@misc{BreussDietrich, author = {Breuß, Michael and Dietrich, Dominik}, title = {On the Optimization of Flux Limiter Schemes for Hyperbolic Conservation Laws}, series = {Numerical Methods for Partial Differential Equations}, volume = {Vol. 29}, journal = {Numerical Methods for Partial Differential Equations}, number = {3}, issn = {1098-2426}, pages = {884 -- 896}, language = {en} } @misc{BreussCristianiDurouetal., author = {Breuß, Michael and Cristiani, Emiliano and Durou, Jean-Denis and Falcone, Maurizio and Vogel, Oliver}, title = {Perspective Shape from Shading: Ambiguity Analysis and Numerical Approximations}, series = {SIAM Journal on Imaging Sciences}, volume = {5}, journal = {SIAM Journal on Imaging Sciences}, number = {1}, issn = {1936-4954}, pages = {311 -- 342}, language = {en} } @incollection{BreussBurgethPizarro, author = {Breuß, Michael and Burgeth, Bernhard and Pizarro, Luis}, title = {Numerical Analysis, Tensor-Valued Extension and Application in Image Processing}, series = {Recent Developments in the Numerics of Hyperbolic Conservation Laws}, booktitle = {Recent Developments in the Numerics of Hyperbolic Conservation Laws}, editor = {Ansorge, Rainer}, publisher = {Springer}, address = {Berlin [u.a.]}, isbn = {978-3-642-33220-3}, pages = {73 -- 87}, language = {en} } @incollection{PeterBreuss, author = {Peter, Pascal and Breuß, Michael}, title = {Refined Homotopic Thinning Algorithms and Quality Measures for Skeletonisation Methods}, series = {Innovations for Shape Analysis : Models and Algorithms}, booktitle = {Innovations for Shape Analysis : Models and Algorithms}, editor = {Breuß, Michael and Bruckstein, Alfred and Maragos, Petros}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-642-34140-3}, pages = {77 -- 92}, language = {en} } @incollection{WelkBreuss, author = {Welk, Martin and Breuß, Michael}, title = {Morphological Amoebas and Partial Differential Equations}, series = {Advances in Imaging and Electron Physics}, booktitle = {Advances in Imaging and Electron Physics}, editor = {Hawkes, Peter W.}, publisher = {Elsevier}, address = {Amsterdam}, isbn = {978-0-12-800144-8}, pages = {139 -- 212}, language = {en} } @incollection{WelkKleefeldBreuss, author = {Welk, Martin and Kleefeld, Andreas and Breuß, Michael}, title = {Non-adaptive and Amoeba Quantile Filters for Colour Images}, series = {Mathematical Morphology and Its Applications to Signal and Image Processing}, booktitle = {Mathematical Morphology and Its Applications to Signal and Image Processing}, editor = {Benediktsson, J{\´o}n Atli and Chanussot, Jocelyn and Najman, Laurent and Talbot, Hugues}, publisher = {Springer International Publishing}, address = {Berlin}, isbn = {978-3-319-18719-8}, doi = {10.1007/978-3-319-18720-4_34}, pages = {398 -- 409}, abstract = {Quantile filters, or rank-order filters, are local image filters which assign quantiles of intensities of the input image within neighbourhoods as output image values. Combining a multivariate quantile definition developed in matrix-valued morphology with a recently introduced mapping between the RGB colour space and the space of symmetric 2×2 matrices, we state a class of colour image quantile filters, along with a class of morphological gradient filters derived from these. Using amoeba structuring elements, we devise image-adaptive versions of both filter classes. Experiments demonstrate the favourable properties of the filters.}, language = {en} } @incollection{JuMaurerBreussetal., author = {Ju, Yong Chul and Maurer, Daniel and Breuß, Michael and Bruhn, Andr{\´e}s}, title = {Direct variational perspective shape from shading with Cartesian depth parametrisation}, series = {Perspectives in Shape Analysis, Mathematics and Visualization}, booktitle = {Perspectives in Shape Analysis, Mathematics and Visualization}, editor = {Breuß, Michael and Bruckstein, Alfred and Maragos, Petros and Wuhrer, Stefanie}, publisher = {Springer International Publishing}, address = {Cham}, isbn = {978-3-319-24724-3}, doi = {10.1007/978-3-319-24726-7}, pages = {43 -- 72}, language = {en} } @misc{BaehrBreussQueauetal., author = {B{\"a}hr, Martin and Breuß, Michael and Qu{\`e}au, Yvain and Sharifi Boroujerdi, Ali and Durou, Jean-Denis}, title = {Fast and accurate surface normal integration on non-rectangular domains}, series = {Computational Visual Media}, volume = {3}, journal = {Computational Visual Media}, number = {2}, issn = {2096-0433}, doi = {10.1007/s41095-016-0075-z}, pages = {107 -- 129}, abstract = {The integration of surface normals for the purpose of computing the shape of a surface in 3D space is a classic problem in computer vision. However, even nowadays it is still a challenging task to devise a method that is flexible enough to work on non-trivial computational domains with high accuracy, robustness, and computational efficiency. By uniting a classic approach for surface normal integration with modern computational techniques, we construct a solver that fulfils these requirements. Building upon the Poisson integration model, we use an iterative Krylov subspace solver as a core step in tackling the task. While such a method can be very efficient, it may only show its full potential when combined with suitable numerical preconditioning and problem-specific initialisation. We perform a thorough numerical study in order to identify an appropriate preconditioner for this purpose. To provide suitable initialisation, we compute this initial state using a recently developed fast marching integrator. Detailed numerical experiments illustrate the benefits of this novel combination. In addition, we show on real-world photometric stereo datasets that the developed numerical framework is flexible enough to tackle modern computer vision applications.}, language = {en} } @inproceedings{RadowBreussHoeltgenetal., author = {Radow, Georg and Breuß, Michael and Hoeltgen, Laurent and Fischer, Thomas}, title = {Optimised Anisotropic Poisson Denoising}, series = {Image Analysis, 20th Scandinavian Conference, SCIA 2017, Troms{\o}, Norway, June 12-14, 2017, Proceedings, Part I}, booktitle = {Image Analysis, 20th Scandinavian Conference, SCIA 2017, Troms{\o}, Norway, June 12-14, 2017, Proceedings, Part I}, editor = {Sharma, Puneet and Filippo, Maria Bianchi}, publisher = {Springer}, address = {Cham}, isbn = {978-3-319-59126-1}, doi = {10.1007/978-3-319-59126-1_42}, pages = {502 -- 514}, language = {en} } @inproceedings{DachselBreussHoeltgen, author = {Dachsel, Robert and Breuß, Michael and Hoeltgen, Laurent}, title = {The Classic Wave Equation Can Do Shape Correspondence}, series = {Computer Analysis of Images and Patterns, CAIP International Conference on Computer Analysis of Images and Patterns, Ystad,Sweden, 2017}, booktitle = {Computer Analysis of Images and Patterns, CAIP International Conference on Computer Analysis of Images and Patterns, Ystad,Sweden, 2017}, editor = {Felsberg, Michael and Heyden, Andreas and Kr{\"u}ger, Norbert}, publisher = {Springer International Publishing}, address = {Cham}, isbn = {978-3-319-64688-6}, doi = {10.1007/978-3-319-64689-3_22}, pages = {264 -- 275}, abstract = {A major task in non-rigid shape analysis is to retrieve correspondences between two almost isometric 3D objects. An important tool for this task are geometric feature descriptors. Ideally, a feature descriptor should be invariant under isometric transformations and robust to small elastic deformations. A successful class of feature descriptors employs the spectral decomposition of the Laplace-Beltrami operator. Important examples are the heat kernel signature using the heat equation and the more recent wave kernel signature applying the Schr{\"o}dinger equation from quantum mechanics. In this work we propose a novel feature descriptor which is based on the classic wave equation that describes e.g. sound wave propagation. We explore this new model by discretizing the underlying partial differential equation. Thereby we consider two different time integration methods. By a detailed evaluation at hand of a standard shape data set we demonstrate that our approach may yield significant improvements over state of the art methods for finding correct shape correspondences.}, language = {en} }