Benedikt Wirth

1. B. Wirth. Convergence of spectral discretization for the flow of diffeomorphisms. 2024. [.pdf]
2. M. Mauritz, B. Wirth. Convergence of Poisson point processes and of optimal transport regularization with application in variational analysis of PET reconstruction. 2024. [.pdf]
3. J. Lohmann, B. Schmitzer, B. Wirth. Formulas for the h-mass on 1-currents with coefficients in R^m. 2024. [.pdf]
4. N. Marquardt, T. Hengsbach, M. Mauritz, B. Wirth, K. Schäfers. Motion simulation of radio-labeled cells in whole-body positron emission tomography. 2024. [.pdf]
5. G. Papanikos, B. Wirth. A non-convex variational model for joint polyenergetic CT reconstruction, sensor denoising and material decomposition. 2022. [.pdf]
6. D. Bourne, B. Schmitzer, B. Wirth. Semi-discrete unbalanced optimal transport and quantization. 2018. [.pdf]

1. M. Mauritz, B. Schmitzer, B. Wirth. A Bayesian model for dynamic mass reconstruction from PET listmode data. SIAM Journal on Mathematical Analysis 56(5):5840-5880, 2024. [.pdf]
2. M. Holler, B. Wirth. Exact reconstruction and reconstruction from noisy data with anisotropic total variation. SIAM Journal on Mathematical Analysis 56(3):2938-2967, 2024. [.pdf]
3. J. Braunsmann, M. Rajković, M. Rumpf, B. Wirth. Convergent Autoencoder Approximation of Low Bending and Low Distortion Manifold Embeddings. ESAIM: Mathematical Modelling and Numerical Analysis 58(1):335-361, 2024. [.pdf]
4. M. Holler, A. Schlüter, B. Wirth. Dimension reduction, exact recovery, and error estimates for sparse reconstruction in phase space. Applied and Computational Harmonic Analysis 70:101631, 2024. [.pdf]
5. B. Hahn, B. Wirth. Convex reconstruction of moving particles with inexact motion model. Proceedings of Applied Mathematics and Mechanics e202300054, 2023. [.html]
6. M. Guastini, M. Rajković, M. Rumpf, B. Wirth. The variational approach to the flow of Sobolev-diffeomorphisms model. International Conference on Scale Space Methods and Variational Methods in Computer Vision (SSVM 2023) 551-564, 2023. [.html]
7. J. Sassen, K. Hildebrandt, M. Rumpf, B. Wirth. Parametrizing product shape manifolds by composite networks. Accepted at International Conference on Learning Representations (ICLR), 2023. [.html]
8. J. Lohmann, B. Schmitzer, B. Wirth. Duality in branched transport and urban planning. Applied Mathematics and Optimization 86:45, 2022. [.pdf]
9. J. Lohmann, B. Schmitzer, B. Wirth. Formulation of branched transport as geometry optimization. Journal de Mathématiques Pures et Appliquées 163:739-779, 2022. [.pdf]
10. J. Potthoff, B. Wirth. Optimal fine-scale structures in compliance minimization for a uniaxial load in three space dimensions. ESAIM: Control, Optimisation and Calculus of Variations 28:27, 2022. [.pdf]
11. A. Effland, B. Heeren, M. Rumpf, B. Wirth. Consistent Curvature Approximation on Riemannian Shape Spaces. IMA Journal of Numerical Analysis 42(1):78-106, 2022. [.pdf]
12. C. Dirks, B. 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. Radon Series on Computational and Applied Mathematics, De Gruyter, pp. 189-236, 2022. [.pdf]
13. P. Striewski, B. Wirth. Elastic 3D-2D Image Registration. Journal of Mathematical Imaging and Vision 64:443-462, 2022. [.pdf]
14. H. Hardering, B. Wirth. Quartic Lp-convergence of cubic Riemannian splines. IMA Journal of Numerical Analysis 42(4):3360-3385, 2022. [.pdf]
15. C. Clason, C. Tameling, B. Wirth. Convex relaxation of discrete vector-valued optimization problems. SIAM Review 63(4):783--821, 2021. [.pdf]
16. J. Braunsmann, M. Rajković, M. Rumpf, B. Wirth. Learning low bending and low distortion manifold embeddings. Proceedings of the 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW) 4411-4419, 2021. [.pdf]
17. C. Dirks, P. Striewski, B. Wirth, A. Aalto, A. Olguin-Olguin. A mathematical model for cell polarization in zebrafish primordial germ cells. IMA Mathematical Medicine and Biology 38(2):218-254, 2021. [.pdf]
18. C. Clason, D. Lorenz, H. Mahler, B. Wirth. Entropic regularization of continuous optimal transport problems. Journal of Mathematical Analysis and Applications 494(1):124432, 2021. [.pdf]
19. B. Wirth. Green's function for the Neumann-Poisson problem on n-dimensional balls. American Mathematical Monthly 127(8):737-743, 2020. [.pdf]
20. L. Ferrari, C. Dirks, B. Wirth. Phase field approximations of branched transportation problems. Calculus of Variations and Partial Differential Equations 59:37, 2020. [.pdf]
21. B. Schmitzer, K.P. Schäfers, B. Wirth. Dynamic Cell Imaging in PET with Optimal Transport Regularization. IEEE Transactions on Medical Imaging 39(5):1626-1635, 2020. [.pdf]
22. U. Böttcher, B. Wirth. Convex lifting-type methods for curvature regularization. Handbook of variational methods for nonlinear geometric data, editors: P. Grohs, M. Holler, A. Weinmann, Springer, pp. 207-233, 2019.
