Projects

Research area C: Models and Approximations
Unit C1: Evolution and asymptotics
Unit C2: Multi-scale phenomena and macroscopic structures
Unit C3: Interacting particle systems and phase transitions
Unit C4: Geometry-based modelling, approximation, and reduction

Further Projects
CRC 1450 A05 - Targeting immune cell dynamics by longitudinal whole-body imaging and mathematical modelling online
CRC 1450 A06 - Improving intravital microscopy of inflammatory cell response by active motion compensation using controlled adaptive optics online
SPP 2256: Variational Methods for Predicting Complex Phenomena in Engineering Structures and Materials - Subproject: Multiscale structure in compliance minimization online
Mathematische Rekonstruktion und Modellierung der CAR T-Zell Verteilung in vivo in einem Tumormodell online

Research Interests

Research Interests

$\bullet$ Mathematical image processing.
$\bullet$ Inverse problems.
$\bullet$ Topology and shape optimisation.
$\bullet$ Approximation and optimisation methods in nonlinear spaces.
$\bullet$ Calculus of variations.

Selected Publications

Selected Publications of Benedikt Wirth

$\bullet$ B. Heeren, M. Rumpf, and B. Wirth. Variational time discretization of Riemannian splines. IMA J. Numer. Anal. (in press), drx077, 2018. doi.org/10.1093/imanum/drx077

$\bullet$ A. Brancolini, C. Rossmanith, and B. Wirth. Optimal micropatterns in 2D transport networks and their relation to image inpainting. Arch. for Ration. Mech. Anal., 228(1):279–308, 2018.

$\bullet$ R. V. Kohn and B. Wirth. Optimal fine-scale structures in compliance minimization for a shear load. Comm. Pure Appl. Math., 69(8):1572–1610, 2016.

$\bullet$ P.-A. Absil, P.-Y. Gousenbourger, P. Striewski, and B. Wirth. Differentiable piecewise- Bézier surfaces on Riemannian manifolds. SIAM J. Imaging Sci., 9(4):1788–1828, 2016.

$\bullet$ M. Elsey and B. Wirth. Redistancing dynamics for vector-valued multilabel segmentation with costly fidelity: grain identification in polycrystal images. J. Sci. Comput., 63(1):279–306, 2015.

$\bullet$ K. Bredies, T. Pock, and B. Wirth. A convex, lower semicontinuous approximation of Euler's elastica energy. SIAM J. Math. Anal., 47(1):566–613, 2015.

$\bullet$ R. V. Kohn and B. Wirth. Optimal fine-scale structures in compliance minimization for a uniaxial load. Proc. R. Soc. A, 470(2170), 2014.

$\bullet$ W. Ring and B. Wirth. Optimization methods on Riemannian manifolds and their application to shape space. SIAM J. Optim., 22(2):596–627, 2012.

$\bullet$ P. Penzler, M. Rumpf, and B. Wirth. A phase-field model for compliance shape optimization in nonlinear elasticity. ESAIM Control Optim. Calc. Var., 18(1):229–258, 2012.

$\bullet$ B. Wirth, J. Gerhard, and W. Marquardt. Robust optimisation with normal vectors on critical manifolds of disturbance-induced stability loss. J. Nonlinear Sci., 21(1):57–92, 2011.

Current Publications

Current Publications

$\bullet $ Juliane Braunsmann, Marko Rajković, Martin Rumpf, and Benedikt Wirth. Learning low bending and low distortion manifold embeddings: Theory and applications. arXiv e-prints, August 2022. arXiv:2208.10193.

$\bullet $ Julius Lohmann, Bernhard Schmitzer, and Benedikt Wirth. Formulation of branched transport as geometry optimization. J. Math. Pures Appl., 163:739–779, July 2022. doi:10.1016/j.matpur.2022.05.021.

$\bullet $ Martin Holler and Benedikt Wirth. Exact reconstruction and reconstruction from noisy data with anisotropic total variation. arXiv e-prints, July 2022. arXiv:2207.04757.

$\bullet $ Paul Striewski and Benedikt Wirth. Elastic 3D2D image registration. J. Math. Imaging Vis., 64(5):443–462, June 2022.

$\bullet $ Georgios Papanikos and Benedikt Wirth. A non-convex variational model for joint polyenergetic CT reconstruction, sensor denoising and material decomposition. arXiv e-prints, June 2022. arXiv:2206.02908.

