TY - GEN A1 - Breuß, Michael A1 - Dietrich, Dominik T1 - On the Optimization of Flux Limiter Schemes for Hyperbolic Conservation Laws T2 - Numerical Methods for Partial Differential Equations Y1 - 2013 SN - 1098-2426 VL - Vol. 29 IS - 3 SP - 884 EP - 896 ER - TY - GEN A1 - Breuß, Michael A1 - Cristiani, Emiliano A1 - Durou, Jean-Denis A1 - Falcone, Maurizio A1 - Vogel, Oliver T1 - Perspective Shape from Shading: Ambiguity Analysis and Numerical Approximations T2 - SIAM Journal on Imaging Sciences Y1 - 2012 SN - 1936-4954 VL - 5 IS - 1 SP - 311 EP - 342 ER - TY - CHAP A1 - Breuß, Michael A1 - Burgeth, Bernhard A1 - Pizarro, Luis ED - Ansorge, Rainer T1 - Numerical Analysis, Tensor-Valued Extension and Application in Image Processing T2 - Recent Developments in the Numerics of Hyperbolic Conservation Laws Y1 - 2013 SN - 978-3-642-33220-3 SP - 73 EP - 87 PB - Springer CY - Berlin [u.a.] ER - TY - CHAP A1 - Peter, Pascal A1 - Breuß, Michael ED - Breuß, Michael ED - Bruckstein, Alfred ED - Maragos, Petros T1 - Refined Homotopic Thinning Algorithms and Quality Measures for Skeletonisation Methods T2 - Innovations for Shape Analysis : Models and Algorithms Y1 - 2013 SN - 978-3-642-34140-3 SP - 77 EP - 92 PB - Springer CY - Berlin ER - TY - CHAP A1 - Welk, Martin A1 - Breuß, Michael ED - Hawkes, Peter W. T1 - Morphological Amoebas and Partial Differential Equations T2 - Advances in Imaging and Electron Physics Y1 - 2014 SN - 978-0-12-800144-8 SP - 139 EP - 212 PB - Elsevier CY - Amsterdam ER - TY - CHAP A1 - Welk, Martin A1 - Kleefeld, Andreas A1 - Breuß, Michael ED - Benediktsson, Jón Atli ED - Chanussot, Jocelyn ED - Najman, Laurent ED - Talbot, Hugues T1 - Non-adaptive and Amoeba Quantile Filters for Colour Images T2 - Mathematical Morphology and Its Applications to Signal and Image Processing N2 - 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. KW - Quantile KW - Rank-order filter KW - Color image KW - Matrix field KW - Amoebas Y1 - 2015 SN - 978-3-319-18719-8 SN - 978-3-319-18720-4 U6 - https://doi.org/10.1007/978-3-319-18720-4_34 SP - 398 EP - 409 PB - Springer International Publishing CY - Berlin ER - TY - CHAP A1 - Ju, Yong Chul A1 - Maurer, Daniel A1 - Breuß, Michael A1 - Bruhn, Andrés ED - Breuß, Michael ED - Bruckstein, Alfred ED - Maragos, Petros ED - Wuhrer, Stefanie T1 - Direct variational perspective shape from shading with Cartesian depth parametrisation T2 - Perspectives in Shape Analysis, Mathematics and Visualization Y1 - 2016 SN - 978-3-319-24724-3 U6 - https://doi.org/10.1007/978-3-319-24726-7 SP - 43 EP - 72 PB - Springer International Publishing CY - Cham ER - TY - CHAP A1 - Peter, Pascal A1 - Hoffmann, Sebastian A1 - Nedwed, Frank A1 - Hoeltgen, Laurent A1 - Weickert, Joachim T1 - From Optimised Inpainting with Linear PDEs Towards Competitive Image Compression Codecs T2 - Image and Video Technology, 7th Pacific-Rim Symposium, PSIVT 2015, Auckland, New Zealand, November 25-27, 2015 N2 - 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. KW - Linear diffusion inpainting KW - Homogeneous KW - Biharmonic KW - Image compression KW - Probabilistic tree-densification Y1 - 2016 SN - 978-3-319-29450-6 U6 - https://doi.org/10.1007/978-3-319-29451-3_6 SP - 63 EP - 74 PB - Springer CY - Cham ER - TY - GEN A1 - Bähr, Martin A1 - Breuß, Michael A1 - Quèau, Yvain A1 - Sharifi Boroujerdi, Ali A1 - Durou, Jean-Denis T1 - Fast and accurate surface normal integration on non-rectangular domains T2 - Computational Visual Media N2 - 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. Y1 - 2017 U6 - https://doi.org/10.1007/s41095-016-0075-z SN - 2096-0433 VL - 3 IS - 2 SP - 107 EP - 129 ER - TY - CHAP A1 - Radow, Georg A1 - Breuß, Michael A1 - Hoeltgen, Laurent A1 - Fischer, Thomas ED - Sharma, Puneet ED - Filippo, Maria Bianchi T1 - Optimised Anisotropic Poisson Denoising T2 - Image Analysis, 20th Scandinavian Conference, SCIA 2017, Tromsø, Norway, June 12–14, 2017, Proceedings, Part I Y1 - 2017 SN - 978-3-319-59126-1 SN - 978-3-319-59125-4 U6 - https://doi.org/10.1007/978-3-319-59126-1_42 SP - 502 EP - 514 PB - Springer CY - Cham ER - TY - CHAP A1 - Dachsel, Robert A1 - Breuß, Michael A1 - Hoeltgen, Laurent ED - Felsberg, Michael ED - Heyden, Andreas ED - Krüger, Norbert T1 - The Classic Wave Equation Can Do Shape Correspondence T2 - Computer Analysis of Images and Patterns, CAIP International Conference on Computer Analysis of Images and Patterns, Ystad,Sweden, 2017 N2 - 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 Schrödinger 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. KW - Feature descriptor KW - Shape analysis KW - Wave equation Y1 - 2017 SN - 978-3-319-64688-6 U6 - https://doi.org/10.1007/978-3-319-64689-3_22 SP - 264 EP - 275 PB - Springer International Publishing CY - Cham ER - TY - GEN A1 - Hoeltgen, Laurent T1 - Understanding image inpainting with the help of the Helmholtz equation T2 - Mathematical Sciences N2 - 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. KW - Laplace interpolation Helmholtz equation Image inpainting Finite difference scheme Y1 - 2017 U6 - https://doi.org/10.1007/s40096-017-0207-3 SN - 2008-1359 VL - 11 IS - 1 SP - 73 EP - 77 ER - TY - GEN A1 - Hoeltgen, Laurent A1 - Peter, Pascal A1 - Breuß, Michael T1 - Clustering-based quantisation for PDE-based image compression T2 - Signal, Image and Video Processing N2 - 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. KW - Laplace interpolation KW - Inpainting KW - Compression KW - Quantisation KW - Clustering KW - Partial differential equations Y1 - 2018 U6 - https://doi.org/10.1007/s11760-017-1173-9 SN - 1863-1703 SN - 1863-1711 VL - 12 IS - 3 SP - 411 EP - 419 ER - TY - GEN A1 - Hoeltgen, Laurent A1 - Breuß, Michael A1 - Herold, Gert A1 - Sarradj, Ennes T1 - Sparse ℓ1 regularisation of matrix valued models for acoustic source characterisation T2 - Optimization and Engineering N2 - 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. KW - Convex optimisation KW - Sparse recovery KW - Split Bregman KW - Microphone array KW - Matrix differentiation KW - Acoustic source characterisation Y1 - 2018 U6 - https://doi.org/10.1007/s11081-017-9357-2 SN - 1389-4420 SN - 1573-2924 VL - 19 IS - 1 SP - 39 EP - 70 ER - TY - GEN A1 - Dachsel, Robert A1 - Jöster, Annika A1 - Breuß, Michael ED - Lee, Chilwoo ED - Su, Zhixun ED - Sugimoto, Akihiro T1 - Real-Time Retinal Vessel Segmentation on High-Resolution Fundus Images Using Laplacian Pyramids T2 - Image and Video Technology, 9th Pacific-Rim Symposium, PSIVT 2019, Sydney, NSW, Australia, November 18–22, 2019, Proceedings N2 - 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. KW - Laplacian pyramids Vessel segmentation High-resolution fundus images Real-time retinal imaging Y1 - 2019 SN - 978-3-030-34878-6 SN - 978-3-030-34879-3 U6 - https://doi.org/10.1007/978-3-030-34879-3_26 SN - 0302-9743 SN - 1611-3349 SP - 337 EP - 350 PB - Springer CY - Cham ER - TY - GEN A1 - Welk, Martin A1 - Breuß, Michael A1 - Sridhar, Vivek T1 - Matrix Morphology with Extremum Principle T2 - Mathematical Morphology and Its Applications to Signal and Image Processing : 14th International Symposium, ISMM 2019, Saarbrücken, Germany, July 8-10, 2019, Proceedings N2 - 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. KW - Dilation Erosion Matrix valued images Extremum principle Y1 - 2019 SN - 978-3-030-20866-0 SN - 978-3-030-20867-7 U6 - https://doi.org/10.1007/978-3-030-20867-7_14 SP - 177 EP - 188 PB - Springer CY - Cham ER - TY - GEN A1 - Welk, Martin A1 - Breuß, Michael T1 - The convex-hull-stripping median approximates affine curvature motion T2 - Scale Space and Variational Methods in Computer Vision : 7th International Conference, SSVM 2019, Hofgeismar, Germany, June 30 – July 4, 2019, Proceedings N2 - 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. KW - Median filter Convex hull stripping Partial differential equations Curve evolution Y1 - 2019 SN - 978-3-030-22367-0 U6 - https://doi.org/10.1007/978-3-030-22368-7_16 SP - 199 EP - 210 PB - Springer CY - Cham ER - TY - CHAP A1 - Breuß, Michael A1 - Mansouri Yarahmadi, Ashkan ED - Durou, Jean-Denis ED - Falcone, Maurizio ED - Quéau, Yvain ED - Tozza, Silvia T1 - Perspective Shape from Shading : An