23. B. Heeren, M. Rumpf, M. Wardetzky, B. Wirth. Discrete Riemannian calculus on shell space. Handbook of Numerical Analysis 21: Geometric Partial Differential Equations - Part I, editors: A. Bonito, R. Nochetto, Elsevier, pp. 621-679, 2019.
24. A. Marchese, B. Wirth. Approximation of rectifiable 1-currents and weak-* relaxation of the h-mass. Journal of Mathematical Analysis and Applications 479(2):2268-2283, 2019. [.pdf]
25. P. Dondl, M. Novaga, B. Wirth, S. Wojtowytsch. Approximation of the relaxed perimeter functional under a connectedness constraint by phase-fields. SIAM Journal on Mathematical Analysis 51(5):3902-3920, 2019. [.pdf]
26. B. Wirth. Phase field models for two-dimensional branched transportation problems. Calculus of Variations and Partial Differential Equations 58(5):164, 2019. [.pdf]
27. B. Schmitzer, B. Wirth. Dynamic Models of Wasserstein-1-Type Unbalanced Transport. ESAIM: Control, Optimisation and Calculus of Variations 25:23, 2019. [.pdf]
28. B. Schmitzer, B. Wirth. A Framework for Wasserstein-1-Type Metrics. Journal of Convex Analysis, 26(2):353-396, 2019. [.pdf]
29. B. Heeren, M. Rumpf, B. Wirth. Variational time discretization of Riemannian splines. IMA Journal of Numerical Analysis, 39(1):61-104, 2019. [.pdf]
30. A. Brancolini, B. Wirth. General transport problems with branched minimizers as functionals of 1-currents with prescribed boundary. Calculus of Variations and PDEs, 57(3):82, 2018. [.pdf]
31. C. Clason, C. Tameling, B. Wirth. Vector-valued multibang control of differential equations. SIAM Journal on Control and Optimization, 56(3):2295-2326, 2018. [.pdf]
32. A. Brancolini, C. Rossmanith, B. Wirth. Optimal micropatterns in 2D transport networks and their relation to image inpainting. Archive for Rational Mechanics and Analysis, 228(1):279-308, 2018. [.pdf]
33. C. Bauer, C. Clason, D. Lorenz, B. Wirth. A Sinkhorn-Newton method for entropic optimal transport. Neural Information Processing Systems Conference, 2017. [.pdf]
34. B. Berkels, B. Wirth. Joint denoising and distortion correction of atomic scale scanning transmission electron microscopy images. Inverse Problems, 33(9):095002, 2017. [.pdf]
35. A. Brancolini, B. Wirth. Optimal energy scaling for micropatterns in transport networks. SIAM Journal on Mathematical Analysis, 49(1):311-359, 2016. [.pdf]
36. B. Wirth. On the Γ-limit of joint image segmentation and registration functionals based on phase fields. EMS Interfaces and Free Boundaries, 18(4):441-477, 2016. [.pdf]
37. P.-A. Absil, P.-Y. Gousenbourger, P. Striewski, B. Wirth. Differentiable piecewise-Bezier surfaces on Riemannian manifolds. SIAM Journal on Imaging Sciences, 9(4):1788-1828, 2016. [.html]
38. A. Brancolini, B. Wirth. Equivalent formulations for the branched transport and urban planning problems. Journal de Mathématiques Pures et Appliquées, 106(4):695-724, 2016. [.pdf]
39. P.-A. Absil, P.-Y. Gousenbourger, P. Striewski, B. Wirth. Differentiable piecewise-Bezier interpolation on Riemannian manifolds. Proceedings of the European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN) 2016, 95-100, 2016. [.html]
40. J. Lu, B. Wirth, H. Yang. Combining 2D synchrosqueezed wave packet transform with optimization for crystal image analysis. Journal of the Mechanics and Physics of Solids, 89:194-210, 2016. [.pdf]
41. B. Heeren, M. Rumpf, P. Schröder, M. Wardetzky, B. Wirth. Splines in the space of shells. Computer Graphics Forum, 35(5):111-120, 2016. [.pdf]
