@misc{BreussDietrich, author = {Breuß, Michael and Dietrich, Dominik}, title = {On the Optimization of Flux Limiter Schemes for Hyperbolic Conservation Laws}, series = {Numerical Methods for Partial Differential Equations}, volume = {Vol. 29}, journal = {Numerical Methods for Partial Differential Equations}, number = {3}, issn = {1098-2426}, pages = {884 -- 896}, language = {en} } @misc{BreussCristianiDurouetal., author = {Breuß, Michael and Cristiani, Emiliano and Durou, Jean-Denis and Falcone, Maurizio and Vogel, Oliver}, title = {Perspective Shape from Shading: Ambiguity Analysis and Numerical Approximations}, series = {SIAM Journal on Imaging Sciences}, volume = {5}, journal = {SIAM Journal on Imaging Sciences}, number = {1}, issn = {1936-4954}, pages = {311 -- 342}, language = {en} } @incollection{BreussBurgethPizarro, author = {Breuß, Michael and Burgeth, Bernhard and Pizarro, Luis}, title = {Numerical Analysis, Tensor-Valued Extension and Application in Image Processing}, series = {Recent Developments in the Numerics of Hyperbolic Conservation Laws}, booktitle = {Recent Developments in the Numerics of Hyperbolic Conservation Laws}, editor = {Ansorge, Rainer}, publisher = {Springer}, address = {Berlin [u.a.]}, isbn = {978-3-642-33220-3}, pages = {73 -- 87}, language = {en} } @incollection{PeterBreuss, author = {Peter, Pascal and Breuß, Michael}, title = {Refined Homotopic Thinning Algorithms and Quality Measures for Skeletonisation Methods}, series = {Innovations for Shape Analysis : Models and Algorithms}, booktitle = {Innovations for Shape Analysis : Models and Algorithms}, editor = {Breuß, Michael and Bruckstein, Alfred and Maragos, Petros}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-642-34140-3}, pages = {77 -- 92}, language = {en} } @incollection{WelkBreuss, author = {Welk, Martin and Breuß, Michael}, title = {Morphological Amoebas and Partial Differential Equations}, series = {Advances in Imaging and Electron Physics}, booktitle = {Advances in Imaging and Electron Physics}, editor = {Hawkes, Peter W.}, publisher = {Elsevier}, address = {Amsterdam}, isbn = {978-0-12-800144-8}, pages = {139 -- 212}, language = {en} } @incollection{WelkKleefeldBreuss, author = {Welk, Martin and Kleefeld, Andreas and Breuß, Michael}, title = {Non-adaptive and Amoeba Quantile Filters for Colour Images}, series = {Mathematical Morphology and Its Applications to Signal and Image Processing}, booktitle = {Mathematical Morphology and Its Applications to Signal and Image Processing}, editor = {Benediktsson, J{\´o}n Atli and Chanussot, Jocelyn and Najman, Laurent and Talbot, Hugues}, publisher = {Springer International Publishing}, address = {Berlin}, isbn = {978-3-319-18719-8}, doi = {10.1007/978-3-319-18720-4_34}, pages = {398 -- 409}, abstract = {Quantile filters, or rank-order filters, are local image filters which assign quantiles of intensities of the input image within neighbourhoods as output image values. Combining a multivariate quantile definition developed in matrix-valued morphology with a recently introduced mapping between the RGB colour space and the space of symmetric 2×2 matrices, we state a class of colour image quantile filters, along with a class of morphological gradient filters derived from these. Using amoeba structuring elements, we devise image-adaptive versions of both filter classes. Experiments demonstrate the favourable properties of the filters.}, language = {en} } @incollection{JuMaurerBreussetal., author = {Ju, Yong Chul and Maurer, Daniel and Breuß, Michael and Bruhn, Andr{\´e}s}, title = {Direct variational perspective shape from shading with Cartesian depth parametrisation}, series = {Perspectives in Shape Analysis, Mathematics and Visualization}, booktitle = {Perspectives in Shape Analysis, Mathematics and Visualization}, editor = {Breuß, Michael and Bruckstein, Alfred and Maragos, Petros and Wuhrer, Stefanie}, publisher = {Springer International Publishing}, address = {Cham}, isbn = {978-3-319-24724-3}, doi = {10.1007/978-3-319-24726-7}, pages = {43 -- 72}, language = {en} } @inproceedings{PeterHoffmannNedwedetal., author = {Peter, Pascal and Hoffmann, Sebastian and Nedwed, Frank and Hoeltgen, Laurent and Weickert, Joachim}, title = {From Optimised Inpainting with Linear PDEs Towards Competitive Image Compression Codecs}, series = {Image and Video Technology, 7th Pacific-Rim Symposium, PSIVT 2015, Auckland, New Zealand, November 25-27, 2015}, booktitle = {Image and Video Technology, 7th Pacific-Rim Symposium, PSIVT 2015, Auckland, New Zealand, November 25-27, 2015}, publisher = {Springer}, address = {Cham}, isbn = {978-3-319-29450-6}, doi = {10.1007/978-3-319-29451-3_6}, pages = {63 -- 74}, abstract = {For inpainting with linear partial differential equations (PDEs) such as homogeneous or biharmonic diffusion, sophisticated data optimisation strategies have been found recently. These allow high-quality reconstructions from sparse known data. While they have been explicitly developed with compression in mind, they have not entered actual codecs so far: Storing these optimised data efficiently is a nontrivial task. Since this step is essential for any competetive codec, we propose two new compression frameworks for linear PDEs: Efficient storage of pixel locations obtained from an optimal control approach, and a stochastic strategy for a locally adaptive, tree-based grid. Suprisingly, our experiments show that homogeneous diffusion inpainting can surpass its often favoured biharmonic counterpart in compression. Last but not least, we demonstrate that our linear approach is able to beat both JPEG2000 and the nonlinear state-of-the-art in PDE-based image compression.}, language = {en} } @misc{BaehrBreussQueauetal., author = {B{\"a}hr, Martin and Breuß, Michael and Qu{\`e}au, Yvain and Sharifi Boroujerdi, Ali and Durou, Jean-Denis}, title = {Fast and accurate surface normal integration on non-rectangular domains}, series = {Computational Visual Media}, volume = {3}, journal = {Computational Visual Media}, number = {2}, issn = {2096-0433}, doi = {10.1007/s41095-016-0075-z}, pages = {107 -- 129}, abstract = {The integration of surface normals for the purpose of computing the shape of a surface in 3D space is a classic problem in computer vision. However, even nowadays it is still a challenging task to devise a method that is flexible enough to work on non-trivial computational domains with high accuracy, robustness, and computational efficiency. By uniting a classic approach for surface normal integration with modern computational techniques, we construct a solver that fulfils these requirements. Building upon the Poisson integration model, we use an iterative Krylov subspace solver as a core step in tackling the task. While such a method can be very efficient, it may only show its full potential when combined with suitable numerical preconditioning and problem-specific initialisation. We perform a thorough numerical study in order to identify an appropriate preconditioner for this purpose. To provide suitable initialisation, we compute this initial state using a recently developed fast marching integrator. Detailed numerical experiments illustrate the benefits of this novel combination. In addition, we show on real-world photometric stereo datasets that the developed numerical framework is flexible enough to tackle modern computer vision applications.