

1992  Dr. rer. nat., University of Bonn  1993  1996  Postdoc, University of Freiburg  1996  2001  Professor (C3), University of Bonn  2001  2004  Professor (C4), University of DuisburgEssen  Since 2004  Professor (C4/W3), University of Bonn 


Variational problems and evolution problems arising in computer vision, in geometry processing, and in materials science are the major driving force of my research.
In computer vision I'm interested in the infinite dimensional geometry of shape spaces equipped with a Riemannian metric which is motivated by physical models of viscous dissipation. A central theme is a general variational time discrete Riemannian calculus on different shape spaces, including discrete geodesics, exponential map and parallel transport. Applications are warping of images or shell surfaces, shape extrapolation, and pattern or texture transfer. A comprehensive convergence theory based on convergence, finite element and ODE estimates on Hilbert spaces could be developed. I'm also interested in the close links to the theory of optimal transport.
A major goal is to treat textured images and explore inherent multiple scales in image maps. To this end images are considered as pointwise maps into some patch manifold, describing local, high dimensional texture and structure. Furthermore, spline curves and other low dimensional, smooth submanifolds will be particular interest in time dependent data analysis and in geometry animation.
With respect to materials science, I'm particularly interested in twoscale elastic shape optimization and the formation of optimal branching and folding patterns in elastic materials. The minimization of compliance type cost functionals leads to microstructured shapes and branching patterns arising naturally at material interfaces or at boundary incompatibilities.
My focus is on robust a posteriori error control using functional error estimates for BV functionals, duality techniques and relaxation. The aim is an efficient simulation and optimization of the microscopic patterns, and a better understanding of branchingtype patterns observed in natural elastic structures, as for example bones and thin sheets. The vision is to carry over the twoscale analysis of elastic bulk material to thin elastic plates and shells.


DFG Cluster of Excellence “Hausdorff Center for Mathematics”
Deputy coordinator, 2006 – 2012
Board of Directors of the Hausdorff Center for Mathematics
Member, since 2006
DFGProject “Discrete Riemannian calculus on shape space”
jointly with KarlTheodor Sturm, in the Collaborative Research Center SFB 1060 “The Mathematics of Emergent Effects”, 2012  2020
DFGProject “Numerical optimization of shape microstructures”
jointly with Sergio Conti, in the Collaborative Research Center SFB 1060 “The Mathematics of Emergent Effects”, 2012  2020
DFGProject “Geodesic Paths in Shape Space”
in the research network of the FWF S117 “Geometry + Simulation”, 2012  2020
DFG Collaborative Research Center SFB 1060 “The Mathematics of Emergent Effects”
Deputy coordinator, since 2014
GIFProject “A Functional Map Approach to Shape Spaces”
by the GermanIsraeli Foundation for Scientific Research and Development, jointly with Miri BenChen, 2017  2020
Oberwolfach Workshops on “Image and Surface Processing”
Organizer, 2005, 2007, 2011, 2016


Research Area A The proper discretization of geometric variational problems and geometric partial differential equations is a particular research focus in my group. In many applications in materials science, biology and geometric modeling evolution problems do not reside on a flat Euclidean domain but on curved surfaces. I am interested in geometrically consistent discretization concepts which lead to robust and efficient numerical algorithms [1].
Furthermore, we study higher order geometric functionals as they appear in shell models with bending energies. Instead of a discretization of the associated higher order differential operator, we propose a nested variational approach, where in an inner minimization problem curvature quantities in the integrand of the functional are themselves approximated by the solution of another associated geometric variational problem.  Research Area B One of my major research interests is the simulation and optimisation of material microstructures.
Here, a particular focus is on the elastic behavior of trabecular bone microstructures with strong characteristic variations between different species and different health status. Elasticity also plays an important role in polycrystalline or composite shape memory material [2].
Numerically, we combine composite finite element [3] and boundary element methods with parametric, level set, or phase field models. Observing certain geometric microstructures, the question naturally arises if these structures are optimal under certain usually stochastic loading conditions [4,5].
Furthermore, a leading motive of my research is the application of concepts from rational mechanics in imaging and vision. We use models from nonlinear elasticity to define shape averages and a principle component analysis of shapes [6].
Furthermore, we link the geometry of shape space to concepts of viscous flow [7]. 


