Address:  Institut für Numerische Simulation Rheinische FriedrichWilhelmsUniversität Bonn Endenicher Allee 60 53115 Bonn Germany 
Room:  Z2.065 
Phone:  +49 (0)228  733334 
Fax:  +49 (0)228  739015 
eMail: 

BMBF competence network:
CROP.SENSe.net: Networking sensor technology R&D for crop breeding and management Project D4: 4D structural analysis of the sugar beet geometry Our goal is developing techniques for modelbased 3D reconstruction and classification of storage root geometry from tomographic data, i.e. data obtained from laser scans and MRI. We aim in comparing different cultivars subject to different soil, management and environmental conditions. Furthermore we investigate the temporal variation of sugar beet growth by applying and generalizing regression methods to the space of beets. Our tools are robust and nonsupervised, that means they improve previous andmeasured methods and corresponding empirical scales. Furthermore, recent results suggest that our methods are capable to statistically separate genotypic from environmental features. Hence the proposed techniques are relevant and effective tools to optimize plant breeding. 

DFG SFB 1060:
The Mathematics of Emergent Effects Project C05: Discrete Riemannian calculus on shape space The theory of shape spaces in vision is linked both to concepts from geometry and from physics. The flow of diffeomorphism approach and the optimal transportation approach are prominent examples for Riemannian metric structures on the space of shapes, intensively studied in the last decade. In general, the numerical realization of the underlying infinite dimensional Riemannian calculus poses enormous computational challenges. In this project we propose suitable time and space discrete approximations. They will be based on optimal matching deformations, which are significantly cheaper to compute but by construction nonRiemannian. We will also study abstract concepts of transportation between metric measure spaces with particular focus on spaces consisting only of a fixed number of points. In the time discrete calculus a discrete path energy is defined as the sum of pairwise deformation energies along a discrete path. Using a variational approach one can deduce from this step by step a discrete logarithm, a discrete exponential map, a discrete parallel transport, a discrete LeviCivita connection, and finally a discrete Riemannian curvature tensor. This concept will be applied and analyzed in particular for the flow of diffeomorphism and the optimal transportation approach. Furthermore, with respect to a spatially discrete covering of shape space, the approach of deformation based shape dissimilarities will be combined with the diffusion map paradigm expedited by Coifman and coworkers to introduce physically sound and computationally efficient approximations of metric structures on shape spaces. Overall, we aim at combining methods from geometry, stochastic analysis and numerics to advance theory in computer vision and explore new applications with efficient computational tools. 