}, language = {en} } @inproceedings{RadowBreussHoeltgenetal., author = {Radow, Georg and Breuß, Michael and Hoeltgen, Laurent and Fischer, Thomas}, title = {Optimised Anisotropic Poisson Denoising}, series = {Image Analysis, 20th Scandinavian Conference, SCIA 2017, Troms{\o}, Norway, June 12-14, 2017, Proceedings, Part I}, booktitle = {Image Analysis, 20th Scandinavian Conference, SCIA 2017, Troms{\o}, Norway, June 12-14, 2017, Proceedings, Part I}, editor = {Sharma, Puneet and Filippo, Maria Bianchi}, publisher = {Springer}, address = {Cham}, isbn = {978-3-319-59126-1}, doi = {10.1007/978-3-319-59126-1_42}, pages = {502 -- 514}, language = {en} } @inproceedings{DachselBreussHoeltgen, author = {Dachsel, Robert and Breuß, Michael and Hoeltgen, Laurent}, title = {The Classic Wave Equation Can Do Shape Correspondence}, series = {Computer Analysis of Images and Patterns, CAIP International Conference on Computer Analysis of Images and Patterns, Ystad,Sweden, 2017}, booktitle = {Computer Analysis of Images and Patterns, CAIP International Conference on Computer Analysis of Images and Patterns, Ystad,Sweden, 2017}, editor = {Felsberg, Michael and Heyden, Andreas and Kr{\"u}ger, Norbert}, publisher = {Springer International Publishing}, address = {Cham}, isbn = {978-3-319-64688-6}, doi = {10.1007/978-3-319-64689-3_22}, pages = {264 -- 275}, abstract = {A major task in non-rigid shape analysis is to retrieve correspondences between two almost isometric 3D objects. An important tool for this task are geometric feature descriptors. Ideally, a feature descriptor should be invariant under isometric transformations and robust to small elastic deformations. A successful class of feature descriptors employs the spectral decomposition of the Laplace-Beltrami operator. Important examples are the heat kernel signature using the heat equation and the more recent wave kernel signature applying the Schr{\"o}dinger equation from quantum mechanics. In this work we propose a novel feature descriptor which is based on the classic wave equation that describes e.g. sound wave propagation. We explore this new model by discretizing the underlying partial differential equation. Thereby we consider two different time integration methods. By a detailed evaluation at hand of a standard shape data set we demonstrate that our approach may yield significant improvements over state of the art methods for finding correct shape correspondences.}, language = {en} } @misc{Hoeltgen, author = {Hoeltgen, Laurent}, title = {Understanding image inpainting with the help of the Helmholtz equation}, series = {Mathematical Sciences}, volume = {11}, journal = {Mathematical Sciences}, number = {1}, issn = {2008-1359}, doi = {10.1007/s40096-017-0207-3}, pages = {73 -- 77}, abstract = {Partial differential equations have recently been used for image compression purposes. One of the most successful frameworks solves the Laplace equation using a weighting scheme to determine the importance of individual pixels. We provide a physical interpretation of this approach in terms of the Helmholtz equation which explains its superiority. For better reconstruction quality, we subsequently formulate an optimisation task for the corresponding finite difference discretisation to maximise the influence of the physical traits of the Helmholtz equation. Our findings show that sharper contrasts and lower errors in the reconstruction are possible.}, language = {en} } @misc{HoeltgenPeterBreuss, author = {Hoeltgen, Laurent and Peter, Pascal and Breuß, Michael}, title = {Clustering-based quantisation for PDE-based image compression}, series = {Signal, Image and Video Processing}, volume = {12}, journal = {Signal, Image and Video Processing}, number = {3}, issn = {1863-1703}, doi = {10.1007/s11760-017-1173-9}, pages = {411 -- 419}, abstract = {Optimal known pixel data for inpainting in compression codecs based on partial differential equations is real-valued and thereby expensive to store. Thus, quantisation is required for efficient encoding. In this paper, we interpret the quantisation step as a clustering problem. Due to the global impact of each known pixel and correlations between spatial and tonal data, we investigate the central question, which kind of feature vectors should be used for clustering with popular strategies such as k-means. Our findings show that the number of colours can be reduced significantly without impacting the reconstruction quality. Surprisingly, these benefits are negated by an increased coding cost in compression applications.}, language = {en} } @misc{HoeltgenBreussHeroldetal., author = {Hoeltgen, Laurent and Breuß, Michael and Herold, Gert and Sarradj, Ennes}, title = {Sparse ℓ1 regularisation of matrix valued models for acoustic source characterisation}, series = {Optimization and Engineering}, volume = {19}, journal = {Optimization and Engineering}, number = {1}, issn = {1389-4420}, doi = {10.1007/s11081-017-9357-2}, pages = {39 -- 70}, abstract = {We present a strategy for the recovery of a sparse solution of a common problem in acoustic engineering, which is the reconstruction of sound source levels and locations applying microphone array measurements. The considered task bears similarities to the basis pursuit formalism but also relies on additional model assumptions that are challenging from a mathematical point of view. Our approach reformulates the original task as a convex optimisation model. The sought solution shall be a matrix with a certain desired structure. We enforce this structure through additional constraints. By combining popular splitting algorithms and matrix differential theory in a novel framework we obtain a numerically efficient strategy. Besides a thorough theoretical consideration we also provide an experimental setup that certifies the usability of our strategy. Finally, we also address practical issues, such as the handling of inaccuracies in the measurement and corruption of the given data. We provide a post processing step that is capable of yielding an almost perfect solution in such circumstances.