TY - GEN A1 - Breuß, Michael A1 - Kemm, Friedemann A1 - Vogel, Oliver T1 - A numerical study of Newton interpolation with extremely high degrees T2 - Kybernetika : international journal published by Institute of Information Theory and Automation N2 - In current textbooks the use of Chebyshev nodes with Newton interpolation is advocated as the most efficient numerical interpolation method in terms of approximation accuracy and computational effort. However, we show numerically that the approximation quality obtained by Newton interpolation with Fast Leja (FL) points is competitive to the use of Chebyshev nodes, even for extremely high degree interpolation. This is an experimental account of the analytic result that the limit distribution of FL points and Chebyshev nodes is the same when letting the number of points go to infinity. Since the FL construction is easy to perform and allows to add interpolation nodes on the fly in contrast to the use of Chebyshev nodes, our study suggests that Newton interpolation with FL points is currently the most efficient numerical technique for polynomial interpolation. Moreover, we give numerical evidence that any reasonable function can be approximated up to machine accuracy by Newton interpolation with FL points if desired, which shows the potential of this method. KW - polynomial interpolation KW - Newton interpolation KW - interpolation nodes KW - Chebyshev nodes KW - Leja ordering KW - fast Leja points Y1 - 2018 U6 - https://doi.org/10.14736/kyb-2018-2-0279 SN - 0023-5954 VL - 54 IS - 2 SP - 279 EP - 288 ER - TY - GEN A1 - Bähr, Martin A1 - Radow, Georg A1 - Breuß, Michael A1 - Fügenschuh, Armin ED - Fortz, Bernard ED - Labbé, Martine T1 - Computation of Stable Honeycomb Structures for Additive Manufacturing T2 - Operations Research Proceedings 2018, Selected Papers of the Annual International Conference of the German Operations Research Society (GOR), Brussels, Belgium, September 12-14, 2018 N2 - In certain additive manufacturing processes of industrial interest, the task arises to build up structures layer-wise in a purely vertical manner. The question arises how to construct such a structure in a convenient way so that it is structurally as stable as possible. In this paper, we consider the automatic construction of a honeycomb structure, given the boundary of a shape of interest. In doing this we employ Lloyd’s algorithm in two different realisations. For computing the incorporated Voronoi tessellation we consider the use of a Delaunay triangulation or the Eikonal equation. As a main point of our paper, we give a comparison of these two methods. We show that one can make use of the arising graph of the honeycomb structure as input for a specific routing scheme that enhances printability when the printing material stays soft for some time during the printing process. KW - Additive manufacturing Centroidal, Voronoi tessellation, Energy minimisation, Geometric optimisation, Eikonal equation, Fast marching Y1 - 2019 SN - 978-3-030-18499-5 U6 - https://doi.org/10.1007/978-3-030-18500-8_45 SN - 978-3-030-18500-8 SP - 363 EP - 369 PB - Springer CY - Cham ER - TY - GEN A1 - Hoeltgen, Laurent A1 - Breuß, Michael A1 - Radow, Georg ED - Lellmann, Jan ED - Burger, Martin ED - Modersitzki, Jan T1 - Towards PDE-Based Video Compression with Optimal Masks and Optic Flow T2 - Scale Space and Variational Methods in Computer Vision : 7th International Conference, SSVM 2019, Hofgeismar, Germany, June 30 – July 4, 2019, Proceedings N2 - Lossy image compression methods based on partial differential equations have received much attention in recent years. They may yield high quality results but rely on the computationally expensive task of finding optimal data. For the possible extension to video compression, the data selection is a crucial issue. In this context one could either analyse the video sequence as a whole or perform a frame-by-frame optimisation strategy. Both approaches are prohibitive in terms of memory and run time. In this work we propose to restrict the expensive computation of optimal data to a single frame and to approximate the optimal reconstruction data for the remaining frames by prolongating it by means of an optic flow field. We achieve a notable decrease in the computational complexity. As a proof-of-concept, we evaluate the proposed approach for multiple sequences with different characteristics. We show that the method preserves a reasonable quality in the reconstruction, and is very robust against errors in the flow field. KW - Partial differential equations Inpainting Laplace interpolation Optic flow Video reconstruction Y1 - 2019 SN - 978-3-030-22367-0 