Exposition on Recent Works with New Experiments T2 - Advances in Photometric 3D-Reconstruction N2 - 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. KW - Shape from Shading Perspective projection Hamilton Jacobi equations Numerical methods Fast marching method Y1 - 2020 SN - 978-3-030-51865-3 SN - 978-3-030-51866-0 U6 - https://doi.org/https://doi.org/10.1007/978-3-030-51866-0_2 SN - 2191-6586 SN - 2191-6594 SP - 31 EP - 72 PB - Springer CY - Cham ER - TY - GEN A1 - Schneidereit, Toni A1 - Breuß, Michael T1 - Solving Ordinary Differential Equations using Artificial Neural Networks - A study on the solution variance T2 - Proceedings of the Conference Algoritmy 2020 N2 - 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. Y1 - 2020 UR - http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/1547/811 SP - 21 EP - 30 PB - Open Journal Systems , Public Knowledge Project ER - TY - GEN A1 - Köhler, Alexander A1 - Rigi, Ashkan A1 - Breuß, Michael T1 - Fast Shape Classification Using Kolmogorov-Smirnov Statistics T2 - WSCG'2022 - 30. International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision'2022 N2 - 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. KW - Statistical Shape Analysis; Shape Classification; Shape Similarity; Kolmogorov-Smirnov; Hypothesis Testing; Sampling Methods Y1 - 2022 U6 - https://doi.org/10.24132/CSRN.3201.22 IS - CSRN 3201 SP - 172 EP - 180 ER - TY - GEN A1 - Eltaher, Mahmoud A1 - Breuß, Michael T1 - Unsupervised Description of 3D Shapes by Superquadrics Using Deep Learning T2 - Computer Vision and Machine Intelligence : Proceedings of CVMI 2022 N2 - 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. KW - Implicit shape representation Superquadrics Deep learning 3D shape description Y1 - 2023 SN - 978-981-19-7866-1 U6 - https://doi.org/10.1007/978-981-19-7867-8_9 SN - 978-981-19-7867-8 SP - 95 EP - 107 PB - Springer CY - Singapore ER - TY - GEN A1 - Mansouri Yarahmadi, Ashkan A1 - Breuß, Michael A1 - Hartmann, Carsten A1 - Schneidereit, Toni T1 - Unsupervised Optimization of Laser Beam Trajectories for Powder Bed Fusion Printing and Extension to Multiphase Nucleation Models T2 - Mathematical Methods for Objects Reconstruction : From 3D Vision to 3D Printing N2 - 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. KW - Additive manufacturing Multiphase alloys Trajectory optimization Powder bed fusion printing Heat simulation Linear-quadratic control Y1 - 2023 SN - 978-981-99-0775-5 U6 - https://doi.org/10.1007/978-981-99-0776-2_6 SN - 978-981-99-0776-2 SP - 157 EP - 176 PB - Springer CY - Singapor ER - TY - GEN A1 - Mansouri Yarahmadi, Ashkan A1 - Breuß, Michael A1 - Khan Mohammadi, Mohsen T1 - Explaining StyleGAN Synthesized Swimmer Images in Low-Dimensional Space T2 - Computer Analysis of Images and Patterns : 20th International Conference, CAIP 2023, Limassol, Cyprus, September 25–28, 2023, Proceedings, Part I N2 - 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. Y1 - 2023 SN - 978-3-031-44236-0 U6 - https://doi.org/10.1007/978-3-031-44237-7_16 SN - 978-3-031-44237-7 SP - 164 EP - 173 ER - TY - GEN A1 - Mansouri Yarahmadi, Ashkan A1 - Breuß, Michael A1 - Hartmann, Carsten T1 - Long Short-Term Memory Neural Network for Temperature Prediction in Laser Powder Bed Additive Manufacturing T2 - Proceedings of SAI Intelligent Systems Conference N2 - 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. KW - Additive manufacturing Laser beam trajectory optimization Powder bed fusion printing Heat simulation Linear-quadratic control Y1 - 2022 SN - 978-3-031-16074-5 U6 - https://doi.org/10.1007/978-3-031-16075-2_8 SN - 978-3-031-16075-2 SP - 119 EP - 132 PB - Springer CY - Cham ER - TY - GEN A1 - Kahra, Marvin A1 - Breuß, Michael T1 - Properties of Morphological Dilation in Max-Plus and Plus-Prod Algebra in Connection with the Fourier Transformation T2 - Journal of Mathematical Imaging and Vision N2 - 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. KW - Mathematical morphology KW - Fourier transform KW - Dilation KW - Max-plus algebra KW - Slope transform Y1 - 2023 U6 - https://doi.org/10.1007/s10851-022-01138-3 SN - 0924-9907 VL - 65 IS - 4 SP - 577 EP - 591 ER - TY - GEN A1 - Kahra, Marvin A1 - Breuß, Michael A1 - Kleefeld, Andreas A1 - Welk, Martin T1 - An Approach to Colour Morphological Supremum Formation using the LogSumExp Approximation T2 - arXiv N2 - Mathematical morphology is a part of image processing that has proven to be fruitful for numerous applications. Two main operations in mathematical morphology are dilation and erosion. These are based on the construction of a supremum or infimum with respect to an order over the tonal range in a certain section of the image. The tonal ordering can easily be realised in grey-scale morphology, and some morphological methods have been proposed for colour morphology. However, all of these have certain limitations. In this paper we present a novel approach to colour morphology extending upon previous work in the field based on the Loewner order. We propose to consider an approximation of the supremum by means of a log-sum exponentiation introduced by Maslov. We apply this to the embedding of an RGB image in a field of symmetric 2×2 matrices. In this way we obtain nearly isotropic matrices representing colours and the structural advantage of transitivity. In numerical experiments we highlight some remarkable properties of the proposed approach. Y1 - 2023 U6 - https://doi.org/10.48550/arXiv.2312.13792 SP - 1 EP - 12 ER - TY - GEN A1 - Köhler, Alexander A1 - Breuß, Michael T1 - Towards Efficient Time Stepping for Numerical Shape Correspondence T2 - arXiv Y1 - 2023 U6 - https://doi.org/10.48550/arXiv.2312.13841 SP - 1 EP - 12 ER - TY - GEN A1 - Sridhar, Vivek A1 - Breuß, Michael T1 - Morphological Sampling Theorem and its Extension to Grey-value Images T2 - arXiv N2 - Sampling is a basic operation in image processing. In classic literature, a morphological sampling theorem has been established, which shows how sampling interacts by morphological operations with image reconstruction. Many aspects of morphological sampling have been investigated for binary images, but only some of them have been explored for grey-value imagery. With this paper, we make a step towards completion of this open matter. By relying on the umbra notion, we show how to transfer classic theorems in binary morphology about the interaction of sampling with the fundamental morphological operations dilation, erosion, opening and closing, to the grey-value setting. In doing this we also extend the theory relating the morphological operations and corresponding reconstructions to use of non-flat structuring elements. We illustrate the theoretical developments at hand of examples. Y1 - 2023 U6 - https://doi.org/10.48550/arXiv.2305.13279 SP - 1 EP - 24 ER - TY - GEN A1 - Shabani, Shima A1 - Breuß, Michael T1 - An Efficient Line Search for Sparse Reconstruction T2 - Scale Space and Variational Methods in Computer Vision : 9th International Conference, SSVM 2023, Santa Margherita di Pula, Italy, May 21–25, 2023, Proceedings N2 - 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. KW - Nonsmooth minimization Line search method Goldstein quotient Compressed sensing Global convergence R-linear convergence Y1 - 2023 SN - 978-3-031-31974-7 SN - 978-3-031-31975-4 U6 - https://doi.org/10.1007/978-3-031-31975-4_36 SN - 0302-9743 SN - 1611-3349 SP - 471 EP - 483 PB - Springer CY - Cham ER - TY - CHAP A1 - Scheffler, Robert A1 - Mansouri Yarahmadi, Ashkan A1 - Breuß, Michael A1 - Köhler, Ekkehard ED - Pelillo, Marcello ED - Hancock, Edwin T1 - A Graph Theoretic Approach for Shape from Shading T2 - Energy minimization methods in computer vision and pattern recognition , 11th International Conference, EMMCVPR 2017, Venice, Italy, October 30 – November 1, 2017 N2 - 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. KW - Shape from shading KW - Ambiguity KW - Configuration graph KW - Cycle basis Y1 - 2018 SN - 978-3-319-78198-3 U6 - https://doi.org/10.1007/978-3-319-78199-0_22 SP - 328 EP - 341 PB - Springer CY - Cham ER - TY - CHAP A1 - Breuß, Michael A1 - Mansouri Yarahmadi, Ashkan A1 - Cunningham, Douglas W. ED - Welk, Martin ED - Urschler, Martin ED - Roth, Peter M. T1 - The Convex-Concave Ambiguity in Perspective Shape from Shading T2 - Proceedings of the OAGM Workshop 2018 Medical Image Analysis, May 15 - 16, 2018, Hall/Tyrol, Austria N2 - 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. KW - Shape from Shading Y1 - 2018 SN - 978-3-85125-603-1 U6 - https://doi.org/10.3217/978-3-85125-603-1-13 SP - 57 EP - 63 PB - Verlag der TU Graz CY - Graz ER - TY - CHAP A1 - Sharifi Boroujerdi, Ali A1 - Khanian, Maryam A1 - Breuß, Michael T1 - Deep Interactive Region Segmentation and Captioning T2 - 2017 13th International Conference on Signal-Image Technology & Internet-Based Systems (SITIS), Jaipur, India N2 - 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. KW - Machine learning KW - deep learning Y1 - 2018 SN - 978-1-5386-4283-2 U6 - https://doi.org/10.1109/SITIS.2017.27 SP - 103 EP - 110 PB - IEEE CY - Piscataway, NJ ER - TY - CHAP A1 - Dachsel, Robert A1 - Breuß, Michael A1 - Hoeltgen, Laurent ED - Welk, Martin ED - Urschler, Martin ED - Roth, Peter M. T1 - A Study of Spectral Expansion for Shape Correspondence T2 - Proceedings of the OAGM Workshop 2018 Medical Image Analysis, May 15 - 16, 2018, Hall/Tyrol, Austria N2 - 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 Schrödinger 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. Y1 - 2018 SN - 978-3-85125-603-1 U6 - https://doi.org/10.3217/978-3-85125-603-1-15 SP - 73 EP - 79 PB - Verlag der TU Graz CY - Graz ER - TY - CHAP A1 - Bähr, Martin A1 - Dachsel, Robert A1 - Breuß, Michael ED - Welk, Martin ED - Urschler, Martin ED - Roth, Peter M. T1 - Fast Solvers for Solving Shape Matching by Time Integration T2 - Proceedings of the OAGM Workshop 2018 Medical Image Analysis, May 15 - 16, 2018, Hall/Tyrol, Austria N2 - 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. Y1 - 2018 SN - 978-3-85125-603-1 U6 - https://doi.org/10.3217/978-3-85125-603-1-14 SP - 65 EP - 72 PB - Verlag der TU Graz CY - Graz ER - TY - CHAP A1 - Breuß, Michael A1 - Hoeltgen, Laurent A1 - Kleefeld, Andreas T1 - Matrix-Valued Levelings for Colour Images T2 - Mathematical morphology and its applications to signal and image processing, 13th international symposium, ISMM 2017, Fontainebleau, France, May 15-17, 2017, proceedings N2 - 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. KW - Mathematical morphology Dilation Erosion Loewner order Leveling Y1 - 2017 SN - 978-3-319-57239-0 U6 - https://doi.org/10.1007/978-3-319-57240-6_24 SP - 296 EP - 308 PB - Springer International Publishing CY - Cham ER - TY - CHAP A1 - Hoeltgen, Laurent A1 - Harris, I. A1 - Breuß, Michael A1 - Kleefeld, Andreas T1 - Analytic Existence and Uniqueness Results for PDE-Based Image Reconstruction with the Laplacian T2 - 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 N2 - 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. KW - Partial differential equations Laplace equation Mixed boundary conditions Image reconstruction Image inpainting Y1 - 2017 SN - 978-3-319-58770-7 U6 - https://doi.org/10.1007/978-3-319-58771-4_6 SP - 66 EP - 79 PB - Springer International Publishing CY - Cham ER - TY - CHAP A1 - Dachsel, Robert A1 - Breuß, Michael A1 - Hoeltgen, Laurent T1 - Shape Matching by Time Integration of Partial Differential Equations T2 - 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 N2 - 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. KW - Shape matching Point descriptor Shape analysis Heat equation Schrödinger equation Y1 - 2017 SN - 978-3-319-58770-7 U6 - https://doi.org/10.1007/978-3-319-58771-4_53 SP - 669 EP - 680 PB - Springer International Publishing CY - Cham ER - TY - CHAP A1 - Sharifi Boroujerdi, Ali A1 - Breuß, Michael A1 - Burgeth, Bernhard A1 - Kleefeld, Andreas ED - Aujol, Jean-François ED - Nikolova, Mila ED - Papadakis, Nicolas T1 - PDE-Based Color Morphology Using Matrix Fields T2 - Scale Space and Variational Methods in Computer Vision, 5th International Conference, SSVM 2015, Lège-Cap Ferret, France, May 31 - June 4, 2015, Proceedings N2 - 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. KW - PDE-based morphology KW - Matrix fields KW - Color morphology KW - Finite difference schemes KW - FCT scheme KW - Pseudo supremum KW - Pseudo infimum Y1 - 2015 SN - 978-3-319-18460-9 U6 - https://doi.org/10.1007/978-3-319-18461-6_37 SP - 461 EP - 473 PB - Springer CY - Berlin ER - TY - CHAP A1 - Kleefeld, Andreas A1 - Breuß, Michael A1 - Welk, Martin A1 - Burgeth, Bernhard ED - Trémeau, Alain ED - Schettini, Raimondo ED - Tominaga, Shoji T1 - Adaptive Filters for Color Images: Median Filtering and Its Extensions T2 - Computational Color Imaging N2 - 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. KW - Matrix field KW - Color image KW - Median filter KW - M-smoother KW - Amoeba filter Y1 - 2015 UR - http://link.springer.com/chapter/10.1007/978-3-319-15979-9_15# SN - 978-3-319-15978-2 U6 - https://doi.org/10.1007/978-3-319-15979-9_15 SP - 149 EP - 158 PB - Springer CY - Berlin ER - TY - CHAP A1 - Kleefeld, Andreas A1 - Ju, Yong Chul A1 - Tozza, Silvia A1 - Breuß, Michael A1 - Bruhn, Andrés ED - Burghardt, Tilo ED - Damen, Dima ED - Mayol-Cuevas, Walterio ED - Mirmehdi, Majid T1 - Generalised Perspective Shape from Shading with Oren-Nayar Reflectance T2 - Proceedings 24th British Machine Vision Conference, BMVC 2013, Bristol, UK, September 2013 N2 - 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. Y1 - 2013 UR - http://www.bmva.org/bmvc/2013/Papers/paper0042/index.html U6 - https://doi.org/10.5244/C.27.42 SP - 42.1 EP - 42.11 PB - BMVA Press ER - TY - CHAP A1 - Chul Ju, Yong A1 - Bruhn, Andrés A1 - Breuß, Michael ED - Aujol, Jean-François ED - Nikolova, Mila ED - Papadakis, Nicolas T1 - Variational Perspective Shape from Shading T2 - Scale Space and Variational Methods in Computer Vision, 5th International Conference, SSVM 2015, Lège-Cap Ferret, France, May 31 - June 4, 2015, Proceedings KW - Shape from shading KW - Variational methods KW - Perspective camera model Y1 - 2015 UR - http://link.springer.com/chapter/10.1007%2F978-3-319-18461-6_43 SN - 978-3-319-18460-9 U6 - https://doi.org/10.1007/978-3-319-18461-6_43 SP - 538 EP - 550 PB - Springer International Publishing CY - Berlin ER - TY - CHAP A1 - Breuß, Michael A1 - Cunningham, Douglas W. A1 - Welk, Martin ED - Cunningham, Douglas W. ED - Hofstedt, Petra ED - Meer, Klaus ED - Schmitt, Ingo T1 - Scale spaces for cognitive systems: a position paper T2 - Informatik 2015, Tagung vom 28. September – 2. Oktober 2015 in Cottbus KW - Scale spaces KW - partial differential equations KW - cognitive systems KW - perception Y1 - 2015 UR - http://subs.emis.de/LNI/Proceedings/Proceedings246/1253.pdf SN - 978-3-88579-640-4 SP - 1253 EP - 1255 PB - Gesellschaft für Informatik CY - Bonn ER - TY - CHAP A1 - Khanian, Maryam A1 - Breuß, Michael A1 - Davari, Ali ED - Simos, Theodore E. ED - Tsitouras, Charalambos T1 - An improved stopping criterion for anisotropic diffusion T2 - Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014 (ICNAAM-2014), Rhodes, Greece, 22-28 September 2014 KW - Amoeba filter Matrix field KW - Color image KW - M-smoother KW - Matrix field KW - Median filter Y1 - 2015 UR - http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4919928 SN - 978-0-7354-1287-3 U6 - https://doi.org/10.1063/1.4919928 PB - AIP Publishing CY - Melville, New York ER - TY - CHAP A1 - Hoeltgen, Laurent A1 - Breuß, Michael ED - Handlovičová, A. ED - Ševčovič, D. T1 - Efficient Co-Domain Quantisation for PDE-Based Image Compression T2 - Proceedings of the Conference Algoritmy 2016, 20th Conference on Scientific Computing, Vysoké Tatry - Podbanské, Slovakia, March 14 - 18 KW - Laplace interpolation KW - inpainting KW - compression KW - quantisation KW - clustering KW - partial differential equations Y1 - 2016 UR - http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/408 SN - 978-80-227-4544-4 SP - 194 EP - 203 PB - Publishing House of Slovak University of Technology in Bratislava CY - Bratislava ER - TY - CHAP A1 - Khanian, Maryam A1 - Sharifi Boroujerdi, Ali A1 - Breuß, Michael ED - Meriaudeau, Fabrice ED - Aubreton, Olivier T1 - Perspective photometric stereo beyond Lambert T2 - Twelfth International Conference on