}, language = {en} } @misc{DachselJoesterBreuss, author = {Dachsel, Robert and J{\"o}ster, Annika and Breuß, Michael}, title = {Real-Time Retinal Vessel Segmentation on High-Resolution Fundus Images Using Laplacian Pyramids}, series = {Image and Video Technology, 9th Pacific-Rim Symposium, PSIVT 2019, Sydney, NSW, Australia, November 18-22, 2019, Proceedings}, journal = {Image and Video Technology, 9th Pacific-Rim Symposium, PSIVT 2019, Sydney, NSW, Australia, November 18-22, 2019, Proceedings}, editor = {Lee, Chilwoo and Su, Zhixun and Sugimoto, Akihiro}, publisher = {Springer}, address = {Cham}, isbn = {978-3-030-34878-6}, issn = {0302-9743}, doi = {10.1007/978-3-030-34879-3_26}, pages = {337 -- 350}, abstract = {In ophthalmology, fundus images are commonly used to examine the human eye. The image data shows among others the capillary system of the retina. Recognising alternations in the retinal blood vessels is pivotal to diagnosing certain diseases. The visual inspection of those fundus images is a time-consuming process and a challenging task which has to be done by medical experts. Furthermore, rapid advances in medical imaging allow for generating fundus images of increased quality and resolution. Therefore, the support by computers for the analysis and evaluation of complex fundus image information is growing in importance and there is a corresponding need for fast and efficient algorithms. In this paper, we present a well-engineered, robust real-time segmentation algorithm which is adapted to the recent and upcoming challenges of high resolution fundus images. Thereby we make use of the multiscale representation of the Laplacian pyramid which is fast to compute and useful for detecting coarse as well as finely branched blood vessels. It is possible to process images of size 3504×2336 pixels in 0.8 s on a standard desktop computer and 0.3 on a Nvidia Titan XP GPU. By a detailed evaluation at hand of an accessible high-resolution data set we demonstrate that our approach is competitive in quality to state of the art methods for segmenting blood vessels but much faster.}, language = {en} } @misc{WelkBreussSridhar, author = {Welk, Martin and Breuß, Michael and Sridhar, Vivek}, title = {Matrix Morphology with Extremum Principle}, series = {Mathematical Morphology and Its Applications to Signal and Image Processing : 14th International Symposium, ISMM 2019, Saarbr{\"u}cken, Germany, July 8-10, 2019, Proceedings}, journal = {Mathematical Morphology and Its Applications to Signal and Image Processing : 14th International Symposium, ISMM 2019, Saarbr{\"u}cken, Germany, July 8-10, 2019, Proceedings}, publisher = {Springer}, address = {Cham}, isbn = {978-3-030-20866-0}, doi = {10.1007/978-3-030-20867-7_14}, pages = {177 -- 188}, abstract = {The fundamental operations of mathematical morphology are dilation and erosion. In previous works, these operations have been generalised in a discrete setting to work with fields of symmetric matrices, and also corresponding methods based on partial differential equations have been constructed. However, the existing methods for dilation and erosion in the matrix-valued setting are not overall satisfying. By construction they may violate a discrete extremum principle, which means that results may leave the convex hull of the matrices that participate in the computation. This may not be desirable from the theoretical point of view, as the corresponding property is fundamental for discrete and continuous-scale formulations of dilation and erosion in the scalar setting. Moreover, if such a principle could be established in the matrix-valued framework, this would help to make computed solutions more interpretable. In our paper we address this issue. We show how to construct a method for matrix-valued morphological dilation and erosion that satisfies a discrete extremum principle. We validate the construction by showing experimental results on synthetic data as well as colour images, as the latter can be cast as fields of symmetric matrices.}, language = {en} } @misc{WelkBreuss, author = {Welk, Martin and Breuß, Michael}, title = {The convex-hull-stripping median approximates affine curvature motion}, series = {Scale Space and Variational Methods in Computer Vision : 7th International Conference, SSVM 2019, Hofgeismar, Germany, June 30 - July 4, 2019, Proceedings}, journal = {Scale Space and Variational Methods in Computer Vision : 7th International Conference, SSVM 2019, Hofgeismar, Germany, June 30 - July 4, 2019, Proceedings}, publisher = {Springer}, address = {Cham}, isbn = {978-3-030-22367-0}, doi = {10.1007/978-3-030-22368-7_16}, pages = {199 -- 210}, abstract = {The median filter is one of the fundamental filters in image processing. Its standard realisation relies on a rank ordering of given data which is easy to perform if the given data are scalar values. However, the generalisation of the median filter to multivariate data is a delicate issue. One of the methods of potential interest for computing a multivariate median is the convex-hull-stripping median from the statistics literature. Its definition is of purely algorithmical nature, and it offers the advantageous property of affine equivariance. While it is a classic result that the standard median filter approximates mean curvature motion, no corresponding assertion has been established up to now for the convex-hull-stripping median. The aim of our paper is to close this gap in the literature. In order to provide a theoretical foundation for the convex-hull-stripping median of multivariate images, we investigate its continuous-scale limit. It turns out that the resulting evolution is described by the well-known partial differential equation of affine curvature motion. Thus we have established in this paper a relation between two important models from image processing and statistics. We also present some experiments that support our theoretical findings.}, language = {en} } @incollection{BreussMansouriYarahmadi, author = {Breuß, Michael and Mansouri Yarahmadi, Ashkan}, title = {Perspective Shape from Shading : An Exposition on Recent Works with New Experiments}, series = {Advances in Photometric 3D-Reconstruction}, booktitle = {Advances in Photometric 3D-Reconstruction}, editor = {Durou, Jean-Denis and Falcone, Maurizio and Qu{\´e}au, Yvain and Tozza, Silvia}, publisher = {Springer}, address = {Cham}, isbn = {978-3-030-51865-3}, issn = {2191-6586}, doi = {https://doi.org/10.1007/978-3-030-51866-0_2}, pages = {31 -- 72}, abstract = {Shape from Shading (SFS) is a fundamental task in computer vision. By given information about the reflectance of an object's surface and the position of the light source, the SFS problem is to reconstruct the 3D depth of the object from a single grayscale 2D input image. A modern class of SFS models relies on the property that the camera performs a perspective projection. The corresponding perspective SFS methods have been the subject of many investigations within the last years. The goal of this chapter is to give an overview of these developments. In our discussion, we focus on important model aspects, and we investigate some prominent algorithms appearing in the literature in more detail than it was done in previous works.}, language = {en} } @misc{SchneidereitBreuss, author = {Schneidereit, Toni and Breuß, Michael}, title = {Solving Ordinary Differential Equations using Artificial Neural Networks - A study on the solution variance}, series = {Proceedings of the Conference Algoritmy 2020}, journal = {Proceedings of the Conference Algoritmy 2020}, publisher = {Open Journal Systems , Public Knowledge Project}, pages = {21 -- 30}, abstract = {Solving differential equations can be realised with simple artificial neural network architectures. Several methods make use of trial solutions with different construction approaches and can provide reliable results. However, many parameters, different optimisation methods and random weight initialisation result in a non constant variance to the exact solution. To our knowledge, this variance has not been studied yet. We investigate several parameters and constant versus random weight initialisation for two solution methods to determine their reliability with the use of backpropagation and ADAM optimisation.