42. R. V. Kohn, B. Wirth. Optimal fine-scale structures in compliance minimization for a shear load. Communications in Pure and Applied Mathematics, 69:1572-1610, 2016. [.pdf]
43. A. Effland, M. Rumpf, S. Simon, K. Stahn, B. Wirth. Bezier curves in the space of images. Proceedings of the Fifth International Conference on Scale Space Methods and Variational Methods in Computer Vision (SSVM 2015), Lecture Notes in Computer Science, 9087:372-384, 2015. [.pdf]
44. K. Bredies, T. Pock, B. Wirth. A convex, lower semi-continuous approximation of Euler's elastica energy. SIAM Journal on Mathematical Analysis, 47(1):566-613, 2015. [.pdf]
45. M. Rumpf, B. Wirth. Variational time discretization of geodesic calculus. IMA Journal of Numerical Analysis, 35(3):1011-1046, 2015. [.html]
46. M. Elsey, B. Wirth. Redistancing dynamics for vector-valued multilabel segmentation with costly fidelity: grain identification in polycrystal images. Journal of Scientific Computing, 63(1):279-306, 2015. [.pdf]
47. R. V. Kohn and B. Wirth. Optimal fine-scale structures in compliance minimization for a uniaxial load. Proceedings of the Royal Society A, 470(2170):20140432-20140448, 2014. [.pdf]
48. B. Heeren, M. Rumpf, P. Schröder, M. Wardetzky, B. Wirth. Exploring the geometry of the space of shells. Computer Graphics Forum, 33(5):247-256, 2014. [.pdf]
49. M. Elsey, B. Wirth. Fast automated detection of crystal distortion and crystal defects in polycrystal images. SIAM Multiscale Modeling and Simulation, 12(1):1-24, 2014. [.pdf]
50. B. Wirth, I. Sobey, A. Eisenträger. Conditions for choking in a poroelastic flow model. IMA Journal of Applied Mathematics, 79(2):254-273, 2014. [preprint]
51. M. Rumpf, B. Wirth. Discrete geodesic calculus in the space of viscous fluidic objects. SIAM Journal on Imaging Sciences, 6(4):2581-2602, 2013. [.html]
52. B. Berkels, T. Fletcher, B. Heeren, M. Rumpf, B. Wirth. Discrete geodesic regression in shape space. 9th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR'13), Lecture Notes in Computer Science, 8081:108-123, 2013. [.pdf]
53. M. Elsey, B. Wirth. A simple and efficient scheme for phase field crystal simulation. ESAIM: M2AN, 47(5):1413-1432, 2013. [.pdf]
54. M. Elsey, B. Wirth. Segmentation of Crystal Defects via Local Analysis of Crystal Distortion. Proceedings of the 8'th International Conference on Computer Vision Theory and Applications (VISAPP'13), 2013. [.pdf]
55. K. Bredies, T. Pock, B. Wirth. Convex relaxation of a class of vertex penalizing functionals. Journal of Mathematical Imaging and Vision, 47(3):278-302, 2013. [.pdf]
56. M. Franken, M. Rumpf, B. Wirth. A phase field based pde constrained optimization approach to time discrete Willmore flow. International Journal of Numerical Analysis and Modelling, 10(1):116-138, 2013. [.pdf]
57. B. Heeren, M. Rumpf, M. Wardetzky, B. Wirth. Time-Discrete Geodesics in the Space of Shells. Proceedings of Eurographics Symposium on Geometry Processing; Computer Graphics Forum, 31(5):1755-1764, 2012. [.pdf]
58. W. Ring, B. Wirth. Optimization methods on Riemannian manifolds and their application to shape space. SIAM Journal on Optimization, 22(2):596-627, 2012. [.pdf]
59. P. Penzler, M. Rumpf, B. Wirth. A phase-field model for compliance shape optimization in nonlinear elasticity. ESAIM: COCV, 18(1):229-258, 2012. [.pdf]
60. I. Sobey, A. Eisenträger, B. Wirth, M. Czosnyka. Simulation of cerebral infusion tests using a poroelastic model. International Journal of Numerical Analysis and Modeling Series B, 3(1):52-64, 2012. [.html]