[ 1] Martin Lenz, Simplice Firmin Nemadjieu, Martin Rumpf
A convergent finite volume scheme for diffusion on evolving surfaces SIAM J. Numer. Anal. , 49: (1): 1537 2011 DOI: 10.1137/090776767[ 2] S. Conti, M. Lenz, M. Rumpf
Modeling and simulation of magneticshapememory polymer composites J. Mech. Phys. Solids , 55: (7): 14621486 2007 DOI: 10.1016/j.jmps.2006.12.008[ 3] Tobias Preusser, Martin Rumpf, Stefan Sauter, Lars Ole Schwen
3D composite finite elements for elliptic boundary value problems with discontinuous coefficients SIAM J. Sci. Comput. , 33: (5): 21152143 2011 DOI: 10.1137/100791750[ 5] Patrick Penzler, Martin Rumpf, Benedikt Wirth
A phasefield model for compliance shape optimization in nonlinear elasticity ESAIM Control Optim. Calc. Var. , 18: (1): 229258 2012 DOI: 10.1051/cocv/2010045[ 6] Martin Rumpf, Benedikt Wirth
An elasticitybased covariance analysis of shapes Int. J. Comput. Vis. , 92: (3): 281295 2011 DOI: 10.1007/s1126301003582[ 7] Benedikt Wirth, Leah Bar, Martin Rumpf, Guillermo Sapiro
A continuum mechanical approach to geodesics in shape space Int. J. Comput. Vis. , 93: (3): 293318 2011 DOI: 10.1007/s1126301004169[ 8] Patrick Dondl, Behrend Heeren, Martin Rumpf
Optimization of the branching pattern in coherent phase transitions C. R. Math. Acad. Sci. Paris , 354: (6): 639644 2016 DOI: 10.1016/j.crma.2016.03.013[ 9] Martin Rumpf, Benedikt Wirth
Variational time discretization of geodesic calculus IMA J. Numer. Anal. , 35: (3): 10111046 2015 DOI: 10.1093/imanum/dru027[ 10] B. Berkels, A. Effland, M. Rumpf
Time discrete geodesic paths in the space of images SIAM J. Imaging Sci. , 8: (3): 14571488 2015 DOI: 10.1137/140970719[ 11] Sergio Conti, Harald Held, Martin Pach, Martin Rumpf, Rüdiger Schultz
Risk averse shape optimization SIAM J. Control Optim. , 49: (3): 927947 2011 DOI: 10.1137/090754315[ 12] U. Clarenz, U. Diewald, G. Dziuk, M. Rumpf, R. Rusu
A finite element method for surface restoration with smooth boundary conditions Comput. Aided Geom. Design , 21: (5): 427445 2004 DOI: 10.1016/j.cagd.2004.02.004[ 13] Günther Grün, Martin Rumpf
Nonnegativity preserving convergent schemes for the thin film equation Numer. Math. , 87: (1): 113152 2000 DOI: 10.1007/s002110000197[ 14] M. Flucher, M. Rumpf
Bernoulli's freeboundary problem, qualitative theory and numerical approximation J. Reine Angew. Math. , 486: : 165204 1997[ 15] Benjamin Berkels, Alexander Effland, Martin Rumpf
A Posteriori Error Control for the Binary MumfordShah Model Mathematics of Computation 2015 DOI: doi.org/10.1090/mcom/3138[16] Benjamin Berkels, Sebastian Bauer, Svenja Ettl, Oliver Arold, Joachim Hornegger, Martin Rumpf
Joint Surface Reconstruction and 4D Deformation Estimation from Sparse Data and Prior Knowledge for MarkerLess Respiratory Motion Tracking Medical Physics , 40: (9): 091703 2013 DOI: 10.1118/1.4816675



• Computing and Visualization in Science (since 1999)
• SIAM Journal on Imaging Science (since 2007)
• SIAM Journal on Numerical Analysis (since 2015)
• Journal of Mathematical Imaging and Vision (since 2015)


2003  Plenary lecture, GAMM annual meeting, Padua / Abano Terme, Italy  2004  Plenary lecture, SIAM Conference on Image Science, Salt Lake City, UT, USA  2005  Plenary lecture, EQUADIFF, Bratislava, Slovakia  2006  Plenary lecture, Curves and Surface, Avignon, France  2008  Invited lecture course, CIME summer school, Cetraro, Italy  2010  Invited lecture course, CNA summer school, Pittsburgh, PA, USA  2013  Plenary lecture, SSVM, Graz, Austria  2015  Invited lecture course, CRC summer school, Barcelona, Spain  2016  Invited lecture, Geometry Summit, Berlin 


2002  Chair in Mathematics, University of Zürich, Switzerland  2003  Chair, MATHEON, FU Berlin  2012  Director position of the Weierstrass Institute Berlin combined with a chair at the HU Berlin 


Olga Wilderotter (2001): “Adaptive FiniteElementeMethode für singuläre parabolische Probleme”,
now Professor, HS Karlsruhe
Ulrich Weikard (2002): “Numerische Loesungen der CahnHilliardGleichung und der CahnLarcheGleichung”,
now Senior Economist, DekaBank Deutsche Girozentrale
Tobias Preußer (2003): “Anisotropic Geometric Diffusion in Image and ImageSequence Processing”,
now Professor, Jacobs University Bremen, and Member of Management Board, and Head of Modelling & Simulation, Fraunhofer MEVIS, Bremen
Robert Strzodka (2004): “Hardware Efficient PDE Solvers in Quantized Image Processing”,
now Professor, University of Heidelberg
Benedikt Wirth (2010): “Variational Methods in Shape Space”,
now Associate Professor, University of Münster
Benjamin Berkels (2012): “Joint Methods in imaging based on diffuse image representations”,
now Professor, RWTH Aachen


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