@misc{ShabaniBreuss, author = {Shabani, Shima and Breuß, Michael}, title = {Semi-Monotone Goldstein Line Search Strategy with Application in Sparse Recovery}, series = {arXiv}, journal = {arXiv}, doi = {https://doi.org/10.48550/arXiv.2503.13099}, pages = {1 -- 12}, abstract = {Line search methods are a prominent class of iterative methods to solve unconstrained minimization problems. These methods produce new iterates utilizing a suitable step size after determining proper directions for minimization. In this paper we propose a semi-monotone line search technique based on the Goldstein quotient for dealing with convex non-smooth optimization problems. The method allows to employ large step sizes away from the optimum thus improving the efficacy compared to standard Goldstein approach. For the presented line search method, we prove global convergence to a stationary point and local R-linear convergence rate in strongly convex cases. We report on some experiments in compressed sensing. By comparison with several state-of-the-art algorithms in the field, we demonstrate the competitive performance of the proposed approach and specifically its high efficiency.}, language = {en} } @misc{ShabaniKhoshghiaferezaeeBreuss, author = {Shabani, Shima and Khoshghiaferezaee, Mohammadsadegh and Breuß, Michael}, title = {Sparse dictionary learning for image recovery by iterative shrinkage}, series = {arXiv}, journal = {arXiv}, doi = {10.48550/arXiv.2503.10732}, pages = {1 -- 19}, abstract = {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.}, language = {en} } @misc{SchneidereitGohrenzBreuss, author = {Schneidereit, Toni and Gohrenz, Stefan and Breuß, Michael}, title = {Object detection characteristics in a learning factory environment using YOLOv8}, volume = {2503.10356}, doi = {https://doi.org/10.48550/arXiv.2503.10356}, pages = {1 -- 18}, abstract = {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.}, language = {en} } @misc{KahraBreuss, author = {Kahra, Marvin and Breuß, Michael}, title = {Colour morphological distance ordering based on the Log-Exp-Supremum}, series = {arXiv}, journal = {arXiv}, doi = {https://doi.org/10.48550/arXiv.2503.11329}, pages = {1 -- 13}, abstract = {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.}, language = {en} } @incollection{KahraBreuss, author = {Kahra, Marvin and Breuß, Michael}, title = {Colour morphological distance ordering based on the log-exp-supremum}, series = {Scale space and variational methods in computer vision : 10th international conference, SSVM 2025, Dartington, UK, May 18-22, 2025, proceedings, part II}, booktitle = {Scale space and variational methods in computer vision : 10th international conference, SSVM 2025, Dartington, UK, May 18-22, 2025, proceedings, part II}, publisher = {Springer Nature Switzerland}, address = {Cham}, isbn = {9783031923685}, issn = {0302-9743}, doi = {https://doi.org/10.1007/978-3-031-92369-2_20}, pages = {258 -- 270}, abstract = {Mathematical morphology, a field within image processing, incorporates a variety of filters that either highlight, modify, or eliminate specific information within a mask that traverses the image. 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.}, language = {en} } @incollection{ShabaniBreuss, author = {Shabani, Shima and Breuß, Michael}, title = {Semi-monotone Goldstein line search strategy with application in sparse recovery}, series = {Scale space and variational methods in computer vision : 10th international conference, SSVM 2025, Dartington, UK, May 18-22, 2025, proceedings, part II}, booktitle = {Scale space and variational methods in computer vision : 10th international conference, SSVM 2025, Dartington, UK, May 18-22, 2025, proceedings, part II}, publisher = {Springer Nature Switzerland}, address = {Cham}, isbn = {9783031923685}, issn = {0302-9743}, doi = {https://doi.org/10.1007/978-3-031-92369-2_6}, pages = {69 -- 81}, abstract = {Line search methods are a prominent class of iterative methods to solve unconstrained minimization problems. These methods produce new iterates utilizing a suitable step size after determining proper directions for minimization. In this paper we propose a semi-monotone line search technique based on the Goldstein quotient for dealing with convex non-smooth optimization problems. The method allows to employ large step sizes away from the optimum thus improving the efficacy compared to standard Goldstein approach. For the presented line search method, we prove global convergence to a stationary point and local R-linear convergence rate in strongly convex cases. We report on some experiments in compressed sensing. By comparison with several state-of-the-art algorithms in the field, we demonstrate the competitive performance of the proposed approach and specifically its high efficiency.