61. B. Wirth, J. Gerhard, W. Marquardt. Stability-preserving optimization in presence of fast disturbances. IEEE Transactions on Automatic Control, 56(11):2683-2687, 2011. [.pdf]
62. B. Wirth, J. Gerhard, W. Marquardt. Robust optimisation with normal vectors on critical manifolds of transient stability loss. Journal of Nonlinear Science, 21:57-92, 2011. [.pdf]
63. M. Rumpf, B. Wirth. Variational methods in shape analysis. In Handbook of Mathematical Methods in Imaging, Springer, 1363-1401, 2011. [.pdf]
64. B. Wirth, L. Bar, M. Rumpf, G. Sapiro. A continuum mechanical approach to geodesics in shape space. International Journal of Computer Vision, 93(3):293-318, 2011. [.pdf]
65. M. Rumpf, B. Wirth. An elasticity-based covariance analysis of shapes. International Journal of Computer Vision, 92(3):281-295, 2011. [.pdf]
66. I. Sobey, A. Eisenträger, B. Wirth, M. Czosnyka. Multi-fluid poro-elastic modelling of the CSF infusion test. In C.T. Lim and J.C.H. Goh, editors, 6th World Congress of Biomechanics (WCB 2010), IFMBE Proceedings, Springer, 31:362-365, 2010. [http]
67. B. Wirth, L. Bar, M. Rumpf, G. Sapiro. Geodesics in shape space via variational time discretization. Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR'09), Lecture Notes in Computer Science, 5681:288-302, 2009. [.pdf]
68. M. Rumpf, B. Wirth. An elasticity approach to principal modes of shape variation. Proceedings of the Second International Conference on Scale Space Methods and Variational Methods in Computer Vision (SSVM 2009), Lecture Notes in Computer Science, 5567:709-720, 2009. [.pdf]
69. M. Rumpf, B. Wirth. A nonlinear elastic shape averaging approach. SIAM Journal on Imaging Sciences, 2(3):800-833, 2009. [.pdf]
70. B. Wirth, I. Sobey. Analytic solution of the linear unsteady poroelastic equations in a spherically symmetric brain during an infusion test. Mathematical Medicine and Biology, 26:25-61, 2009. [.pdf]
71. B. Wirth, I. Sobey. A model for an inverse power constitutive law for cerebral compliance. Mathematical Medicine and Biology, 25:113-131, 2008. [.pdf]
72. B. Wirth, I. Sobey. An axisymmetric and fully 3D poroelastic model for the onset and treatment of hydrocephalus. Mathematical Medicine and Biology, 23:363-388, 2006. [.pdf]
73. I. Sobey, B. Wirth. Effect of nonlinear permeability in a spherical model of hydrocephalus. Mathematical Medicine and Biology, 23:339-361, 2006. [.pdf]

1. M. Kunisch, S. Beutler, C. Pilger, F. Kiefer, T. Huser, B. Wirth. Active Axial Motion Compensation in Multiphoton-Excited Fluorescence Microscopy. Accepted at Optics Express, 2024. [.pdf]
2. B. Heeren, S. Paulus, H. Goldbach, H. Kuhlmann, A.-K. Mahlein, M. Rumpf, B. Wirth. Statistical shape analysis of tap roots: a methodological case study on laser scanned sugar beets. BMC Bioinformatics 21(1):335, 2020.[.pdf]
3. M. Taha, M. Aldirawi, S. März, J. Seebach, M. Odenthal-Schnittler, O. Bondareva, V. Bojovic, T. Schmandra, B. Wirth, M. Mietkowska, K. Rottner, H. Schnittler. EPLIN-α and -β isoforms modulate endothelial cell dynamics through a spatio-temporally differentiated interaction with actin. Cell Reports, 29(4):P1010-1026.E6, 2019.
4. C. Zhang, B. Berkels, B. Wirth, P.M. Voyles. Joint Denoising and Distortion Correction for Atomic Column Detection in Scanning Transmission Electron Microscopy Images. Microscopy and Microanalysis, 23(S1):164-165, 2017.
