TY - GEN A1 - Köhler, Alexander A1 - Breuß, Michael T1 - Towards Efficient Time Stepping for Numerical Shape Correspondence T2 - arXiv Y1 - 2023 U6 - https://doi.org/10.48550/arXiv.2312.13841 SP - 1 EP - 12 ER - TY - GEN A1 - Sridhar, Vivek A1 - Breuß, Michael T1 - Morphological Sampling Theorem and its Extension to Grey-value Images T2 - arXiv N2 - Sampling is a basic operation in image processing. In classic literature, a morphological sampling theorem has been established, which shows how sampling interacts by morphological operations with image reconstruction. Many aspects of morphological sampling have been investigated for binary images, but only some of them have been explored for grey-value imagery. With this paper, we make a step towards completion of this open matter. By relying on the umbra notion, we show how to transfer classic theorems in binary morphology about the interaction of sampling with the fundamental morphological operations dilation, erosion, opening and closing, to the grey-value setting. In doing this we also extend the theory relating the morphological operations and corresponding reconstructions to use of non-flat structuring elements. We illustrate the theoretical developments at hand of examples. Y1 - 2023 U6 - https://doi.org/10.48550/arXiv.2305.13279 SP - 1 EP - 24 ER - TY - GEN A1 - Sridhar, Vivek A1 - Shahin, Keyvan A1 - Breuß, Michael A1 - Reichenbach, Marc T1 - The Polynomial Connection between Morphological Dilation and Discrete Convolution T2 - arXiv Y1 - 2023 U6 - https://doi.org/10.48550/arXiv.2305.03018 SP - 1 EP - 11 ER - TY - GEN A1 - Masouri Yarahmadi, Ashkan A1 - Breuß, Michael A1 - Hartmann, Carsten T1 - Long Short-Term Memory Neural Network for Temperature Prediction in Laser Powder Bed Additive Manufacturing T2 - arXiv Y1 - 2023 U6 - https://doi.org/10.48550/arXiv.2301.12904 SP - 1 EP - 15 ER - TY - GEN A1 - Kahra, Marvin A1 - Breuß, Michael A1 - Kleefeld, Andreas A1 - Welk, Martin T1 - An Approach to Colour Morphological Supremum Formation using the LogSumExp Approximation T2 - arXiv 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 2×2 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 - 2023 U6 - https://doi.org/10.48550/arXiv.2312.13792 SP - 1 EP - 12 ER - TY - GEN A1 - Shabani, Shima A1 - Khoshghiaferezaee, Mohammadsadegh A1 - Breuß, Michael T1 - Sparse dictionary learning for image recovery by iterative shrinkage T2 - arXiv N2 - In this paper we study the sparse coding problem in the context of sparse dictionary learning for image recovery. To this end, we consider and compare several state-of-the-art sparse optimization methods constructed using the shrinkage operation. As the mathematical setting of these methods, we consider an online approach as algorithmical basis together with the basis pursuit denoising problem that arises by the convex optimization approach to the dictionary learning problem. By a dedicated construction of datasets and corresponding dictionaries, we study the effect of enlarging the underlying learning database on reconstruction quality making use of several error measures. Our study illuminates that the choice of the optimization method may be practically important in the context of availability of training data. In the context of different settings for training data as may be considered part of our study, we illuminate the computational efficiency of the assessed optimization methods. Y1 - 2025 U6 - https://doi.org/10.48550/arXiv.2503.10732 SP - 1 EP - 19 ER - TY - GEN A1 - Schneidereit, Toni A1 - Gohrenz, Stefan A1 - Breuß, Michael T1 - Object detection characteristics in a learning factory environment using YOLOv8 N2 - AI-based object detection, and efforts to explain and investigate their characteristics, is a topic of high interest. The impact of, e.g., complex background structures with similar appearances as the objects of interest, on the detection accuracy and, beforehand, the necessary dataset composition are topics of ongoing research. In this paper, we present a systematic investigation of background influences and different features of the object to be detected. The latter includes various materials and surfaces, partially transparent and with shiny reflections in the context of an Industry 4.0 learning factory. Different YOLOv8 models have been trained for each of the materials on different sized datasets, where the appearance was the only changing parameter. In the end, similar characteristics tend to show different behaviours and sometimes unexpected results. While some background components tend to be detected, others with the same features are not part of the detection. Additionally, some more precise conclusions can be drawn from the results. Therefore, we contribute a challenging dataset with detailed investigations on 92 trained YOLO models, addressing some issues on the detection accuracy and possible overfitting. Y1 - 2025 U6 - https://doi.org/https://doi.org/10.48550/arXiv.2503.10356 VL - 2503.10356 SP - 1 EP - 18 ER - TY - GEN A1 - Kahra, Marvin A1 - Breuß, Michael T1 - Colour morphological distance ordering based on the Log-Exp-Supremum T2 - arXiv N2 - Mathematical morphology, a field within image processing, includes various filters that either highlight, modify, or eliminate certain information in images based on an application's needs. Key operations in these filters are dilation and erosion, which determine the supremum or infimum for each pixel with respect to an order of the tonal values over a subset of the image surrounding the pixel. This subset is formed by a structuring element at the specified pixel, which weighs the tonal values. Unlike grey-scale morphology, where tonal order is clearly defined, colour morphology lacks a definitive total order. As no method fully meets all desired properties for colour, because of this difficulty, some limitations are always present. This paper shows how to combine the theory of the log-exp-supremum of colour matrices that employs the Loewner semi-order with a well-known colour distance approach in the form of a pre-ordering. The log-exp-supremum will therefore serve as the reference colour for determining the colour distance. To the resulting pre-ordering with respect to these distance values, we add a lexicographic cascade to ensure a total order and a unique result. The objective of this approach is to identify the original colour within the structuring element that most closely resembles a supremum, which fulfils a number of desired properties. Consequently, this approach avoids the false-colour problem. The behaviour of the introduced operators is illustrated by application examples of dilation and closing for synthetic and natural images. Y1 - 2025 U6 - https://doi.org/https://doi.org/10.48550/arXiv.2503.11329 SP - 1 EP - 13 ER - TY - GEN A1 - Shabani, Shima A1 - Breuß, Michael A1 - Kahra, Marvin A1 - Teiser, Jens A1 - Völke, Gretha Swantje A1 - Wenders, Nico T1 - Morphological granulometric analysis of particle imagery from microgravity experiments T2 - arXiv N2 - The aim of our work is to analyze size distributions of particles and their agglomerates in imagery from astrophysical microgravity experiments. The data acquired in these experiments are given by sequences consisting of several hundred images. It is desirable to establish an automated routine that helps to assess size distributions of important image structures and their dynamics in a statistical way. The main technique we adopt to this end is the morphological granulometry. After preprocessing steps that facilitate granulometric analysis, we show how to extract useful information on size of particle agglomerates as well as underlying dynamics. At hand of the discussion of two different microgravity key experiments we demonstrate that the granulometric analysis enables to assess important experimental aspects. We conjecture that our developments are a useful basis for the quantitative assessment of microgravity particle experiments. Y1 - 2025 U6 - https://doi.org/10.48550/arXiv.2508.06593 SP - 1 EP - 12 PB - Cornell University CY - Ithaca, NY ER -