SN - 978-3-030-22368-7 U6 - https://doi.org/10.1007/978-3-030-22368-7_7 SP - 79 EP - 91 PB - Springer CY - Cham ER - TY - GEN A1 - Radow, Georg A1 - Breuß, Michael ED - Vento, Mario ED - Percannella, Gennaro T1 - Variational Optical Flow: Warping and Interpolation Revisited T2 - Computer Analysis of Images and Patterns 18th International Conference, CAIP 2019, Salerno, Italy, September 3–5, 2019, Proceedings, Part I N2 - One of the fundamental problems in computer vision is to attain the apparent motion in image sequences, the optical flow. As evaluations at hand of recent benchmarks show, this field is highly competitive. High ranking variational methods often consist of a combination of techniques, where frequently the presentation in the literature focuses on novel contributions in modelling. In this paper we investigate the warping technique and related algorithmic design choices that are fundamental for practical implementation. At hand of a detailed yet straightforward derivation we discuss different warping variations. These are evaluated in numerical experiments, and furthermore we investigate the impact of a variety of interpolation methods that can be used. KW - Optical flow Variational methods Warping Interpolation B-splines Y1 - 2019 SN - 978-3-030-29887-6 U6 - https://doi.org//10.1007/978-3-030-29888-3_33 SN - 978-3-030-29888-3 SP - 409 EP - 420 PB - Springer CY - Cham ER - TY - GEN A1 - Maurer, Daniel A1 - Ju, Yong Chul A1 - Breuß, Michael A1 - Bruhn, Andrés T1 - Combining Shape from Shading and Stereo: A Variational Approach for the Joint Estimation of Depth, Illumination and Albedo N2 - Shape from shading (SfS) and stereo are two fundamentally different strategies for image-based 3-D reconstruction. While approaches for SfS infer the depth solely from pixel intensities, methods for stereo are based on a matching process that establishes correspondences across images. In this paper we propose a joint variational method that combines the advantages of both strategies. By integrating recent stereo and SfS models into a single minimisation framework, we obtain an approach that exploits shading information to improve upon the reconstruction quality of robust stereo methods. To this end, we fuse a Lambertian SfS approach with a robust stereo model and supplement the resulting energy functional with a detail-preserving anisotropic second-order smoothness term. Moreover, we extend the novel model in such a way that it jointly estimates depth, albedo and illumination. This in turn makes it applicable to objects with non-uniform albedo as well as to scenes with unknown illumination. Experiments for synthetic and real-world images show the advantages of our combined approach: While the stereo part overcomes the albedo-depth ambiguity inherent to all SfS methods, the SfS part improves the degree of details of the reconstruction compared to pure stereo methods. Y1 - 2016 N1 - Das Poster wurde auf der BMVC in York im September 2016 präsentiert PB - BMVA Press CY - York, UK ER - TY - GEN A1 - Hoeltgen, Laurent A1 - Queau, Yvain A1 - Breuß, Michael A1 - Radow, Georg T1 - Optimised photometric stereo via non-convex variational minimisation Y1 - 2016 UR - http://www.bmva.org/bmvc/2016/papers/paper036/ N1 - Poster für die BMVC in York, September 2016 PB - BMVA Press CY - York, UK ER - TY - GEN A1 - Schneidereit, Slavomira A1 - Mansouri Yarahmadi, Ashkan A1 - Schneidereit, Toni A1 - Breuß, Michael A1 - Gebauer, Marc T1 - YOLO- based Object detection in industry 4.0 Fischertechnik Model Environment T2 - Computer Science > Computer Vision and Pattern Recognition, Intelligent Systems Conference 2023 (IntelliSys 2023) N2 - In this paper we extensively explore the suitability of YOLO architectures to monitor the process flow across a Fischertechnik industry 4.0 application. Specifically, different YOLO architectures in terms of size and complexity design along with different prior-shapes assignment strategies are adopted. To simulate the real world factory environment, we prepared a rich dataset augmented with different distortions that highly enhance and in some cases degrade our image qualities. The degradation is performed to account for environmental variations and enhancements opt to compensate the color correlations that we face while preparing our dataset. The analysis of our conducted experiments shows the effectiveness of the presented approach evaluated using different measures along with the training and validation strategies that we tailored to tackle the unavoidable color correlations that the problem at hand inherits by nature. Y1 - 2023 U6 - https://doi.org/10.48550/arXiv.2301.12827 ER -