}, language = {en} } @misc{KoehlerRigiBreuss, author = {K{\"o}hler, Alexander and Rigi, Ashkan and Breuß, Michael}, title = {Fast Shape Classification Using Kolmogorov-Smirnov Statistics}, series = {WSCG'2022 - 30. International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision'2022}, journal = {WSCG'2022 - 30. International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision'2022}, number = {CSRN 3201}, doi = {10.24132/CSRN.3201.22}, pages = {172 -- 180}, abstract = {The fast classification of shapes is an important problem in shape analysis and of high relevance for many possible applications. In this paper, we consider the use of very fast and easy to compute statistical techniques for assessing shapes, which may for instance be useful for a first similarity search in a shape database. To this end, we construct shape signatures at hand of stochastic sampling of distances between points of interest in a given shape. By employing the Kolmogorov-Smirnov statistics we then propose to formulate the problem of shape classification as a statistical hypothesis test that enables to assess the similarity of the signature distributions. In order to illustrate some important properties of our approach, we explore the use of simple sampling techniques. At hand of experiments conducted with a variety of shapes in two dimensions, we give a discussion of potentially interesting features of the method.}, language = {en} } @misc{EltaherBreuss, author = {Eltaher, Mahmoud and Breuß, Michael}, title = {Unsupervised Description of 3D Shapes by Superquadrics Using Deep Learning}, series = {Computer Vision and Machine Intelligence : Proceedings of CVMI 2022}, journal = {Computer Vision and Machine Intelligence : Proceedings of CVMI 2022}, publisher = {Springer}, address = {Singapore}, isbn = {978-981-19-7866-1}, issn = {978-981-19-7867-8}, doi = {10.1007/978-981-19-7867-8_9}, pages = {95 -- 107}, abstract = {The decomposition of 3D shapes into simple yet representative components is a very intriguing topic in computer vision as it is very useful for many possible applications. Superquadrics may be used with benefit to obtain an implicit representation of the 3D shapes, as they allow to represent a wide range of possible forms by few parameters. However, in the computation of the shape representation, there is often an intricate trade-off between the variation of the represented geometric forms and the accuracy in such implicit approaches. In this paper, we propose an improved loss function, and we introduce beneficial computational techniques. By comparing results obtained by our new technique to the baseline method, we demonstrate that our results are more reliable and accurate, as well as much faster to obtain.}, language = {en} } @misc{MansouriYarahmadiBreussHartmannetal., author = {Mansouri Yarahmadi, Ashkan and Breuß, Michael and Hartmann, Carsten and Schneidereit, Toni}, title = {Unsupervised Optimization of Laser Beam Trajectories for Powder Bed Fusion Printing and Extension to Multiphase Nucleation Models}, series = {Mathematical Methods for Objects Reconstruction : From 3D Vision to 3D Printing}, journal = {Mathematical Methods for Objects Reconstruction : From 3D Vision to 3D Printing}, publisher = {Springer}, address = {Singapor}, isbn = {978-981-99-0775-5}, issn = {978-981-99-0776-2}, doi = {10.1007/978-981-99-0776-2_6}, pages = {157 -- 176}, abstract = {In laser powder bed fusion, it is known that the quality of printing results crucially depends on the temperature distribution and its gradient over the manufacturing plate. We propose a computational model for the motion of the laser beam and the simulation of the time-dependent heat evolution over the plate. For the optimization of the laser beam trajectory, we propose a cost function that minimizes the average thermal gradient and allows to steer the laser beam. The optimization is performed in an unsupervised way. Specifically, we propose an optimization heuristic that is inspired by the well-known traveling salesman problem and that employs simulated annealing to determine a nearly optimal pathway. By comparison of the heat transfer simulations of the derived trajectories with trajectory patterns from standard printing protocols we show that the method gives superior results in terms of the given cost functional.}, language = {en} } @misc{MansouriYarahmadiBreussKhanMohammadi, author = {Mansouri Yarahmadi, Ashkan and Breuß, Michael and Khan Mohammadi, Mohsen}, title = {Explaining StyleGAN Synthesized Swimmer Images in Low-Dimensional Space}, series = {Computer Analysis of Images and Patterns : 20th International Conference, CAIP 2023, Limassol, Cyprus, September 25-28, 2023, Proceedings, Part I}, journal = {Computer Analysis of Images and Patterns : 20th International Conference, CAIP 2023, Limassol, Cyprus, September 25-28, 2023, Proceedings, Part I}, isbn = {978-3-031-44236-0}, issn = {978-3-031-44237-7}, doi = {10.1007/978-3-031-44237-7_16}, pages = {164 -- 173}, abstract = {In many existing AI methods, the reasons behind the decisions made by a trained model are not easy to explain. This often leads to a black-box design that is not interpretable, which makes it a delicate issue to adopt such methods in an application related to safety. We consider generative adversarial networks that are often used to generate data for further use in deep learning applications where not much data is available. In particular, we deal with the StyleGAN approach for generating synthetic observations of swimmers. This paper provides a pipeline that can clearly explain the synthesized images after projecting them to a lower dimensional space. These understood images can later be chosen to train a swimmer safety observation framework. The main goal of our paper is to achieve a higher level of abstraction by which one can explain the variation of synthesized swimmer images in low dimension space. A standard similarity measure is used to evaluate our pipeline and validate a low intra-class variation of established swimmer clusters representing similar swimming style within a low dimensional space.