TY - CHAP A1 - Chul Ju, Yong A1 - Bruhn, Andrés A1 - Breuß, Michael ED - Aujol, Jean-François ED - Nikolova, Mila ED - Papadakis, Nicolas T1 - Variational Perspective Shape from Shading T2 - Scale Space and Variational Methods in Computer Vision, 5th International Conference, SSVM 2015, Lège-Cap Ferret, France, May 31 - June 4, 2015, Proceedings KW - Shape from shading KW - Variational methods KW - Perspective camera model Y1 - 2015 UR - http://link.springer.com/chapter/10.1007%2F978-3-319-18461-6_43 SN - 978-3-319-18460-9 U6 - https://doi.org/10.1007/978-3-319-18461-6_43 SP - 538 EP - 550 PB - Springer International Publishing CY - Berlin ER - TY - CHAP A1 - Khanian, Maryam A1 - Sharifi Boroujerdi, Ali A1 - Breuß, Michael ED - Meriaudeau, Fabrice ED - Aubreton, Olivier T1 - Perspective photometric stereo beyond Lambert T2 - Twelfth International Conference on Quality Control by Artificial Vision, 3 - 5 June 2015, Le Creusot, France KW - Cameras KW - Reflection KW - Reflectivity KW - Specular reflections Y1 - 2015 UR - http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=2290117 SN - 978-80-227-4544-4 U6 - https://doi.org/10.1117/12.2182839 PB - SPIE CY - Bellingham, Wash. ER - TY - CHAP A1 - Khanian, Maryam A1 - Breuß, Michael A1 - Davari, Ali ED - Simos, Theodore E. ED - Tsitouras, Charalambos T1 - An improved stopping criterion for anisotropic diffusion T2 - Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014 (ICNAAM-2014), Rhodes, Greece, 22-28 September 2014 KW - Amoeba filter Matrix field KW - Color image KW - M-smoother KW - Matrix field KW - Median filter Y1 - 2015 UR - http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4919928 SN - 978-0-7354-1287-3 U6 - https://doi.org/10.1063/1.4919928 PB - AIP Publishing CY - Melville, New York ER - TY - CHAP A1 - Ju, Yong Chul A1 - Maurer, Daniel A1 - Breuß, Michael A1 - Bruhn, Andrés ED - Breuß, Michael ED - Bruckstein, Alfred ED - Maragos, Petros ED - Wuhrer, Stefanie T1 - Direct variational perspective shape from shading with Cartesian depth parametrisation T2 - Perspectives in Shape Analysis, Mathematics and Visualization Y1 - 2016 SN - 978-3-319-24724-3 U6 - https://doi.org/10.1007/978-3-319-24726-7 SP - 43 EP - 72 PB - Springer International Publishing CY - Cham ER -