5. J. Song, K. Buscher, Y. Wang, H. Wang, L. Li, J. Di Russo, X. Zhang, S. Lütke-Enking, A. Zarbock, P. Striewski, B. Wirth, I. Kuzmanov, H. Wiendl, L. Sorokin. Endothelial Basement Membrane Laminin 511 Contributes to Endothelial Junctional Tightness and thereby Inhibits Leukocyte Transmigration. Cell Reports, 18(5):1256-1269, 2017.
6. K. Buscher, H. Wang, X. Zhang, P. Striewski, B. Wirth, G. Saggu, S. Lütke-Enking, T. N. Mayadas, K. Ley, L. Sorokin, J. Song. Protection from septic peritonitis by rapid neutrophil recruitment through omental high endothelial venules. Nature Communications, 7:10828, 2016.
7. B. Wirth, M. Warnecke, B. Schmenk, G. Seide, T. Gries. Filament breaches during air-gap spinning (Filamentbrucharten beim Air-Gap-Spinnverfahren). Chemical Fibers International, 61:38-39, 2011 (Melliand Textilberichte, 91:226, 2010).

1. B. Wirth. Patterns emerging in the optimization of elastic structures. Springer INdAM series, Geometric Measure Theory and applications 2024. [.pdf]
2. B. Wirth. Optimal transport bounds on pattern-forming energies with divergence constraint. Oberwolfach Reports, 2406, 2024. [.pdf]
3. B. Wirth. Exact reconstruction and reconstruction from noisy data: Going beyond point sources? Oberwolfach Reports, 2318:1116-1119, 2023. [.pdf]
4. B. Wirth. Discrete geodesic calculus in the manifold of Sobolev curves. Oberwolfach Reports, 2234:65-67, 2022. [.pdf]
5. B. Wirth. Dimension reduction for measures in position velocity space. Oberwolfach Reports, 2108:564-567, 2021. [.pdf]
6. B. Wirth. Thin plate spline type fitting to Riemannian data. Oberwolfach Reports, 2047c:6-9, 2020. [.pdf]
7. B. Wirth. The inverse problem of finding a phase field energy for 2D branched transport and other functionals of normal currents. Oberwolfach Reports, 1831:35-38, 2018. [.pdf]
8. B. Wirth. The existence problem of cubic spline interpolation on Riemannian manifolds. Oberwolfach Reports, 1817:35-38, 2018. [.pdf]
9. B. Wirth. Unbalanced optimial transport and quantization. Oberwolfach Reports, 1809:35-37, 2018. [.pdf]
10. B. Wirth. Models for transport networks and their relation to inpainting. Oberwolfach Reports, 1704:329-331, 2017. [.pdf]
11. B. Wirth. Data fitting tools in Riemannian spaces. Dagstuhl Reports, 7(1):17021.16, 2017. [.pdf]
12. B. Wirth. How to discretize elastic curves in infinite-dimensional shape spaces? Oberwolfach Reports, 1604:197-199, 2016. [.pdf]
13. B. Wirth. Optimal fine-scale structure in elastic shape optimization. Oberwolfach Reports, 1313:941-943, 2013. [.pdf]
14. B. Wirth. On the sharp interface limit of joint Ambrosio-Tortorelli segmentation and phase-field matching. Oberwolfach Reports, 1105:45-48, 2011. [.pdf]
15. C. Matzke, B. Wirth. Product pricing when demand follows a rule of thumb. Bonn Econ Discussion Papers, 2009. [.pdf]
16. C. Matzke, B. Wirth. A non-standard approach to a market with boundedly rational consumers and strategic firms. Part I: A microfoundation for the evolution of sales. Bonn Econ Discussion Papers, 2008. [.pdf]

1. B. Wirth. Variational methods in shape space. Dissertation, Bonn University, 2009. [http]
2. B. Wirth. Robust optimisation with normal vectors on critical manifolds of transient stability loss. Diploma thesis, RWTH Aachen, 2007.
3. B. Wirth. A mathematical model for hydrocephalus. Master's thesis, University of Oxford, 2005. [.pdf]

1. B. Wirth. Statement zu Perspektiven für junge Wissenschaftlerinnen und Wissenschaftler. Forschung und Lehre 15(5):357, 2015. [http]
2. C. Böhm, B. Wirth. Mathematik Münster: Dynamik, Geometrie, Struktur. Beispiele einer geometrischen Sichtweise. Mitteilungen der Deutschen Mathematiker-Vereinigung 26(4):197-200, 2018. [http]