Quality Control by Artificial Vision, 3 - 5 June 2015, Le Creusot, France KW - Cameras KW - Reflection KW - Reflectivity KW - Specular reflections Y1 - 2015 UR - http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=2290117 SN - 978-80-227-4544-4 U6 - https://doi.org/10.1117/12.2182839 PB - SPIE CY - Bellingham, Wash. ER - TY - CHAP A1 - Bähr, Martin A1 - Breuß, Michael ED - Gall, Juergen ED - Gehler, Peter ED - Leibe, Bastian T1 - An Improved Eikonal Method for Surface Normal Integration T2 - Pattern Recognition, 37th German Conference, GCPR 2015, Aachen, Germany, October 7-10, 2015, Proceedings Y1 - 2015 UR - http://link.springer.com/chapter/10.1007%2F978-3-319-24947-6_22 SN - 978-3-319-24946-9 U6 - https://doi.org/10.1007/978-3-319-24947-6_22 SP - 274 EP - 284 PB - Springer International Publishing CY - Berlin ER - TY - CHAP A1 - Rhodin, Helge A1 - Breuß, Michael ED - Kuijper, A. ED - Pock, T. ED - Bredies, K. ED - Bischof, H. T1 - A Mathematically Justified Algorithm for Shape from Texture T2 - Proceedings Fourth International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2013, Graz, Austria, June 2013 Y1 - 2013 SN - 978-3-642-38266-6 SN - 978-3-642-38267-3 SP - 294 EP - 305 PB - Springer CY - Berlin ER - TY - CHAP A1 - Weickert, Joachim A1 - Hagenburg, Kai Uwe A1 - Breuß, Michael A1 - Vogel, Oliver ED - Heyden, A. ED - Kahl, F. ED - Olsson, C. ED - Oskarsson, M. ED - Tai, X.-C. T1 - Linear osmosis models for visual computing T2 - Energy Minimization Methods in Computer Vision and Pattern Recognition, EMMCVPR 2013, Lund, Sweden, August 2013 Y1 - 2013 SN - 978-3-642-40394-1 SN - 978-3-642-40395-8 SP - 26 EP - 39 PB - Springer CY - Berlin ER - TY - CHAP A1 - Galliani, S. A1 - Ju, Yong Chul A1 - Breuß, Michael A1 - Bruhn, Andrés ED - Kuijper, A. ED - Pock, T. ED - Bredies, K. ED - Bischof, H. T1 - Generalised Perspective Shape from Shading in Spherical Coordinates T2 - Proceedings Fourth International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2013, Graz, Austria, June 2013 Y1 - 2013 SN - 978-3-642-38266-6 SP - 222 EP - 233 PB - Springer CY - Berlin ER - TY - GEN A1 - Schneidereit, Toni A1 - Breuß, Michael T1 - Adaptive neural-domain refinement for solving time-dependent differential equations T2 - Advances in Continuous and Discrete Models N2 - 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. KW - Neural forms KW - Adaptive neural refinement KW - Domain decomposition KW - Physics-informed neural networks KW - Differential equations Y1 - 2023 U6 - https://doi.org/10.1186/s13662-023-03789-x SN - 2731-4235 IS - 1 ER - TY - CHAP A1 - Breuß, Michael A1 - Quèau, Yvain A1 - Bähr, Martin A1 - Durou, Jean-Denis T1 - Highly Efficient Surface Normal Integration T2 - Proceedings of the Conference Algoritmy 2016, 20th Conference on Scientific Computing, Vysoké Tatry - Podbanské, Slovakia, March 14 - 18 KW - surface normal integration KW - Poisson integration KW - Krylov subspace methods KW - fast marching methods Y1 - 2016 UR - http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/409 SN - 978-80-227-4544-4 SP - 204 EP - 213 PB - Publishing House of Slovak University of Technology in Bratislava CY - Bratislava ER - TY - CHAP A1 - Ju, Yong Chul A1 - Breuß, Michael A1 - Bruhn, Andrés A1 - Galiani, Silvano ED - Browden, R. ED - Collomosse, J. ED - Mikolajczyk, K. T1 - Shape from Shading for Rough Surfaces: Analysis of the Oren-Nayar Model T2 - Proceedings 23rd British Machine Vision Conference, BMVC 2012, Surrey, UK, September 3-7, 2012 Y1 - 2012 SN - 1-901725-46-4 U6 - https://doi.org/10.5244/C.26.104 SP - 104.1 EP - 104.11 PB - BMVA Press ER - TY - CHAP A1 - Galliani, S. A1 - Breuß, Michael A1 - Ju, Yong Chul ED - Bowden, R. ED - Collomosse, J. ED - Mikolajczyk, K. T1 - Fast and Robust Surface Normal Integration by a Discrete Eikonal Equation T2 - Proceedings, 23rd British Machine Vision Conference, BMVC 2012, Surrey, UK, September 3-7, 2012 Y1 - 2012 SN - 1-901725-46-4 U6 - https://doi.org/10.5244/C.26.106 SP - 106.1 EP - 106.11 PB - BMVA Press ER - TY - GEN A1 - Breuß, Michael A1 - Buhl, Johannes A1 - Mansouri Yarahmadi, Ashkan A1 - Bambach, Markus A1 - Peter, Pascal T1 - A Simple Approach to Stiffness Enhancement of a Printable Shape by Hamilton-Jacobi Skeletonization T2 - Procedia Manufacturing N2 - The 3D-Printing technology is ready to produce parts with specific properties like individual stiffness. Based on a predefined outer shape, the inner structure of a printed part defines mainly the mechanical features. By Hamilton-Jacobi skeletonization, a stiffness enhancement of a printable shape can be achieved in a way, that a novel AM-corner includes linear axis function. Originating in the field of shape analysis in computer vision and graphics, the so-called medial axis transform (MAT) is designed for the computation of a structure that resembles the bone structure of biological shapes. The input for MAT computation is typically a shape’s boundary. The arising topological skeletons have proven to provide a useful concept for many applications; however, their computation is generally intricate and also known to rely on many parameters, diminishing the accessibility of skeletonization methods. In this work, the classical Hamilton-Jacobi skeletonization approach is adopted to compute a stability enhancing shape structure. As the basic method has not been designed for the context of additive manufacturing, a set of suitable modifications are introduced to design an algorithm that suits our intended purpose. Unlike the traditional skeletonization schemes, the resulting method appears to be robust and in practice almost completely automated as we can identify useful generic parameter settings. By a finite element method (FEM) study, the elastic stress properties of the AM-corner with linear axis function is validated and printed with in metal (1.4404) with the 3D Selected Laser Melting (SLM) system AconityMIDI. The AM-knot with skeletonization guides approximately 20 times better than a standard knot. While the first obtained results are shown as 2.5 dimensional shapes, it is emphasized that the proposed algorithm offers many possibilities for extensions to three dimensions and variations in context of additive manufacturing. KW - Skeletonization KW - Hamilton-Jacobi skeletonization KW - stiffness enhancement KW - 3D printing KW - additive manufacturing Y1 - 2020 U6 - https://doi.org/10.1016/j.promfg.2020.04.147 SN - 2351-9789 N1 - 23rd International Conference on Material Forming (ESAFORM 2020) VL - Vol. 47 SP - 1190 EP - 1196 ER - TY - GEN A1 - Bähr, Martin A1 - Buhl, Johannes A1 - Radow, Georg A1 - Schmidt, Johannes A1 - Bambach, Markus A1 - Breuß, Michael A1 - Fügenschuh, Armin T1 - Stable honeycomb structures and temperature based trajectory optimization for wire-arc additive manufacturing T2 - Optimization and Engineering N2 - 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. KW - Mixed-integer linear programming KW - Geometric optimization KW - Eikonal equation KW - Heat transmission KW - Additive manufacturing KW - Centroidal Voronoi tesselation Y1 - 2021 U6 - https://doi.org/10.1007/s11081-020-09552-5 SN - 1573-2924 VL - 22 IS - 2 SP - 913 EP - 974 ER - TY - GEN A1 - Bähr, Martin A1 - Breuß, Michael T1 - Efficient Long-Term Simulation of the Heat Equation with Application in Geothermal Energy Storage T2 - Mathematics N2 - Long-term evolutions of parabolic partial differential equations, such as the heat equation, are the subject of interest in many applications. There are several numerical solvers marking the state-of-the-art in diverse scientific fields that may be used with benefit for the numerical simulation of such long-term scenarios. We show how to adapt some of the currently most efficient numerical approaches for solving the fundamental problem of long-term linear heat evolution with internal and external boundary conditions as well as source terms. Such long-term simulations are required for the optimal dimensioning of geothermal energy storages and their profitability assessment, for which we provide a comprehensive analytical and numerical model. Implicit methods are usually considered the best choice for resolving long-term simulations of linear