| 2024J.W. Jang E.Dematte and JJL Velázquez
Compactness and existence theory for a general class of stationary radiative transfer equations
2024
https://arxiv.org/abs/2401.12828
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| 2023Manuel Esser and Anna Kraut
Effective growth rates in a periodically changing environment: From mutation to invasion
2023
https://arxiv.org/abs/2310.20509
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| 2021Manuel Esser and Anna Kraut
A general multi-scale description of metastable adaptive motion across fitness valleys
2021
https://arxiv.org/abs/2112.12675
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| 2019Alexander Effland, Sebastian Neumayer and Martin Rumpf
Convergence of the Time Discrete Metamorphosis Model on Hadamard Manifolds
2019
https://arxiv.org/abs/1902.10930
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| Alexander Effland, Erich Kobler, Thomas Pock, Marko Rajković and Martin Rumpf
Image Morphing in Deep Feature Spaces: Theory and Applications
2019
https://arxiv.org/abs/1910.12672
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| Alexander Effland, Erich Kobler, Thomas Pock and Martin Rumpf
Time Discrete Geodesics in Deep Feature Spaces for Image Morphing
In Lellmann, Jan and Burger, Martin and Modersitzki, Jan, editor, Scale Space and Variational Methods in Computer Vision
page 171--182.
Publisher: Springer International Publishing
2019
https://dx.doi.org/10.1007/978-3-030-22368-7_14
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| Alexander Effland, Erich Kobler, Anne Brandenburg, Teresa Klatzer, Leonie Neuhäuser, Michael Hölzel, Jennifer Landsberg, Thomas Pock and Martin Rumpf
Joint reconstruction and classification of tumor cells and cell interactions in melanoma tissue sections with synthesized training data
International Journal of Computer Assisted Radiology and Surgery, 14(4): 587--599 2019
https://dx.doi.org/10.1007/s11548-019-01919-z
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| Matthias Erbar, Jan Maas and Melchior Wirth
On the geometry of geodesics in discrete optimal transport
Calc. Var. Partial Differential Equations, 58(1): Art. 19, 19 2019
10.1007/s00526-018-1456-1
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| Matthias Erbar and Karl-Theodor Sturm
Riggidity of cones with bounded curvature
to appear in JEMS, arxiv e-print 1712.08093 2019
https://arxiv.org/abs/1712.08093
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| 2018Alexander Effland, Martin Rumpf and Florian Schäfer
Image extrapolation for the time discrete metamorphosis model -- existence and applications
SIAM J. Imaging Sci. 2018
https://arxiv.org/abs/1705.04490
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| C. Eichenberg
Special Solutions to a Nonlinear Coarsening Model with Local Interactions
Journal of NonLinear Science 2018
10.1007/s00332-018-9519-1
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| Matthias Erbar and Nicolas Juillet
Smoothing and non-smoothing via a flow tangent to the Ricci flow
J. Math. Pures Appl. (9), 110: 123--154 2018
10.1016/j.matpur.2017.07.006
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| Matthias Erbar and Max Fathi
Poincaré, modified logarithmic Sobolev and isoperimetric inequalities for Markov chains with non-negative Ricci curvature
J. Funct. Anal., 274(11): 3056--3089 2018
10.1016/j.jfa.2018.03.011
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| Matthias Erbar and Eva Kopfer
Super Ricci flows for Markov chains
arxiv e-print 1805.06703 2018
https://arxiv.org/abs/1805.06703
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| Matthias Erbar, Martin Huesmann and Thomas Leblé
The one-dimensional log-gas free energy has a unique minimiser
arxiv e-print 1812.06929 2018
https://arxiv.org/abs/1812.06929
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| 2017Benjamin Berkels, Michael Buchner, Alexander Effland, Martin Rumpf and Steffen Schmitz-Valckenberg
GPU Based Image Geodesics for Optical Coherence Tomography
In Bildverarbeitung für die Medizin, Informatik aktuell
page 68--73.
Publisher: Springer
2017
http://dx.doi.org/10.1007/978-3-662-54345-0_21
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| Alexander Effland, Martin Rumpf and Florian Schäfer
Time discrete extrapolation in a Riemannian space of images
In Proc. of International Conference on Scale Space and Variational Methods in Computer Vision, Volume 10302
page 473--485.
Publisher: Springer, Cham
2017
https://dx.doi.org/10.1007/978-3-319-58771-4_38
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| Matthias Erbar, Martin Rumpf, Bernhard Schmitzer and Stefan Simon
Computation of Optimal Transport on Discrete Metric Measure Spaces
Unknown
https://arxiv.org/abs/1707.06859
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| Matthias Erbar
A gradient flow approach to the Boltzmann equation
arxiv e-print 1603.0540 2017
https://arxiv.org/abs/1603.0540
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| 2015Benjamin Berkels, Alexander Effland and Martin Rumpf
A Posteriori Error Control for the Binary Mumford-Shah Model
ArXiv Preprint 2015
http://arxiv.org/abs/1505.05284
Abstract: The binary Mumford-Shah model is a widespread tool for image segmentation and can be considered as a basic model in shape optimization with a broad range of applications in computer vision, ranging from basic segmentation and labeling to object reconstruction. This paper presents robust a posteriori error estimates for a natural error quantity, namely the area of the non properly segmented region. To this end, a suitable strictly convex and non-constrained relaxation of the originally non-convex functional is investigated and Repin's functional approach for a posteriori error estimation is used to control the numerical error for the relaxed problem in the $L^2$-norm. In combination with a suitable cut out argument, a fully practical estimate for the area mismatch is derived. This estimate is incorporated in an adaptive meshing strategy. Two different adaptive primal-dual finite element schemes, and the most frequently used finite difference discretization are investigated and compared. Numerical experiments show qualitative and quantitative properties of the estimates and demonstrate their usefulness in practical applications. |
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