}, language = {en} } @misc{MansouriYarahmadiBreussHartmann, author = {Mansouri Yarahmadi, Ashkan and Breuß, Michael and Hartmann, Carsten}, title = {Long Short-Term Memory Neural Network for Temperature Prediction in Laser Powder Bed Additive Manufacturing}, series = {Proceedings of SAI Intelligent Systems Conference}, journal = {Proceedings of SAI Intelligent Systems Conference}, publisher = {Springer}, address = {Cham}, isbn = {978-3-031-16074-5}, issn = {978-3-031-16075-2}, doi = {10.1007/978-3-031-16075-2_8}, pages = {119 -- 132}, abstract = {n context of laser powder bed fusion (L-PBF), it is known that the properties of the final fabricated product highly depend on the temperature distribution and its gradient over the manufacturing plate. In this paper, we propose a novel means to predict the temperature gradient distributions during the printing process by making use of neural networks. This is realized by employing heat maps produced by an optimized printing protocol simulation and used for training a specifically tailored recurrent neural network in terms of a long short-term memory architecture. The aim of this is to avoid extreme and inhomogeneous temperature distribution that may occur across the plate in the course of the printing process. In order to train the neural network, we adopt a well-engineered simulation and unsupervised learning framework. To maintain a minimized average thermal gradient across the plate, a cost function is introduced as the core criteria, which is inspired and optimized by considering the well-known traveling salesman problem (TSP). As time evolves the unsupervised printing process governed by TSP produces a history of temperature heat maps that maintain minimized average thermal gradient. All in one, we propose an intelligent printing tool that provides control over the substantial printing process components for L-PBF, i.e. optimal nozzle trajectory deployment as well as online temperature prediction for controlling printing quality.}, language = {en} } @misc{KahraBreuss, author = {Kahra, Marvin and Breuß, Michael}, title = {Properties of Morphological Dilation in Max-Plus and Plus-Prod Algebra in Connection with the Fourier Transformation}, series = {Journal of Mathematical Imaging and Vision}, volume = {65}, journal = {Journal of Mathematical Imaging and Vision}, number = {4}, issn = {0924-9907}, doi = {10.1007/s10851-022-01138-3}, pages = {577 -- 591}, 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 quantisation.}, language = {en} } @misc{KahraBreussKleefeldetal., author = {Kahra, Marvin and Breuß, Michael and Kleefeld, Andreas and Welk, Martin}, title = {An Approach to Colour Morphological Supremum Formation using the LogSumExp Approximation}, series = {arXiv}, journal = {arXiv}, doi = {10.48550/arXiv.2312.13792}, pages = {1 -- 12}, abstract = {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.}, language = {en} } @misc{KoehlerBreuss, author = {K{\"o}hler, Alexander and Breuß, Michael}, title = {Towards Efficient Time Stepping for Numerical Shape Correspondence}, series = {arXiv}, journal = {arXiv}, doi = {10.48550/arXiv.2312.13841}, pages = {1 -- 12}, language = {en} } @misc{SridharBreuss, author = {Sridhar, Vivek and Breuß, Michael}, title = {Morphological Sampling Theorem and its Extension to Grey-value Images}, series = {arXiv}, journal = {arXiv}, doi = {10.48550/arXiv.2305.13279}, pages = {1 -- 24}, abstract = {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.}, language = {en} } @misc{ShabaniBreuss, author = {Shabani, Shima and Breuß, Michael}, title = {An Efficient Line Search for Sparse Reconstruction}, series = {Scale Space and Variational Methods in Computer Vision : 9th International Conference, SSVM 2023, Santa Margherita di Pula, Italy, May 21-25, 2023, Proceedings}, journal = {Scale Space and Variational Methods in Computer Vision : 9th International Conference, SSVM 2023, Santa Margherita di Pula, Italy, May 21-25, 2023, Proceedings}, publisher = {Springer}, address = {Cham}, isbn = {978-3-031-31974-7}, issn = {0302-9743}, doi = {10.1007/978-3-031-31975-4_36}, pages = {471 -- 483}, abstract = {A line search strategy is an iterative approach to finding a local minimizer of a nonlinear objective function. First, it finds a sensible direction and then an acceptable step size is computed that determines how far to move along that direction. This paper introduces an efficient line search method for convex nonsmooth optimization problems. Like the Goldstein and Armijo conditions, the presented line search scheme uses only function values, apart from one gradient evaluation at each current iteration. For the novel line search method, we prove global convergence to a stationary point and R-linear convergence rate under some standard assumptions. Based on that, we propose an algorithm for the -minimization problem we call the iterative Shrinkage-Goldstein algorithm (ISGA). In numerical results, we report experiments that demonstrate the competitive performance of the ISGA approach for compressed sensing problems in comparison with some state-of-the-art algorithms.}, language = {en} } @inproceedings{SchefflerMansouriYarahmadiBreussetal., author = {Scheffler, Robert and Mansouri Yarahmadi, Ashkan and Breuß, Michael and K{\"o}hler, Ekkehard}, title = {A Graph Theoretic Approach for Shape from Shading}, series = {Energy minimization methods in computer vision and pattern recognition , 11th International Conference, EMMCVPR 2017, Venice, Italy, October 30 - November 1, 2017}, booktitle = {Energy minimization methods in computer vision and pattern recognition , 11th International Conference, EMMCVPR 2017, Venice, Italy, October 30 - November 1, 2017}, editor = {Pelillo, Marcello and Hancock, Edwin}, publisher = {Springer}, address = {Cham}, isbn = {978-3-319-78198-3}, doi = {10.1007/978-3-319-78199-0_22}, pages = {328 -- 341}, abstract = {Resolving ambiguities is a fundamental problem in shape from shading (SFS). The classic SFS approach allows to reconstruct the surface locally around singular points up to an ambiguity of convex, concave or saddle point type. In this paper we follow a recent approach that seeks to resolve the local ambiguities in a global graph-based setting so that the complete surface reconstruction is consistent. To this end, we introduce a novel graph theoretic formulation for the underlying problem that allows to prove for the first time in the literature that the underlying surface orientation problem is NP-complete. Moreover, we show that our novel framework allows to define an algorithmic framework that solves the disambiguation problem. It makes use of cycle bases for dealing with the graph construction and enables an easy embedding into an optimization method that amounts here to a linear program.}, language = {en} } @inproceedings{BreussMansouriYarahmadiCunningham, author = {Breuß, Michael and Mansouri Yarahmadi, Ashkan and Cunningham, Douglas W.