parabolic problems; however, in practice the efficiency of such schemes in terms of the combination of computational load and obtained accuracy may be a delicate issue, as it depends very much on the properties of the underlying model. For example, one of the challenges in long-term simulation may arise by the presence of time-dependent boundary conditions, as in our application. In order to provide both a computationally efficient and accurate enough simulation, we give a thorough discussion of the various numerical solvers along with many technical details and own adaptations. By our investigation, we focus on two largely competitive approaches for our application, namely the fast explicit diffusion method originating in image processing and an adaptation of the Krylov subspace model order reduction method. We validate our numerical findings via several experiments using synthetic and real-world data. We show that we can obtain fast and accurate long-term simulations of typical geothermal energy storage facilities. We conjecture that our techniques can be highly useful for tackling long-term heat evolution in many applications. KW - heat equation KW - internal boundary conditions KW - efficient long-term evolution KW - fast explicit diffusion KW - Krylov subspace model order reduction KW - geothermal energy storage Y1 - 2022 U6 - https://doi.org/10.3390/math10132309 SN - 2227-7390 VL - 10 IS - 13 ER - TY - GEN A1 - Schneidereit, Toni A1 - Breuß, Michael T1 - Computational characteristics of feedforward neural networks for solving a stiff differential equation T2 - Neural Computing and Applications N2 - Feedforward neural networks offer a possible approach for solving differential equations. However, the reliability and accuracy of the approximation still represent delicate issues that are not fully resolved in the current literature. Computational approaches are in general highly dependent on a variety of computational parameters as well as on the choice of optimisation methods, a point that has to be seen together with the structure of the cost function. The intention of this paper is to make a step towards resolving these open issues. To this end, we study here the solution of a simple but fundamental stiff ordinary differential equation modelling a damped system. We consider two computational approaches for solving differential equations by neural forms. These are the classic but still actual method of trial solutions defining the cost function, and a recent direct construction of the cost function related to the trial solution method. Let us note that the settings we study can easily be applied more generally, including solution of partial differential equations. By a very detailed computational study, we show that it is possible to identify preferable choices to be made for parameters and methods. We also illuminate some interesting effects that are observable in the neural network simulations. Overall we extend the current literature in the field by showing what can be done in order to obtain useful and accurate results by the neural network approach. By doing this we illustrate the importance of a careful choice of the computational setup. KW - Feedforward neural networks KW - Ordinary differential equations KW - Trial solution KW - Adam KW - Backpropagation Y1 - 2022 U6 - https://doi.org/10.1007/s00521-022-06901-6 VL - 34 IS - 10 SP - 7975 EP - 7989 ER - TY - GEN A1 - Radow, Georg A1 - Rodriguez, Giuseppe A1 - Mansouri Yarahmadi, Ashkan A1 - Breuß, Michael ED - Cristiani, Emiliano T1 - Photometric Stereo with Non-Lambertian Preprocessing and Hayakawa Lighting Estimation for Highly Detailed Shape Reconstruction T2 - Mathematical Methods for Objects Reconstruction : From 3D Vision to 3D Printing N2 - In many realistic scenarios, the use of highly detailed photometric 3D reconstruction techniques is hindered by several challenges in given imagery. Especially, the light sources are often unknown and need to be estimated, and the light reflectance is often non-Lambertian. In addition, when approaching the problem to apply photometric techniques at real-world imagery, several parameters appear that need to be fixed in order to obtain high-quality reconstructions. In this chapter, we attempt to tackle these issues by combining photometric stereo with non-Lambertian preprocessing and Hayakawa lighting estimation. At hand of a dedicated study, we discuss the applicability of these techniques for their use in automated 3D geometry recovery for 3D printing. KW - Photometric stereo Shape from shading Hayakawa procedure Lighting estimation Oren-Nayar model Lambertian reflector Y1 - 2023 SN - 978-981-99-0775-5 U6 - https://doi.org/10.1007/978-981-99-0776-2_2 SN - 978-981-99-0776-2 SN - 2281-518X SP - 35 EP - 56 PB - Springer CY - Singapore ER - TY - GEN A1 - Masouri Yarahmadi, Ashkan A1 - Breuß, Michael A1 - Hartmann, Carsten T1 - Long Short-Term Memory Neural Network for Temperature Prediction in Laser Powder Bed Additive Manufacturing T2 - arXiv Y1 - 2023 U6 - https://doi.org/10.48550/arXiv.2301.12904 SP - 1 EP - 15 ER - TY - GEN A1 - Kahra, Marvin A1 - Sridhar, Vivek A1 - Breuß, Michael T1 - Fast Morphological Dilation and Erosion for Grey Scale Images Using the Fourier Transform T2 - Scale Space and Variational Methods in Computer Vision N2 - The basic filters in mathematical morphology are dilation and erosion. They are defined by a flat or non-flat structuring element that is usually shifted pixel-wise over an image and a comparison process that takes place within the corresponding mask. Existing fast algorithms that realise dilation and erosion for grey value images are often limited with respect to size or shape of the structuring element. Usually their algorithmic complexity depends on these aspects. Many fast methods only address flat morphology. In this paper we propose a novel way to make use of the fast Fourier transform for the computation of dilation and erosion. Our method is by design highly flexible, as it can be used with flat and non-flat structuring elements of any size and shape. Moreover, its complexity does not depend on size or shape of the structuring element, but only on the number of pixels in the filtered images. We show experimentally that we obtain results of very reasonable quality with the proposed method. KW - Mathematical morphology / Fast Fourier Transform / Dilation / Erosion / Efficient algorithms Y1 - 2021 SN - 978-3-030-75548-5 U6 - https://doi.org/10.1007/978-3-030-75549-2_6 SN - 978-3-030-75549-2 SP - 65 EP - 77 PB - Springer CY - Cham ER - TY - GEN A1 - Schneidereit, Toni A1 - Breuß, Michael T1 - Polynomial Neural Forms Using Feedforward Neural Networks for Solving Differential Equations T2 - Artificial Intelligence and Soft Computing N2 - Several neural network approaches for solving differential equations employ trial solutions with a feedforward neural network. There are different means to incorporate the trial solution in the construction, for instance one may include them directly in the cost function. Used within the corresponding neural network, the trial solutions define the so-called neural form. Such neural forms represent general, flexible tools by which one may solve various differential equations. In this article we consider time-dependent initial value problems, which requires to set up the trial solution framework adequately. The neural forms presented up to now in the literature for such a setting can be considered as first order polynomials. In this work we propose to extend the polynomial order of the neural forms. The novel construction includes several feedforward neural networks, one for each order. The feedforward neural networks are optimised using a stochastic gradient descent method (ADAM). As a baseline model problem we consider a simple yet stiff ordinary differential equation. In experiments we illuminate some interesting properties of the proposed approach. KW - Feedforward neural networks / Initial value problem / Trial solution /Differential equations Y1 - 2021 SN - 978-3-030-87985-3 U6 - https://doi.org/10.1007/978-3-030-87986-0_21 SN - 978-3-030-87986-0 SP - 236 EP - 245 PB - Springer CY - Cham ER - TY - GEN A1 - Sridhar, Vivek