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Benedikt Wirth

Courant Instructor

Address: Courant Institute of Mathematical Sciences
251 Mercer Street
New York, NY 10012, USA
Office:730 Warren Weaver Hall
Phone: +1 (212) 998 3240
eMail:

 

 

Interests

My main interest lies in the development and examination of physics-based models for applications ranging from medicine and biology up to imaging and computer vision. I am particularly intrigued by models involving nonlinear elasticity in combination with free discontinuities, which can for example be employed in classical image registration, shape space analysis, and shape or compliance optimization. Such models offer a broad scope for a rigorous mathematical analysis and at the same time allow numerical simulations for realistic problems. I am also more generally interested in the calculus of variations, phase field and total variation methods, as well as numerical schemes for geometric evolution problems and their numerical analysis.

 

Teaching

If you are interested in a student's or PhD project: There are many interesting topics in the area of image processing, shape analysis, variational methods, constrained opimization, materials science, numerical analysis, ...

 

Publications

[1] M. Rumpf and B. Wirth. Discrete geodesic calculus in the space of viscous fluidic objects. Accepted at SIAM Journal on Imaging Sciences, 2013. [.html]
[2] M. Elsey and B. Wirth. Fast automated detection of crystal distortion and crystal defects in polycrystal images. Accepted at SIAM Multiscale Modeling and Simulation, 2013. [.pdf]
[3] B. Berkels and T. Fletcher and B. Heeren and M. Rumpf and B. Wirth. Discrete geodesic regression in shape space. 9th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR'13), 2013. [.pdf]
[4] M. Elsey and B. Wirth. A simple and efficient scheme for phase field crystal simulation. ESAIM: M2AN, 47(5):1413-1432, 2013. [.pdf]
[5] M. Elsey and 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]
[6] K. Bredies and T. Pock and B. Wirth. Convex relaxation of a class of vertex penalizing functionals. Accepted at Journal of Mathematical Imaging and Vision, 2012. [.pdf]
[7] B. Wirth, I. Sobey, and A. Eisenträger. Conditions for choking in a poroelastic flow model. Accepted at The IMA Journal of Applied Mathematics, 2012. [preprint]
[8] B. Heeren and M. Rumpf and M. Wardetzky and 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]
[9] M. Franken and M. Rumpf and 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]
[10] W. Ring and B. Wirth. Optimization methods on Riemannian manifolds and their application to shape space. SIAM Journal on Optimization, 22(2):596-627, 2012. [.pdf]
[11] P. Penzler and M. Rumpf and B. Wirth. A phase-field model for compliance shape optimization in nonlinear elasticity. ESAIM: COCV, 18(1):229-258, 2012. [.pdf]
[12] I. Sobey and A. Eisenträger and B. Wirth and 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]
[13] B. Wirth and J. Gerhard and W. Marquardt. Stability-preserving optimization in presence of fast disturbances. IEEE Transactions on Automatic Control, 56(11):2683-2687, 2011. [.pdf]
[14] B. Wirth and J. Gerhard and W. Marquardt. Robust optimisation with normal vectors on critical manifolds of transient stability loss. Journal of Nonlinear Science, 21:57-92, 2011. [.pdf]
[15] M. Rumpf and B. Wirth. Variational methods in shape analysis. In Handbook of Mathematical Methods in Imaging, Springer, 1363-1401, 2011. [.pdf]
[16] B. Wirth and L. Bar and M. Rumpf and G. Sapiro. A continuum mechanical approach to geodesics in shape space. International Journal of Computer Vision, 93(3):293-318, 2011. [.pdf]
[17] M. Rumpf and B. Wirth. An elasticity-based covariance analysis of shapes. International Journal of Computer Vision, 92(3):281-295, 2011. [.pdf]
[18] I. Sobey, A. Eisenträger, B. Wirth, and 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]
[19] B. Wirth and L. Bar and M. Rumpf and 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]
[20] M. Rumpf and 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]
[21] M. Rumpf and B. Wirth. A nonlinear elastic shape averaging approach. SIAM Journal on Imaging Sciences, 2(3):800-833, 2009. [.pdf]
[22] B. Wirth and 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]
[23] B. Wirth and I. Sobey. A model for an inverse power constitutive law for cerebral compliance. Mathematical Medicine and Biology, 25:113-131, 2008. [.pdf]
[24] B. Wirth and 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]
[25] I. Sobey and B. Wirth. Effect of nonlinear permeability in a spherical model of hydrocephalus. Mathematical Medicine and Biology, 23:339-361, 2006. [.pdf]

Preprints

[1] K. Bredies and T. Pock and B. Wirth. A convex, lower semi-continuous approximation of Euler's elastica energy. [.pdf]
[2] M. Rumpf and B. Wirth. Variational time discretization of geodesic calculus. [.html]
[3] M. Rumpf and B. Wirth. On the Gamma-convergence of joint segmentation and registration problems. [.pdf]
[4] C. Matzke and B. Wirth. Product pricing when demand follows a rule of thumb. Bonn Econ Discussion Papers. [.pdf]
[5] C. Matzke and 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. [.pdf]

Theses

[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]