}, 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{SharifiBoroujerdiKhanianBreuss, author = {Sharifi Boroujerdi, Ali and Khanian, Maryam and Breuß, Michael}, title = {Deep Interactive Region Segmentation and Captioning}, series = {2017 13th International Conference on Signal-Image Technology \& Internet-Based Systems (SITIS), Jaipur, India}, booktitle = {2017 13th International Conference on Signal-Image Technology \& Internet-Based Systems (SITIS), Jaipur, India}, publisher = {IEEE}, address = {Piscataway, NJ}, isbn = {978-1-5386-4283-2}, doi = {10.1109/SITIS.2017.27}, pages = {103 -- 110}, abstract = {Based on recent developments in dense image captioning, it is now possible to describe every object of a photographed scene with a caption while objects are determined by bounding boxes. However, the user interpretation of such an output is not trivial due to the existence of many overlapping bounding boxes. Furthermore, in current captioning frameworks, the user is not able to involve personal preferences to exclude areas that are out of interest. In this paper, we propose a novel hybrid deep learning architecture for interactive region segmentation and captioning whereby the user is able to specify an arbitrary region of the image that should be highlighted and described. To this end, we trained three different highly deep architectures on our special training data to identify the User Intention Region (UIR). In parallel, a dense image captioning model is utilized to locate all the objects of the scene by drawing bounding boxes and produce their linguistic descriptions. During our fusion approach, the detected UIR will be explained with the caption of the best match bounding box. To the best of our knowledge, this is the first work that provides such a comprehensive output. Our experiments show the superiority of the proposed approach over state-of-the-art interactive segmentation methods on several well-known segmentation benchmarks. In addition, replacement of the bounding boxes with the result of the interactive segmentation leads to a better understanding of the dense image captioning output as well as an enhancement in object localization accuracy.}, language = {en} } @inproceedings{DachselBreussHoeltgen, author = {Dachsel, Robert and Breuß, Michael and Hoeltgen, Laurent}, title = {A Study of Spectral Expansion for Shape Correspondence}, 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 = {10.3217/978-3-85125-603-1-15}, pages = {73 -- 79}, abstract = {The main task in three dimensional non-rigid shape correspondence is to retrieve similarities between two or more similar three dimensional objects. A useful way to tackle this problem is to construct a simplified shape representation, called feature descriptor, which is invariant under deformable transformations. A successful class of such feature descriptors is based on physical phenomena, concretely by the heat equation for the heat kernel signature and the Schr{\"o}dinger equation for the wave kernel signature. Both approaches employ the spectral decomposition of the Laplace-Beltrami operator, meaning that solutions of the corresponding equations are expressed by a series expansion in terms of eigenfunctions. The feature descriptor is then computed at hand of those solutions. In this paper we explore the influence of the amount of used eigenfunctions on shape correspondence applications, as this is a crucial point with respect to accuracy and overall computational efficiency of the method. Our experimental study will be performed at hand of a standard shape data set.}, language = {en} } @inproceedings{BaehrDachselBreuss, author = {B{\"a}hr, Martin and Dachsel, Robert and Breuß, Michael}, title = {Fast Solvers for Solving Shape Matching by Time Integration}, 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 = {10.3217/978-3-85125-603-1-14}, pages = {65 -- 72}, abstract = {The main task in three-dimensional non-rigid shape correspondence is to retrieve similarities between two or more similar three-dimensional objects. An important building block of many methods constructed to achieve this goal is a simplified shape representation called feature descriptor, which is invariant under almost isometric transformations. A recent feature descriptor relies on the full numerical integration of the geometric heat equation. This approach involves to solve a system of linear equations with multiple right-hand sides. To this end, it is necessary to find a fast and accurate numerical scheme in conjunction with the solution of a sparse linear system and many different right sides. In this paper we evaluate direct, iterative and model order reduction (MOR) methods and their influence to shape correspondence applications which will be validated on standard shape data sets with different resolutions.}, language = {en} } @inproceedings{BreussHoeltgenKleefeld, author = {Breuß, Michael and Hoeltgen, Laurent and Kleefeld, Andreas}, title = {Matrix-Valued Levelings for Colour Images}, series = {Mathematical morphology and its applications to signal and image processing, 13th international symposium, ISMM 2017, Fontainebleau, France, May 15-17, 2017, proceedings}, booktitle = {Mathematical morphology and its applications to signal and image processing, 13th international symposium, ISMM 2017, Fontainebleau, France, May 15-17, 2017, proceedings}, publisher = {Springer International Publishing}, address = {Cham}, isbn = {978-3-319-57239-0}, doi = {10.1007/978-3-319-57240-6_24}, pages = {296 -- 308}, abstract = {Morphological levelings represent a useful tool for the decomposition of an image into cartoon and texture components. Moreover, they can be used to construct a morphological scale space. However, the classic construction of levelings is limited to the use of grey scale images, since an ordering of pixel values is required. In this paper we propose an extension of morphological levelings to colour images. To this end, we consider the formulation of colour images as matrix fields and explore techniques based on the Loewner order for formulating morphological levelings in this setting. Using the matrix-valued colours we study realisations of levelings relying on both the completely discrete construction and the formulation using a partial differential equation. Experimental results confirm the potential of our matrix-based approaches for analysing texture in colour images and for extending the range of applications of levelings in a convenient way to colour image processing.}, language = {en} } @inproceedings{HoeltgenHarrisBreussetal., author = {Hoeltgen, Laurent and Harris, I. and Breuß, Michael and Kleefeld, Andreas}, title = {Analytic Existence and Uniqueness Results for PDE-Based Image Reconstruction with the Laplacian}, series = {Scale Space and Variational Methods in Computer Vision, 6th International Conference on Scale Space and Variational Methods in Computer Vision (SSVM 2017, Kolding, Denmark, June 2017), proceedings}, booktitle = {Scale Space and Variational Methods in Computer Vision, 6th International Conference on Scale Space and Variational Methods in Computer Vision (SSVM 2017, Kolding, Denmark, June 2017), proceedings}, publisher = {Springer International Publishing}, address = {Cham}, isbn = {978-3-319-58770-7}, doi = {10.1007/978-3-319-58771-4_6}, pages = {66 -- 79}, abstract = {Partial differential equations are well suited for dealing with image reconstruction tasks such as inpainting. One of the most successful mathematical frameworks for image reconstruction relies on variations of the Laplace equation with different boundary conditions. In this work we analyse these formulations and discuss the existence and uniqueness of solutions of corresponding boundary value problems, as well as their regularity from an analytic point of view. Our work not only sheds light on useful aspects of the well posedness of several standard problem formulations in image reconstruction but also aggregates them in a common framework. In addition, the performed analysis guides us to specify two new formulations of the classic image reconstruction problem that may give rise to new developments in image reconstruction.