A1 - Breuß, Michael T1 - Sampling of Non-flat Morphology for Grey Value Images T2 - Computer Analysis of Images and Patterns N2 - Sampling is a basic operation in image processing. In previous literature, a morphological sampling theorem has been established showing how sampling interacts with image reconstruction by morphological operations. However, while many aspects of morphological sampling have been investigated for binary images in classic works, only some of them have been extended to grey scale imagery. Especially, previous attempts to study the relation between sampling and grey scale morphology are restricted by construction to flat morphological filters. In order to establish a sampling theory for non-flat morphology, we establish an alternative definition for grey scale opening and closing relying on the umbra notion. Making use of this, we prove a sampling theorem about the interaction of sampling with fundamental morphological operations for non-flat morphology. This allows to make precise corresponding relations between sampling and image reconstruction, extending classic results for flat morphology of grey value images. KW - Non-flat morphology/ Sampling theorem/ Mathematical morphology / Opening / Closing Y1 - 2021 SN - 978-3-030-89130-5 U6 - https://doi.org/10.1007/978-3-030-89131-2_8 SN - 978-3-030-89131-2 VL - 2021 SP - 88 EP - 97 PB - Springer CY - Cham ER - TY - GEN A1 - Mansouri Yarahmadi, Ashkan A1 - Breuß, Michael T1 - Automatic Watermeter Reading in Presence of Highly Deformed Digits T2 - Computer Analysis of Images and Patterns N2 - The task we face in this paper is to automate the reading of watermeters as can be found in large apartment houses. Typically water passes through such watermeters, so that one faces a wide range of challenges caused by water as the medium where the digits are positioned. One of the main obstacles is given by the frequently produced bubbles inside the watermeter that deform the digits. To overcome this problem, we propose the construction of a novel data set that resembles the watermeter digits with a focus on their deformations by bubbles. We report on promising experimental recognition results, based on a deep and recurrent network architecture performed on our data set. KW - Underwater digit recognition / Sequence models / Connectionist Temporal Classification Y1 - 2021 SN - 978-3-030-89130-5 U6 - https://doi.org/10.1007/978-3-030-89131-2_14 SN - 978-3-030-89131-2 SP - 153 EP - 163 PB - Springer CY - Cham ER - TY - GEN A1 - Breuß, Michael A1 - Sharifi Boroujerdi, Ali A1 - Mansouri Yarahmadi, Ashkan T1 - Modelling the Energy Consumption of Driving Styles Based on Clustering of GPS Information T2 - Modelling N2 - This paper presents a novel approach to distinguishing driving styles with respect to their energy efficiency. A distinct property of our method is that it relies exclusively on the global positioning system (GPS) logs of drivers. This setting is highly relevant in practice as these data can easily be acquired. Relying on positional data alone means that all features derived from them will be correlated, so we strive to find a single quantity that allows us to perform the driving style analysis. To this end we consider a robust variation of the so-called "jerk" of a movement. We give a detailed analysis that shows how the feature relates to a useful model of energy consumption when driving cars. We show that our feature of choice outperforms other more commonly used jerk-based formulations for automated processing. Furthermore, we discuss the handling of noisy, inconsistent, and incomplete data, as this is a notorious problem when dealing with real-world GPS logs. Our solving strategy relies on an agglomerative hierarchical clustering combined with an L-term heuristic to determine the relevant number of clusters. It can easily be implemented and delivers a quick performance, even on very large, real-world datasets. We analyse the clustering procedure, making use of established quality criteria. Experiments show that our approach is robust against noise and able to discern different driving styles KW - clustering KW - energy efficiency KW - driving style analysis KW - jerk-based feature KW - Gjerk-based feature KW - PS data Y1 - 2022 U6 - https://doi.org/10.3390/modelling3030025 SN - 2673-3951 VL - 3 IS - 3 SP - 385 EP - 399 ER - TY - GEN A1 - Köhler, Alexander A1 - Breuß, Michael T1 - Computational Analysis of PDE-Based Shape Analysis Models by Exploring the Damped Wave Equation T2 - Algorithms N2 - The computation of correspondences between shapes is a principal task in shape analysis. In this work, we consider correspondences constructed by a numerical solution of partial differential equations (PDEs). The underlying model of interest is thereby the classic wave equation, since this may give the most accurate shape matching. As has been observed in previous works, numerical time discretisation has a substantial influence on matching quality. Therefore, it is of interest to understand the underlying mechanisms and to investigate at the same time if there is an analytical model that could best describe the most suitable method for shape matching. To this end, we study here the damped wave equation, which mainly serves as a tool to understand and model properties of time discretisation. At the hand of a detailed study of possible parameters, we illustrate that the method that gives the most reasonable feature descriptors benefits from a damping mechanism which can be introduced numerically or within the PDE. This sheds light on some basic mechanisms of underlying computational and analytic models, as one may conjecture by our investigation that an ideal model could be composed of a transport mechanism and a diffusive component that helps to counter grid effects. KW - shape analysis KW - partial differential equations KW - damped wave equation KW - time discretisation KW - numerical methods KW - Laplnumerical methods KW - ace–Beltrami operator Y1 - 2022 U6 - https://doi.org/10.3390/a15090304 SN - 1999-4893 VL - 15 IS - 9 SP - 304 ER - TY - GEN A1 - Welk, Martin A1 - Kleefeld, Andreas A1 - Breuß, Michael T1 - Quantile Filtering of Colour Images via Symmetric Matrices T2 - Mathematical Morphology - Theory and Applications N2 - 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.We consider variants of these filters based on three matrix norms – the nuclear, Frobenius, and spectral norm – and study their differences. We investigate the properties of the quantile and gradient filters and their links to dilation and erosion operators. Using amoeba structuring elements,we devise image-adaptive versions of our quantile and gradient filters. Experiments are presented to demonstrate the favourable properties of the filters, and compare them to existing approaches in colour morphology. KW - quantile KW - rank-order filter KW - colour image KW - matrix field KW - amoebas Y1 - 2016 U6 - https://doi.org/10.1515/mathm-2016-0008 SN - 2353-3390 VL - 1 IS - 1 SP - 136 EP - 174 ER - TY - GEN A1 - Schneidereit, Toni A1 - Breuß, Michael T1 - Collocation polynomial neural forms and domain fragmentation for solving initial value problems T2 - Neural Computing and Applications N2 - Several neural network approaches for solving differential equations employ trial solutions with a feedforward neural network. There are different means to incorporate the trial solution in the construction, for instance, one may include them directly in the cost function. Used within the corresponding neural network, the trial solutions define the so-called neural form. Such neural forms represent general, flexible tools by which one may solve various differential equations. In this article, we consider time-dependent initial value problems, which require to set up the neural form framework adequately. The neural forms presented up to now in the literature for such a setting can be considered as first-order polynomials. In this work, we propose to extend the polynomial order of the neural forms. The novel collocation-type construction includes several feedforward neural networks, one for each order. Additionally, we propose the fragmentation of the computational