}, language = {en} } @misc{CastilloCunninghamWingeretal., author = {Castillo, Susana and Cunningham, Douglas William and Winger, Christian and Breuß, Michael}, title = {Morphological Amoeba-based Patches for Exemplar-Based Inpainting}, series = {Journal of WSCG}, volume = {26}, journal = {Journal of WSCG}, number = {2}, issn = {1213-6972}, pages = {112 -- 121}, language = {en} } @inproceedings{BreussMansouriYarahmadiCunningham, author = {Breuß, Michael and Mansouri Yarahmadi, Ashkan and Cunningham, Douglas William}, title = {The Convex-Concave Ambiguity in Perspective Shape from Shading}, series = {Proceedings of the OAGM Workshop 2018 Medical Image Analysis, May 15 - 16, 2018, Hall/Tyrol, Austria}, booktitle = {Proceedings of the OAGM Workshop 2018 Medical Image Analysis, May 15 - 16, 2018, Hall/Tyrol, Austria}, editor = {Welk, Martin and Urschler, Martin and Roth, Peter M.}, publisher = {Verlag der TU Graz}, address = {Graz}, isbn = {978-3-85125-603-1}, doi = {10.3217/978-3-85125-603-1-13}, pages = {57 -- 63}, abstract = {Shape from Shading (SFS) is a classic problem in computer vision. In recent years many perspective SFS models have been studied that yield useful SFS approaches when a photographed object is close to the camera. However, while the ambiguities inherent to the classical, orthographic SFS models are well-understood, there has been no discussion of possible ambiguities in perspective SFS models. In this paper we deal with the latter issue. Therefore we adopt a typical perspective SFS setting. We show how to transform the corresponding image irradiance equation into the format of the classical orthographic setting by employing spherical coordinates. In the latter setting we construct a convex-concave ambiguity for perspective SFS. It is to our knowledge the first time in the literature that this type of ambiguity is constructed and verified for a perspective SFS model.}, language = {en} } @inproceedings{BreussCunninghamWelk, author = {Breuß, Michael and Cunningham, Douglas William and Welk, Martin}, title = {Scale spaces for cognitive systems: a position paper}, series = {Informatik 2015, Tagung vom 28. September - 2. Oktober 2015 in Cottbus}, booktitle = {Informatik 2015, Tagung vom 28. September - 2. Oktober 2015 in Cottbus}, editor = {Cunningham, Douglas William and Hofstedt, Petra and Meer, Klaus and Schmitt, Ingo}, publisher = {Gesellschaft f{\"u}r Informatik}, address = {Bonn}, isbn = {978-3-88579-640-4}, pages = {1253 -- 1255}, language = {en} } @misc{HajighasemiBreuss, author = {Hajighasemi, Saeide and Breuß, Michael}, title = {Fuzzy Frankot-Chellappa algorithm for surface normal integration}, series = {Algorithms}, volume = {18}, journal = {Algorithms}, number = {8}, publisher = {MDPI AG}, address = {Basel}, issn = {1999-4893}, doi = {10.3390/a18080488}, pages = {1 -- 19}, abstract = {In this paper, we propose a fuzzy formulation of the classic Frankot-Chellappa algorithm by which surfaces can be reconstructed using normal vectors. In the fuzzy formulation, the surface normal vectors may be uncertain or ambiguous, yielding a fuzzy Poisson partial differential equation that requires appropriate definitions of fuzzy derivatives. The solution of the resulting fuzzy model is approached by adopting a fuzzy variant of the discrete sine transform, which results in a fast and robust algorithm for surface reconstruction. An adaptive defuzzification strategy is also introduced to improve noise handling in highly uncertain regions. In experiments, we demonstrate that our fuzzy Frankot-Chellappa algorithm achieves accuracy on par with the classic approach for smooth surfaces and offers improved robustness in the presence of noisy normal data. We also show that it can naturally handle missing data (such as gaps) in the normal field by filling them using neighboring information.}, language = {en} } @misc{ShabaniBreussKahraetal., author = {Shabani, Shima and Breuß, Michael and Kahra, Marvin and Teiser, Jens and V{\"o}lke, Gretha Swantje and Wenders, Nico}, title = {Morphological granulometric analysis of particle imagery from microgravity experiments}, series = {arXiv}, journal = {arXiv}, publisher = {Cornell University}, address = {Ithaca, NY}, doi = {10.48550/arXiv.2508.06593}, pages = {1 -- 12}, abstract = {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.}, language = {en} }