}, language = {en} } @inproceedings{DachselBreussHoeltgen, author = {Dachsel, Robert and Breuß, Michael and Hoeltgen, Laurent}, title = {Shape Matching by Time Integration of Partial Differential Equations}, series = {Scale Space and Variational Methods in Computer Vision, 6th International Conference on Scale Space and Variational Methods in Computer Vision (SSVM 2017, Kolding, Denmark, June 2017), proceedings}, booktitle = {Scale Space and Variational Methods in Computer Vision, 6th International Conference on Scale Space and Variational Methods in Computer Vision (SSVM 2017, Kolding, Denmark, June 2017), proceedings}, publisher = {Springer International Publishing}, address = {Cham}, isbn = {978-3-319-58770-7}, doi = {10.1007/978-3-319-58771-4_53}, pages = {669 -- 680}, abstract = {The main task in three dimensional shape matching is to retrieve correspondences between two similar three dimensional objects. To this end, a suitable point descriptor which is invariant under isometric transformations is required. A commonly used descriptor class relies on the spectral decomposition of the Laplace-Beltrami operator. Important examples are the heat kernel signature and the more recent wave kernel signature. In previous works, the evaluation of the descriptor is based on eigenfunction expansions. Thereby a significant practical aspect is that computing a complete expansion is very time and memory consuming. Thus additional strategies are usually introduced that enable to employ only part of the full expansion. In this paper we explore an alternative solution strategy. We discretise the underlying partial differential equations (PDEs) not only in space as in the mentioned approaches, but we also tackle temporal parts by using time integration methods. Thus we do not perform eigenfunction expansions and avoid the use of additional strategies and corresponding parameters. We study here the PDEs behind the heat and wave kernel signature, respectively. Our shape matching experiments show that our approach may lead to quality improvements for finding correct correspondences in comparison to the eigenfunction expansion methods.}, language = {en} } @inproceedings{SharifiBoroujerdiBreussBurgethetal., author = {Sharifi Boroujerdi, Ali and Breuß, Michael and Burgeth, Bernhard and Kleefeld, Andreas}, title = {PDE-Based Color Morphology Using Matrix Fields}, series = {Scale Space and Variational Methods in Computer Vision, 5th International Conference, SSVM 2015, L{\`e}ge-Cap Ferret, France, May 31 - June 4, 2015, Proceedings}, booktitle = {Scale Space and Variational Methods in Computer Vision, 5th International Conference, SSVM 2015, L{\`e}ge-Cap Ferret, France, May 31 - June 4, 2015, Proceedings}, editor = {Aujol, Jean-Fran{\c{c}}ois and Nikolova, Mila and Papadakis, Nicolas}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-319-18460-9}, doi = {10.1007/978-3-319-18461-6_37}, pages = {461 -- 473}, abstract = {In this work, we propose a novel way for performing operations of mathematical morphology on color images. To this end, we convert pixelwise the rgb-values into symmetric 2x2 matrices. The new color space can be interpreted geometrically as a biconal color space structure. Motivated by the formulation of the fundamental morphological operations dilation and erosion in terms of partial differential equations (PDEs), we show how to define finite difference schemes making use of the matrix field formulation. The computation of a pseudo supremum and a pseudo infimum of three color matrices is a crucial step for setting up advanced PDE-based methods. We show that this can be achieved for our goal by an algebraic technique. We investigate our approach by dedicated experiments and confirm useful properties of the new PDE-based color morphology operations.}, language = {en} } @incollection{KleefeldBreussWelketal., author = {Kleefeld, Andreas and Breuß, Michael and Welk, Martin and Burgeth, Bernhard}, title = {Adaptive Filters for Color Images: Median Filtering and Its Extensions}, series = {Computational Color Imaging}, booktitle = {Computational Color Imaging}, editor = {Tr{\´e}meau, Alain and Schettini, Raimondo and Tominaga, Shoji}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-319-15978-2}, doi = {10.1007/978-3-319-15979-9_15}, pages = {149 -- 158}, abstract = {In this paper we are concerned with robust structure-preserving denoising filters for color images. We build on a recently proposed transformation from the RGB color space to the space of symmetric 2×2 matrices that has already been used to transfer morphological dilation and erosion concepts from matrix-valued data to color images. We investigate the applicability of this framework to the construction of color-valued median filters. Additionally, we introduce spatial adaptivity into our approach by morphological amoebas that offer excellent capabilities for structure-preserving filtering. Furthermore, we define color-valued amoeba M-smoothers as a generalization of the median-based concepts. Our experiments confirm that all these methods work well with color images. They demonstrate the potential of our approach to define color processing tools based on matrix field techniques.}, language = {en} } @inproceedings{KleefeldJuTozzaetal., author = {Kleefeld, Andreas and Ju, Yong Chul and Tozza, Silvia and Breuß, Michael and Bruhn, Andr{\´e}s}, title = {Generalised Perspective Shape from Shading with Oren-Nayar Reflectance}, series = {Proceedings 24th British Machine Vision Conference, BMVC 2013, Bristol, UK, September 2013}, booktitle = {Proceedings 24th British Machine Vision Conference, BMVC 2013, Bristol, UK, September 2013}, editor = {Burghardt, Tilo and Damen, Dima and Mayol-Cuevas, Walterio and Mirmehdi, Majid}, publisher = {BMVA Press}, doi = {10.5244/C.27.42}, pages = {42.1 -- 42.11}, abstract = {In spite of significant advances in Shape from Shading (SfS) over the last years, it is still a challenging task to design SfS approaches that are flexible enough to handle a wide range of input scenes. In this paper, we address this lack of flexibility by proposing a novel model that extends the range of possible applications. To this end, we consider the class of modern perspective SfS models formulated via partial differential equations (PDEs). By combining a recent spherical surface parametrisation with the advanced non-Lambertian Oren-Nayar reflectance model, we obtain a robust approach that allows to deal with an arbitrary position of the light source while being able to handle rough surfaces and thus more realistic objects at the same time. To our knowledge, the resulting model is currently the most advanced and most flexible approach in the literature on PDE-based perspective SfS. Apart from deriving our model, we also show how the corresponding set of sophisticated Hamilton-Jacobi equations can be efficiently solved by a specifically tailored fast marching scheme. Experiments with medical real-world data demonstrate that our model works in practice and that is offers the desired flexibility.