$\bullet $ Jonas Potthoff and Benedikt Wirth. Optimal fine-scale structures in compliance minimization for a uniaxial load in three space dimensions. ESAIM: Control Optim. Calc. Var., 28:27, May 2022. doi:10.1051/cocv/2022023.

$\bullet $ Julius Lohmann, Bernhard Schmitzer, and Benedikt Wirth. Duality in branched transport and urban planning. arXiv e-prints, May 2022. arXiv:2205.12049.

$\bullet $ Carolin Dirks and Benedikt Wirth. An adaptive finite element approach for lifted branched transport problems. In Optimization and control for partial differential equations—uncertainty quantification, open and closed-loop control, and shape optimization, volume 29 of Radon Ser. Comput. Appl. Math., pages 189–236. March 2022. doi:10.1515/9783110695984-009.

$\bullet $ Alexander Effland, Behrend Heeren, Martin Rumpf, and Benedikt Wirth. Consistent curvature approximation on Riemannian shape spaces. IMA J. Numer. Anal., 42(1):78–106, January 2022. doi:10.1093/imanum/draa092.

$\bullet $ Martin Holler, Alexander Schlüter, and Benedikt Wirth. Dimension reduction, exact recovery, and error estimates for sparse reconstruction in phase space. arXiv e-prints, December 2021. arXiv:2112.09743.

$\bullet $ Jonas Potthoff and Benedikt Wirth. Optimal fine-scale structures in compliance minimization for a uniaxial load in three space dimensions. arXiv e-prints, November 2021. arXiv:2111.06910.

$\bullet $ Julius Lohmann, Bernhard Schmitzer, and Benedikt Wirth. Formulation of branched transport as geometry optimization. arXiv e-prints, September 2021. arXiv:2109.07820.

$\bullet $ Christian Clason, Carla Tameling, and Benedikt Wirth. Convex relaxation of discrete vector-valued optimization problems. arXiv e-prints, August 2021. arXiv:2108.10077.

$\bullet $ Juliane Braunsmann, Marko Rajković, Martin Rumpf, and Benedikt Wirth. Learning low bending and low distortion manifold embeddings. In 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), 4411–4419. June 2021. doi:10.1109/CVPRW53098.2021.00498.

$\bullet $ Juliane Braunsmann, Marko Rajkovic, Martin Rumpf, and Benedikt Wirth. Learning low bending and low distortion manifold embeddings. arXiv e-prints, April 2021. arXiv:2104.13189.

$\bullet $ Carolin Dirks, Paul Striewski, Benedikt Wirth, Anne Aalto, and Adan Olguin-Olguin. A mathematical model for bleb regulation in zebrafish primordial germ cells. Mathematical Medicine and Biology: A Journal of the IMA, February 2021. doi:10.1093/imammb/dqab002.

$\bullet $ Christian Clason, Dirk A. Lorenz, Hinrich Mahler, and Benedikt Wirth. Entropic regularization of continuous optimal transport problems. Journal of Mathematical Analysis and Applications, 494(1):124432, 22, February 2021. doi:10.1016/j.jmaa.2020.124432.

$\bullet $ Paul Striewski and Benedikt Wirth. Elastic 3d-2d image registration. arXiv e-prints, January 2021. arXiv:2101.03393.

$\bullet $ Christian Clason, Carla Tameling, and Benedikt Wirth. Convex relaxation of discrete vector-valued optimization problems. SIAM Review, 63(4):783–821, January 2021. doi:10.1137/21M1426237.

$\bullet $ Hanne Hardering and Benedikt Wirth. Quartic $L^p$-convergence of cubic Riemannian splines. arXiv e-prints, December 2020. arXiv:2012.08289.

$\bullet $ Benedikt Wirth. Green’s function for the Neumann–Poisson problem on $n$-dimensional balls. Am. Math. Mon., 127(8):737–743, September 2020. doi:10.1080/00029890.2020.1790910.

$\bullet $ Behrend Heeren, Stefan Paulus, Heiner Goldbach, Heiner Kuhlmann, Anne-Katrin Mahlein, Martin Rumpf, and Benedikt Wirth. Statistical shape analysis of tap roots: a methodological case study on laser scanned sugar beets. BMC Bioinformatics, 21(1):335, July 2020. doi:10.1186/s12859-020-03654-8.