domain into subdomains. The neural forms are solved on each subdomain, whereas the interfacing grid points overlap in order to provide initial values over the whole fragmentation. We illustrate in experiments that the combination of collocation neural forms of higher order and the domain fragmentation allows to solve initial value problems over large domains with high accuracy and reliability. KW - Collocation neural forms KW - Polynomial neural forms KW - Trial solution KW - Initial value problems KW - Domain fragmentation Y1 - 2022 U6 - https://doi.org/10.1007/s00521-021-06860-4 SN - 1433-3058 SN - 0941-0643 VL - 34 IS - 9 SP - 7141 EP - 7156 ER - TY - CHAP A1 - Sridhar, Vivek A1 - Breuß, Michael T1 - A Novel Approach for Computation of Morphological Operations Using the Number Theoretic Transform T2 - Discrete Geometry and Mathematical Morphology : Second International Joint Conference, DGMM 2022, Strasbourg, France, October 24–27, 2022, Proceedings N2 - The fundamental operations of mathematical morphology are dilation and erosion. They are often implemented using a sliding window with the purpose to compute maximum respectively minimum of pixel values within the corresponding mask. We reformulate the problem of morphological dilation respectively erosion of an image with a non-flat filter as a convolution of their umbras. To this end, we propose to make use of the number theoretic transform to compute the convolution in this setting. In contrast to other possible schemes, this transform represents a completely discrete computational approach. It allows exact convolution of sequences made up of integers. Therefore we propose by the combination of umbra framework and number theoretic transform a well-engineered combination. There is no restriction on size or shape of the structuring element, and also flat and non-flat filters can be realised. KW - Morphological dilation Morphological erosion Number theoretic transform Y1 - 2022 SN - 978-3-031-19896-0 SN - 978-3-031-19897-7 U6 - https://doi.org/10.1007/978-3-031-19897-7_15 SN - 0302-9743 SN - 1611-3349 SP - 182 EP - 192 PB - Springer CY - Cham ER - TY - GEN A1 - Sridhar, Vivek A1 - Breuß, Michael T1 - An Exact Fast Fourier Method for Morphological Dilation and Erosion Using the Umbra Technique T2 - 19th Conference on Robots and Vision (CRV), 2022 N2 - In this paper we consider the fundamental operations dilation and erosion of mathematical morphology. It is well known that many powerful image filtering operations can be constructed by their combinations. We propose a fast and novel algorithm based on the Fast Fourier Transform to compute grey-value morphological operations on an image. The novel method may deal with non-flat filters and incorporates no restrictions on shape and size of the filtering window, in contrast to many other fast methods in the field. Unlike fast Fourier techniques from previous works, the novel method gives exact results and is not an approximation. The key aspect which allows to achieve this is to explore here for the first time in this context the umbra formulation of images and filters. We show that the new method is in practice particularly suitable for filtering images with small tonal range or when employing large filter sizes. KW - morphological dilation, morphological erosion, fast Fourier transform Y1 - 2022 SN - 978-1-6654-9774-9 SN - 978-1-6654-9775-6 U6 - https://doi.org/10.1109/CRV55824.2022.00032 SP - 190 EP - 196 PB - IEEE ER - TY - GEN A1 - Breuß, Michael A1 - Kleefeld, Andreas T1 - Implicit Monotone Difference Methods for Scalar Conservation Laws with Source Terms T2 - Acta Mathematica Vietnamica N2 - In this article, a concept of implicit methods for scalar conservation laws in one or more spatial dimensions allowing also for source terms of various types is presented. This material is a significant extension of previous work of the first author (Breuß SIAM J. Numer. Anal. 43(3), 970–986 2005). Implicit notions are developed that are centered around a monotonicity criterion. We demonstrate a connection between a numerical scheme and a discrete entropy inequality, which is based on a classical approach by Crandall and Majda. Additionally, three implicit methods are investigated using the developed notions. Next, we conduct a convergence proof which is not based on a classical compactness argument. Finally, the theoretical results are confirmed by various numerical tests. KW - Conservation laws KW - Finite difference methods KW - Implicit methods KW - Monotone methods KW - Source term KW - Entropy solution Y1 - 2020 U6 - https://doi.org/10.1007/s40306-019-00354-1 SN - 2315-4144 SN - 0251-4184 VL - 45 IS - 3 SP - 709 EP - 738 ER - TY - GEN A1 - Sridhar, Vivek A1 - Breuß, Michael A1 - Kahra, Marvin ED - Bebis, George T1 - Fast Approximation of Color Morphology T2 - Advances in Visual Computing : 16th International Symposium, ISVC 2021, Virtual Event, October 4-6, 2021, Proceedings, Part II N2 - The basic filters in mathematical morphology are dilation and erosion. They are defined by a flat or non-flat structuring element that is usually shifted pixel-wise over an image and a comparison process that takes place within the corresponding mask. The algorithmic complexity of fast algorithms that realise dilation and erosion for color images usually depends on size and shape of the structuring element. In this paper we propose and investigate an easy and fast way to make use of the fast Fourier transform for an approximate computation of dilation and erosion for color images. Similarly in construction as many other fast algorithms, the method extends a recent scheme proposed for single-channel filtering. It is by design highly flexible, as it can be used with flat and non-flat structuring elements of any size and shape. Moreover, its complexity only depends on the number of pixels in the filtered images. We analyse here some important aspects of the approximation, and we show experimentally that we obtain results of very reasonable quality while the method has very attractive computational properties. KW - Mathematical morphology Fourier transform Fast algorithms Y1 - 2022 SN - 978-3-030-90435-7 U6 - https://doi.org/10.1007/978-3-030-90436-4_39 SP - 488 EP - 499 PB - Springer CY - Cham ER - TY - GEN A1 - Breuß, Michael A1 - Hoeltgen, Laurent A1 - Radow, Georg T1 - Towards PDE-Based Video Compression with Optimal Masks Prolongated by Optic Flow T2 - Journal of Mathematical Imaging and Vision 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 an optimal selection of data. For the possible extension to video compression, this 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. In this way, 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. In doing this, we discuss in detail the influence of possible computational setups. We show that the approach preserves a reasonable quality in the reconstruction and is very robust against errors in the flow field. KW - Partial differential equations KW - Inpainting KW - Laplace interpolation KW - Optic flow KW - Video reconstruction Y1 - 2021 U6 - https://doi.org/10.1007/s10851-020-00973-6 SN - 1573-7683 SN - 0924-9907 VL - 63 IS - 2 SP - 144 EP - 156 ER - TY - GEN A1 - Köhler, Alexander A1 - Breuß, Michael ED - Elmoataz, Abderrahim ED - Fadili, Jalal ED - Quéau, Yvain ED - Rabin, Julien ED - Simon, Loïc T1 - Towards Efficient Time Stepping for Numerical Shape Correspondence T2 - Scale Space and Variational Methods in Computer Vision : 8th International Conference, SSVM 2021, Virtual Event, May 16–20, 2021, Proceedings N2 - The computation of correspondences between shapes is a principal task in shape analysis. To this end, methods based on partial differential equations (PDEs) have been established, encompassing e.g. the classic heat kernel signature as well as numerical solution schemes for geometric PDEs. In this work we focus on the latter approach. We consider here several time stepping schemes. The goal of this investigation is to assess, if one may identify a useful property of methods for time integration for the shape analysis context. Thereby we investigate the dependence on time step size, since the class of implicit schemes that are useful candidates