@techreport{KahraBreuss2022, type = {Working Paper}, author = {Kahra, Marvin and Breuß, Michael}, title = {Properties of morphological dilation in max-plus and plus-prod algebra in connection with the Fourier transformation}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-58483}, year = {2022}, abstract = {The basic filters in mathematical morphology are dilation and erosion. They are defined by a structuring element that is usually shifted pixel-wise over an image, together with a comparison process that takes place within the corresponding mask. This comparison is made in the grey value case by means of maximum or minimum formation. Hence, there is easy access to max-plus algebra and, by means of an algebra change, also to the theory of linear algebra. We show that an approximation of the maximum function forms a commutative semifield (with respect to multiplication) and corresponds to the maximum again in the limit case. In this way, we demonstrate a novel access to the logarithmic connection between the Fourier transform and the slope transformation. In addition, we prove that the dilation by means of a Fast Fourier Transform depends only on the size of the structuring element used. Moreover, we derive a bound above which the Fourier approximation yields results that are exact in terms of grey value quantization.}, subject = {Mathematical morphology; Fourier transform; Dilation; Max-plus algebra; Slope transform; Mathematische Morphologie; Fourier-Transformation; Dilatation; Max-Plus-Algebra; Steigungstransformation; Dilatation ; Fourier-Transformation; Mathematische Morphologie}, language = {en} } @techreport{BaehrBuhlRadowetal.2019, type = {Working Paper}, author = {B{\"a}hr, Martin and Buhl, Johannes and Radow, Georg and Schmidt, Johannes and Bambach, Markus and Breuß, Michael and F{\"u}genschuh, Armin}, title = {Stable honeycomb structures and temperature based trajectory optimization for wire-arc additive manufacturing}, editor = {F{\"u}genschuh, Armin}, issn = {2627-6100}, doi = {10.26127/BTUOpen-5079}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-50796}, year = {2019}, abstract = {We consider two mathematical problems that are connected and occur in the layer-wise production process of a workpiece using Wire-Arc Additive Manufacturing. As the first task, 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 realizations. For computing the incorporated Voronoi tesselation we consider the use of a Delaunay triangulation or alternatively, the eikonal equation. We compare and modify these approaches with the aim of combining their respective advantages. Then in the second task, to find an optimal tool path guaranteeing minimal production time and high quality of the workpiece, a mixed-integer linear programming problem is derived. The model takes thermal conduction and radiation during the process into account and aims to minimize temperature gradients inside the material. Its solvability for standard mixed-integer solvers is demonstrated on several test-instances. The results are compared with manufactured workpieces.}, subject = {Eikonal equation; Centroidal Voronoi tessellation; Additive manufacturing; Heat transmission; Mixed-integer linear programming; Geometric optimization; Additive Fertigung; Gemischt-ganzzahlige Programmierung; Geometrische Optimierung; Eikonal-Gleichung; Zentrierte Voronoi-Parkettierung; W{\"a}rmeleitung; Rapid Prototyping ; Eikonal; Ganzzahlige Optimierung; Geometrische Optimierung; W{\"a}rmeleitung}, language = {en} } @techreport{ZellSchneidereitFuegenschuhetal.2024, type = {Working Paper}, author = {Zell, Sascha and Schneidereit, Toni and F{\"u}genschuh, Armin and Breuß, Michael}, title = {Advanced search and rescue operations for drowning swimmers using autonomous unmanned aircraft systems : location optimization, flight trajectory planning and image-based localization}, doi = {10.26127/BTUOpen-6866}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-68669}, year = {2024}, abstract = {Drowning is among the most prevalent causes of death from unintentional injuries worldwide. Because of the time-sensitive nature of swimming accidents and the shortage of lifeguard staff resulting in unsupervised swimming areas, interest in supportive rescue methods increases. In this paper, we propose an autonomous Unmanned Aircraft System (UAS) usable by Emergency Medical Service (EMS) providers in swimmer rescue scenarios additionally to Standard Rescue Operation (SRO) equipment. The UAS consists of Unmanned Aerial Vehicles (UAVs) and purpose-built hangars located near the swimming area to store the UAVs. When receiving an alert, the UAVs autonomously navigate to the emergency site to conduct a Search and Rescue (S\&R) operation for the drowning person. We introduce a Mixed-Integer Linear Programming (MILP) model to address the Facility Location Problem (FLP), assisting with identification of accessibility-optimal UAV hangar placements near the swimming area. Additionally, we present a MILP model to optimize the UAV flight trajectories in advance of the operation, allowing for efficient coordination of a heterogeneous UAV fleet. We apply the presented MILP models to a real-world scenario in the Lusatian Lake District using the state-of-the-art commercial solver CPLEX to solve the instances. Furthermore, we present a method for automated image-based swimmer localization using the state-of-the-art neural network You Only Look Once (YOLO). Finally, we use a Discrete-Event Simulation (DES) approach to quantify how much time is saved by using additional resources.}, subject = {Unmanned Aerial Vehicle; Unmanned Aircraft System; Water Rescue; Mixed-Integer Linear Programming; You Only Look Once; Drohne; Drohnenhangar; Wasserrettung; Gemischt-ganzzahlige Programmierung; Standortoptimierung; Drohne ; Wasserrettung; Lineare Optimierung}, language = {en} }