$\bullet $ Bernhard Schmitzer, Klaus P. Schäfers, and Benedikt Wirth. Dynamic cell imaging in PET with optimal transport regularization. IEEE Transactions on Medical Imaging, 39(5):1626–1635, May 2020. doi:10.1109/TMI.2019.2953773.

$\bullet $ Ulrich Böttcher and Benedikt Wirth. Convex lifting-type methods for curvature regularization. In Philipp Grohs, Martin Holler, and Andreas Weinmann, editors, Handbook of Variational Methods for Nonlinear Geometric Data, chapter 7, pages 207–233. April 2020. doi:10.1007/978-3-030-31351-7_7.

$\bullet $ Carolin Dirks and Benedikt Wirth. An adaptive finite element approach for lifted branched transport problems. arXiv e-prints, March 2020. arXiv:2003.13797.

$\bullet $ Luca Ferrari, Carolin Dirks, and Benedikt Wirth. Phase field approximations of branched transportation problems. Calc. Var. Partial Differential Equations, 59(1):Paper No. 37, 34, January 2020. doi:10.1007/s00526-019-1680-3.

$\bullet $ Behrend Heeren, Martin Rumpf, Max Wardetzky, and Benedikt Wirth. Discrete Riemannian calculus on shell space. In Andrea Bonito and Ricardo Nochetto, editors, Geometric partial differential equations, volume 21 of Handbook of Numerical Analysis, pages 621–679. January 2020. doi:10.1016/bs.hna.2019.06.005.

$\bullet $ Alexander Effland, Behrend Heeren, Martin Rumpf, and Benedikt Wirth. Consistent curvature approximation on Riemannian shape spaces. arXiv e-prints, December 2019. arXiv:1912.07336.

$\bullet $ Andrea Marchese and Benedikt Wirth. Approximation of rectifiable 1-currents and weak- relaxation of the $h$-mass. Journal of Mathematical Analysis and Applications, 479(2):2268–2283, November 2019. doi:10.1016/j.jmaa.2019.07.059.

$\bullet $ Muna Taha, Mohammed Aldirawi, Sigrid März, Jochen Seebach, Maria Odenthal-Schnittler, Olga Bondareva, Vesna Bojovic, Thomas Schmandra, Benedikt Wirth, Magdalena Mietkowska, Klemens Rottner, and Hans Schnittler. EPLIN-α and -β isoforms modulate endothelial cell dynamics through a spatiotemporally differentiated interaction with actin. Cell Reports, 29(4):1010–1026.e6, October 2019. doi:10.1016/j.celrep.2019.09.043.

$\bullet $ Benedikt Wirth. Phase field models for two-dimensional branched transportation problems. Calculus of Variations and Partial Differential Equations, 58(5):164, September 2019. doi:10.1007/s00526-019-1615-z.

$\bullet $ Bernhard Schmitzer and Benedikt Wirth. Dynamic models of Wasserstein-1-type unbalanced transport. ESAIM, 25(23):54, July 2019. doi:10.1051/cocv/2018017.

$\bullet $ Patrick W. Dondl, Matteo Novaga, Benedikt Wirth, and Stephan Wojtowytsch. A phase-field approximation of the perimeter under a connectedness constraint. SIAM J. Math. Anal., 51(5):3902–3920, January 2019.

$\bullet $ Bernhard Schmitzer and Benedikt Wirth. A framework for Wasserstein-1-type metrics. Journal of Convex Analysis, 26(2):353–396, January 2019.

$\bullet $ Patrick W. Dondl, Matteo Novaga, Benedikt Wirth, and Stephan Wojtowytsch. A phase-field approximation of the perimeter under a connectedness constraint. SIAM J. Math. Anal., 51(5):3902–3920, January 2019. doi:10.1137/18M1225197.

$\bullet $ Behrend Heeren, Martin Rumpf, and Benedikt Wirth. Variational time discretization of Riemannian splines. IMA J. Numer. Anal., 39(1):61–104, January 2019. doi:10.1093/imanum/drx077.

$\bullet $ David P. Bourne, Bernhard Schmitzer, and Benedikt Wirth. Semi-discrete unbalanced optimal transport and quantization. arXiv e-prints, August 2018. arXiv:1808.01962.