in this context should ideally yield an invariant behaviour with respect to this parameter. To this end we study integration of heat and wave equation on a manifold. In order to facilitate this study, we propose an efficient, unified model order reduction framework for these models. We show that specific l0 stable schemes are favourable for numerical shape analysis. We give an experimental evaluation of the methods at hand of classical TOSCA data sets. Y1 - 2021 SN - 978-3-030-75548-5 SN - 978-3-030-75549-2 U6 - https://doi.org/10.1007/978-3-030-75549-2_14 SN - 1611-3349 SN - 0302-9743 SP - 165 EP - 176 PB - Springer International Publishing ER - TY - GEN A1 - Radow, Georg A1 - Hoeltgen, Laurent A1 - Quéau, Yvain A1 - Breuß, Michael T1 - Optimisation of Classic Photometric Stereo by Non-convex Variational Minimisation T2 - Journal of Mathematical Imaging and Vision N2 - Estimating shape and appearance of a three-dimensional object from a given set of images is a classic research topic that is still actively pursued. Among the various techniques available, photometric stereo is distinguished by the assumption that the underlying input images are taken from the same point of view but under different lighting conditions. The most common techniques are conceptually close to the classic photometric stereo problem, meaning that the modelling encompasses a linearisation step and that the shape information is computed in terms of surface normals. In this work, instead of linearising we aim to stick to the original formulation of the photometric stereo problem, and we propose to minimise a much more natural objective function, namely the reprojection error in terms of depth. Minimising the resulting non-trivial variational model for photometric stereo allows to recover the depth of the photographed scene directly. As a solving strategy, we follow an approach based on a recently published optimisation scheme for non-convex and non-smooth cost functions. The main contributions of our paper are of theoretical nature. A technical novelty in our framework is the usage of matrix differential calculus. We supplement our approach by a detailed convergence analysis of the resulting optimisation algorithm and discuss possibilities to ease the computational complexity. At hand of an experimental evaluation we discuss important properties of the method. Overall, our strategy achieves more accurate results than other approaches that rely on the classic photometric stereo assumptions. The experiments also highlight some practical aspects of the underlying optimisation algorithm that may be of interest in a more general context. KW - Non-convex minimisation KW - Computer vision KW - Photometric stereo Y1 - 2019 U6 - https://doi.org/10.1007/s10851-018-0828-7 SN - 1573-7683 VL - 61 IS - 1 SP - 84 EP - 105 ER - TY - GEN A1 - Hoeltgen, Laurent A1 - Kleefeld, Andreas A1 - Harries, Isaac A1 - Breuß, Michael T1 - Theoretical foundation of the weighted laplace inpainting problem T2 - Journal of Applications of Mathematics N2 - Laplace interpolation is a popular approach in image inpainting using partial differential equations. The classic approach considers the Laplace equation with mixed boundary conditions. Recently a more general formulation has been proposed, where the differential operator consists of a point-wise convex combination of the Laplacian and the known image data. We provide the first detailed analysis on existence and uniqueness of solutions for the arising mixed boundary value problem. Our approach considers the corresponding weak formulation and aims at using the Theorem of Lax-Milgram to assert the existence of a solution. To this end we have to resort to weighted Sobolev spaces. Our analysis shows that solutions do not exist unconditionally. The weights need some regularity and must fulfil certain growth conditions. The results from this work complement findings which were previously only available for a discrete setup. KW - image inpainting KW - image reconstruction KW - Laplace equation KW - Laplace interpolation KW - mixed boundary condition KW - partial differential equation KW - weighted Sobolev space Y1 - 2019 U6 - https://doi.org/10.21136/AM.2019.0206-18 SN - 1572-9109 SN - 0862-7940 VL - 64 IS - 3 SP - 281 EP - 300 ER - TY - GEN A1 - Maurer, Daniel A1 - Ju, Yong Chul A1 - Breuß, Michael A1 - Bruhn, Andrés T1 - Combining Shape from Shading and Stereo: A Joint Variational Method for Estimating Depth, Illumination and Albedo T2 - International Journal of Computer Vision 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. This difference in approaching the reconstruction problem yields complementary advantages that are worthwhile being combined. So far, however, most “joint” approaches are based on an initial stereo mesh that is subsequently refined using shading information. In this paper we follow a completely different approach. We propose a joint variational method that combines both cues within a single minimisation framework. 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 resulting model in such a way that it jointly estimates depth, albedo and illumination. This in turn makes the approach applicable to objects with non-uniform albedo as well as to scenes with unknown illumination. Experiments for synthetic and real-world images demonstrate the benefits of our combined approach: They not only show that our method is capable of generating very detailed reconstructions, but also that joint approaches are feasible in practice. KW - Stereo reconstruction KW - Shape from Shading KW - Variational methods KW - Illumination estimation KW - Albedo estimation KW - Joint reasoning Y1 - 2018 U6 - https://doi.org/10.1007/s11263-018-1079-1 SN - 0920-5691 SN - 1573-1405 VL - 126 IS - 12 SP - 1342 EP - 1366 ER - TY - GEN A1 - Khanian, Maryam A1 - Sharifi Boroujerdi, Ali A1 - Breuß, Michael T1 - Photometric stereo for strong specular highlights T2 - Computational Visual Media N2 - Photometric stereo is a fundamental technique in computer vision known to produce 3D shape with high accuracy. It uses several input images of a static scene taken from one and the same camera position but under varying illumination. The vast majority of studies in this 3D reconstruction method assume orthographic projection for the camera model. In addition, they mainly use the Lambertian reflectance model as the way that light scatters at surfaces. Thus, providing reliable photometric stereo results from real world objects still remains a challenging task. We address 3D reconstruction by use of a more realistic set of assumptions, combining for the first time the complete Blinn–Phong reflectance model and perspective projection. Furthermore, we compare two different methods of incorporating the perspective projection into our model. Experiments are performed on both synthetic and real world images; the latter do not benefit from laboratory conditions. The results show the high potential of our method even for complex real world applications such as medical endoscopy images which may include many specular highlights. KW - photometric stereo (PS) KW - complete Blinn–Phong model KW - perspective projection KW - diffuse reflection KW - specular reflection Y1 - 2018 U6 - https://doi.org/10.1007/s41095-017-0101-9 SN - 2096-0433 SN - 2096-0662 VL - 4 IS - 1 SP - 83 EP - 102 ER - 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 ED - Breuß, Michael ED - Bruckstein, Alfred ED - Maragos, Petros ED - Wuhrer, Stefanie T1 - Perspectives in Shape Analysis KW - Differentialgeometrie Y1 - 2016 SN - 978-3-319-24724-3 U6 - https://doi.org/10.1007/978-3-319-24726-7 PB - Springer International Publishing CY - Cham ER - TY - GEN ED - Breuß, Michael ED - Bruckstein, Alfred ED - Maragos, Petros T1 - Innovations for Shape Analysis : Models and Algorithms Y1 - 2013 SN - 978-3-642-34140-3 PB - Springer CY - Berlin [u.a.] 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 - TY - GEN A1 - Sridhar, Vivek A1 - Shahin, Keyvan A1 - Breuß, Michael A1 - Reichenbach, Marc T1 - The Polynomial Connection between Morphological Dilation and Discrete Convolution T2 - arXiv Y1 - 2023 U6 - https://doi.org/10.48550/arXiv.2305.03018 SP - 1 EP - 11 ER -