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 -