TY - CHAP A1 - Kahra, Marvin A1 - Breuß, Michael A1 - Kleefeld, Andreas A1 - Welk, Martin ED - Brunetti, Sara ED - Frosini, Andrea ED - Rinaldi, Simone T1 - An Approach to Colour Morphological Supremum Formation Using the LogSumExp Approximation T2 - Discrete Geometry and Mathematical Morphology N2 - Mathematical morphology is a part of image processing that has proven to be fruitful for numerous applications. Two main operations in mathematical morphology are dilation and erosion. These are based on the construction of a supremum or infimum with respect to an order over the tonal range in a certain section of the image. The tonal ordering can easily be realised in grey-scale morphology, and some morphological methods have been proposed for colour morphology. However, all of these have certain limitations. In this paper we present a novel approach to colour morphology extending upon previous work in the field based on the Loewner order. We propose to consider an approximation of the supremum by means of a log-sum exponentiation introduced by Maslov. We apply this to the embedding of an RGB image in a field of symmetric 2x2 matrices. In this way we obtain nearly isotropic matrices representing colours and the structural advantage of transitivity. In numerical experiments we highlight some remarkable properties of the proposed approach. Y1 - 2024 SN - 978-3-031-57793-2 U6 - https://doi.org/10.1007/978-3-031-57793-2_25 N1 - Third International Joint Conference, DGMM 2024, Florence, Italy, April 15–18, 2024 SP - 325 EP - 337 PB - Springer CY - Cham ER - TY - CHAP A1 - Burgeth, Bernhard A1 - Kleefeld, Andreas A1 - Zhang, Eugene A1 - Zhang, Yue ED - Baudrier, Étienne ED - Naegel, Benoît ED - Krähenbühl, Adrien ED - Tajine, Mohamed T1 - Towards Topological Analysis of Non-symmetric Tensor Fields via Complexification T2 - Discrete Geometry and Mathematical Morphology N2 - Fields of asymmetric tensors play an important role in many applications such as medical imaging (diffusion tensor magnetic resonance imaging), physics, and civil engineering (for example Cauchy-Green-deformation tensor, strain tensor with local rotations, etc.). However, such asymmetric tensors are usually symmetrized and then further processed. Using this procedure results in a loss of information. A new method for the processing of asymmetric tensor fields is proposed restricting our attention to tensors of second-order given by a 2x2 array or matrix with real entries. This is achieved by a transformation resulting in Hermitian matrices that have an eigendecomposition similar to symmetric matrices. With this new idea numerical results for real-world data arising from a deformation of an object by external forces are given. It is shown that the asymmetric part indeed contains valuable information. Y1 - 2022 SN - 978-3-031-19897-7 U6 - https://doi.org/10.1007/978-3-031-19897-7_5 N1 - Second International Joint Conference, DGMM 2022, Strasbourg, France, October 24–27, 2022 N1 - Corresponding author: Andreas Kleefeld SP - 48 EP - 59 PB - Springer CY - Cham ER - TY - CHAP A1 - Bornheim, Tobias A1 - Grieger, Niklas A1 - Bialonski, Stephan T1 - FHAC at GermEval 2021: Identifying German toxic, engaging, and fact-claiming comments with ensemble learning T2 - Proceedings of the GermEval 2021 Workshop on the Identification of Toxic, Engaging, and Fact-Claiming Comments : 17th Conference on Natural Language Processing KONVENS 2021 Y1 - 2021 U6 - https://doi.org/10.48415/2021/fhw5-x128 N1 - KONVENS (Konferenz zur Verarbeitung natürlicher Sprache/Conference on Natural Language Processing) 2021, 6. - 9. September 2021, Düsseldorf SP - 105 EP - 111 PB - Heinrich Heine University CY - Düsseldorf ER - TY - CHAP A1 - Iomdina, Elena N. A1 - Kiseleva, Anna A. A1 - Kotliar, Konstantin A1 - Luzhnov, Petr V. T1 - Quantification of Choroidal Blood Flow Using the OCT-A System Based on Voxel Scan Processing T2 - Proceedings of the International Conference on Biomedical Innovations and Applications- BIA 2020 N2 - The paper presents a method for the quantitative assessment of choroidal blood flow using an OCT-A system. The developed technique for processing of OCT-A scans is divided into two stages. At the first stage, the identification of the boundaries in the selected portion was performed. At the second stage, each pixel mark on the selected layer was represented as a volume unit, a voxel, which characterizes the region of moving blood. Three geometric shapes were considered to represent the voxel. On the example of one OCT-A scan, this work presents a quantitative assessment of the blood flow index. A possible modification of two-stage algorithm based on voxel scan processing is presented. Y1 - 2020 SN - 978-1-7281-7073-2 U6 - https://doi.org/10.1109/BIA50171.2020.9244511 N1 - International Conference on Biomedical Innovations and Applications, Varna, Bulgaria, September 24 - 27, 2020 SP - 41 EP - 44 PB - IEEE CY - New York, NY ER -