}, language = {en} } @inproceedings{ChulJuBruhnBreuss, author = {Chul Ju, Yong and Bruhn, Andr{\´e}s and Breuß, Michael}, title = {Variational Perspective Shape from Shading}, series = {Scale Space and Variational Methods in Computer Vision, 5th International Conference, SSVM 2015, L{\`e}ge-Cap Ferret, France, May 31 - June 4, 2015, Proceedings}, booktitle = {Scale Space and Variational Methods in Computer Vision, 5th International Conference, SSVM 2015, L{\`e}ge-Cap Ferret, France, May 31 - June 4, 2015, Proceedings}, editor = {Aujol, Jean-Fran{\c{c}}ois and Nikolova, Mila and Papadakis, Nicolas}, publisher = {Springer International Publishing}, address = {Berlin}, isbn = {978-3-319-18460-9}, doi = {10.1007/978-3-319-18461-6_43}, pages = {538 -- 550}, language = {en} } @inproceedings{BreussCunninghamWelk, author = {Breuß, Michael and Cunningham, Douglas W. 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 W. 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} } @inproceedings{KhanianBreussDavari, author = {Khanian, Maryam and Breuß, Michael and Davari, Ali}, title = {An improved stopping criterion for anisotropic diffusion}, series = {Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014 (ICNAAM-2014), Rhodes, Greece, 22-28 September 2014}, booktitle = {Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014 (ICNAAM-2014), Rhodes, Greece, 22-28 September 2014}, editor = {Simos, Theodore E. and Tsitouras, Charalambos}, publisher = {AIP Publishing}, address = {Melville, New York}, isbn = {978-0-7354-1287-3}, doi = {10.1063/1.4919928}, language = {en} } @inproceedings{HoeltgenBreuss, author = {Hoeltgen, Laurent and Breuß, Michael}, title = {Efficient Co-Domain Quantisation for PDE-Based Image Compression}, series = {Proceedings of the Conference Algoritmy 2016, 20th Conference on Scientific Computing, Vysok{\´e} Tatry - Podbansk{\´e}, Slovakia, March 14 - 18}, booktitle = {Proceedings of the Conference Algoritmy 2016, 20th Conference on Scientific Computing, Vysok{\´e} Tatry - Podbansk{\´e}, Slovakia, March 14 - 18}, editor = {Handlovičov{\´a}, A. and Ševčovič, D.}, publisher = {Publishing House of Slovak University of Technology in Bratislava}, address = {Bratislava}, isbn = {978-80-227-4544-4}, pages = {194 -- 203}, language = {en} } @inproceedings{KhanianSharifiBoroujerdiBreuss, author = {Khanian, Maryam and Sharifi Boroujerdi, Ali and Breuß, Michael}, title = {Perspective photometric stereo beyond Lambert}, series = {Twelfth International Conference on Quality Control by Artificial Vision, 3 - 5 June 2015, Le Creusot, France}, booktitle = {Twelfth International Conference on Quality Control by Artificial Vision, 3 - 5 June 2015, Le Creusot, France}, editor = {Meriaudeau, Fabrice and Aubreton, Olivier}, publisher = {SPIE}, address = {Bellingham, Wash.}, isbn = {978-80-227-4544-4}, doi = {10.1117/12.2182839}, language = {en} } @inproceedings{BaehrBreuss, author = {B{\"a}hr, Martin and Breuß, Michael}, title = {An Improved Eikonal Method for Surface Normal Integration}, series = {Pattern Recognition, 37th German Conference, GCPR 2015, Aachen, Germany, October 7-10, 2015, Proceedings}, booktitle = {Pattern Recognition, 37th German Conference, GCPR 2015, Aachen, Germany, October 7-10, 2015, Proceedings}, editor = {Gall, Juergen and Gehler, Peter and Leibe, Bastian}, publisher = {Springer International Publishing}, address = {Berlin}, isbn = {978-3-319-24946-9}, doi = {10.1007/978-3-319-24947-6_22}, pages = {274 -- 284}, language = {en} } @inproceedings{RhodinBreuss, author = {Rhodin, Helge and Breuß, Michael}, title = {A Mathematically Justified Algorithm for Shape from Texture}, series = {Proceedings Fourth International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2013, Graz, Austria, June 2013}, booktitle = {Proceedings Fourth International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2013, Graz, Austria, June 2013}, editor = {Kuijper, A. and Pock, T. and Bredies, K. and Bischof, H.}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-642-38266-6}, pages = {294 -- 305}, language = {en} } @inproceedings{WeickertHagenburgBreussetal., author = {Weickert, Joachim and Hagenburg, Kai Uwe and Breuß, Michael and Vogel, Oliver}, title = {Linear osmosis models for visual computing}, series = {Energy Minimization Methods in Computer Vision and Pattern Recognition, EMMCVPR 2013, Lund, Sweden, August 2013}, booktitle = {Energy Minimization Methods in Computer Vision and Pattern Recognition, EMMCVPR 2013, Lund, Sweden, August 2013}, editor = {Heyden, A. and Kahl, F. and Olsson, C. and Oskarsson, M. and Tai, X.-C.}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-642-40394-1}, pages = {26 -- 39}, language = {en} } @inproceedings{GallianiJuBreussetal., author = {Galliani, S. and Ju, Yong Chul and Breuß, Michael and Bruhn, Andr{\´e}s}, title = {Generalised Perspective Shape from Shading in Spherical Coordinates}, series = {Proceedings Fourth International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2013, Graz, Austria, June 2013}, booktitle = {Proceedings Fourth International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2013, Graz, Austria, June 2013}, editor = {Kuijper, A. and Pock, T. and Bredies, K. and Bischof, H.}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-642-38266-6}, pages = {222 -- 233}, language = {en} } @misc{SchneidereitBreuss, author = {Schneidereit, Toni and Breuß, Michael}, title = {Adaptive neural-domain refinement for solving time-dependent differential equations}, series = {Advances in Continuous and Discrete Models}, journal = {Advances in Continuous and Discrete Models}, number = {1}, issn = {2731-4235}, doi = {10.1186/s13662-023-03789-x}, abstract = {A classic approach for solving differential equations with neural networks builds upon neural forms, which employ the differential equation with a discretisation of the solution domain. Making use of neural forms for time-dependent differential equations, one can apply the recently developed method of domain segmentation. That is, the domain may be split into several subdomains, on which the optimisation problem is solved. In classic adaptive numerical methods, the mesh as well as the domain may be refined or decomposed, in order to improve the accuracy. Also, the degree of approximation accuracy may be adapted. Therefore, it is desirable to transfer such important and successful strategies to the field of neural-network-based solutions. In the presented work, we propose a novel adaptive neural approach to meet this aim for solving time-dependent problems. To this end, each subdomain is reduced in size until the optimisation is resolved up to a predefined training accuracy. In addition, while the neural networks employed are by default small, we propose a means to adjust also the number of neurons in an adaptive way. We introduce conditions to automatically confirm the solution reliability and optimise computational parameters whenever it is necessary. Results are provided for several initial-value problems that illustrate important computational properties of the method.}, language = {en} }