FWF NFN S117:
Geometry + Simulation Project 5: Geodesic Paths in Shape Space This project will provide robust and flexible tools for the quantitative analysis of shapes in the interplay between applied geometry and numerical simulation. Here, shapes S are curved surfaces which physically represent shelltype geometries, boundary geometries of volumetric physical objects, or material interfaces. In isogeometric analysis one faces a wide range of low and moderatedimensional descriptions of complicated and realistic geometries. Thus, the geometric description of shapes will be flexible, ranging from simple piecewise triangular to subdivisiongenerated spline type surface representations and from explicitly meshed volumes to descriptions via level set or characteristic functions. The fundamental tool for a quantitative shape analysis is the computation of a distance between shapes SA and SB as objects in a high or even 1dimensional Riemannian shape space. Hence, we aim at developing robust models and fast algorithms to compute geodesic paths in shape space. Both for boundary or interface contours and for shelltype surfaces the Riemannian metric will correspond to physical dissipation either of a viscous fluid filling the object volume or due to a viscoplastic behavior of the shells. The key tool of the proposed approach is a coarse time discretization combined with a variational scheme to minimize the underlying least action functional. For purposes of a geometric analysis not only the resulting value for the distance is of interest. In fact the geodesic paths are natural one parameter families of shapes on which physical simulations and PDE computations can be performed. In case of shapes being represented by shell type surfaces we will apply different approaches: subdivision surfaces generated from coarse surface triangulations and subdivisionbased discrete function spaces as a modeling paradigm associated with spline models in CAD, application of methods from discrete exterior calculus on discrete surfaces to derive robust and geometrically consistent discrete shell models, the approximation of curvaturebased functionals in shell models via variational principles on general classes of surface meshes. In the case of shapes being boundary contours or material interfaces of volumetric objects we aim at representing shapes via characteristic functions, working in the context of variational methods in BV. We will compare this approach with corresponding models based on level set or parametric descriptions. Here, recent results on global minimization of convex functionals on BV and coarse to fine multiscale relaxation methodologies will be taken into account. For the numerical discretization we aim at using finite elements. 
Jan 2017 —  PostDoctoral Researcher at the Institute for Numerical Simulation 
Jan 2012 — Dec 2016  PhD student
at the Institute for Numerical Simulation Thesis on "Numerical Methods in Shape Spaces and Optimal Branching Patterns", defended in Feb 2017 Supervisor: Martin Rumpf 
Apr 2012 — May 2012  Visiting student at the California Institute of Technology, Pasadena, USA Supervisor: Peter Schröder 
Apr 2008 — Dec 2011  Student of
Mathematics and Psychology at University of Bonn Diplom in Mathematics at the Institute for Numerical Simulation on "Geodätische im Raum von Schalenformen" Supervisor: Martin Rumpf 
Mar 2008 — Mar 2011  Scholarship of the Studienstiftung des deutschen Volkes 
Jul 2009 — Dec 2009  Student of
Mathematics and Oceanography at the University of New South Wales and the Climate Change Research Centre, Sydney, Australia 
Oct 2005 — Mar 2008  Student of
Mathematics and Psychology at the University of Münster 
[1] 
B. Heeren, M. Rumpf, and B. Wirth.
Variational time discretization of Riemannian splines.
IMA J. Numer. Anal., 2017.
accepted. [ bib  arXiv  .pdf 1 ] 
[2] 
S. Markett, M. Reuter, B. Heeren, B. Lachmann, B. Weber, and C. Montag.
Working memory capacity and the functional connectome  insights from
restingstate fMRI and voxelwise eigenvector centrality mapping.
Brain Imaging and Behavior, 2017.
accepted. [ bib ] 
[3] 
P. W. Dondl, B. Heeren, and M. Rumpf.
Optimization of the branching pattern in coherent phase transitions.
C. R. Math. Acad. Sci. Paris, 354(6):639644, 2016. [ bib  arXiv  Abstract ] 
[4] 
B. Heeren.
Numerical Methods in Shape Spaces and Optimal Branching
Patterns.
PhD thesis, University of Bonn, 2016. [ bib ] 
[5] 
B. Heeren, M. Rumpf, P. Schröder, M. Wardetzky, and B. Wirth.
Splines in the space of shells.
Comput. Graph. Forum, 35(5):111120, 2016. [ bib  .pdf 1 ] 
[6] 
S. Markett, C. Montag, B. Heeren, R. Sariyska, B. Lachmann, B. Weber, and
M. Reuter.
Voxelwise eigenvector centrality mapping of the human functional
connectome reveals an influence of the catecholomethyltransferase val158met
polymorphism on the default mode and somatomotor network.
Brain Structure and Function, 221:27552765, 2016. [ bib  DOI ] 
[7] 
C. Zhang, B. Heeren, M. Rumpf, and W. Smith.
Shell PCA: statistical shape modelling in shell space.
In Proc. of IEEE International Conference on Computer Vision,
2015. [ bib  .pdf 1 ] 
[8] 
B. Heeren, M. Rumpf, P. Schröder, M. Wardetzky, and B. Wirth.
Exploring the geometry of the space of shells.
Comput. Graph. Forum, 33(5):247256, 2014. [ bib  .pdf 1 ] 
[9] 
B. Berkels, P. T. Fletcher, B. Heeren, M. Rumpf, and B. Wirth.
Discrete geodesic regression in shape space.
In Proc. of International Conference on Energy Minimization
Methods in Computer Vision and Pattern Recognition, volume 8081 of
Lecture Notes in Computer Science, pages 108122. Springer, 2013. [ bib  DOI  .pdf 1 ] 
[10] 
B. Heeren, M. Rumpf, M. Wardetzky, and B. Wirth.
Timediscrete geodesics in the space of shells.
Comput. Graph. Forum, 31(5):17551764, 2012. [ bib  DOI  .pdf 1 ] 
[11] 
B. Heeren.
Geodätische im Raum von Schalenformen.
diploma thesis, 2011. [ bib  .pdf 1 ] 
June 21st, 2016  Symposium on Geometry Processing in Berlin, Germany Splines in the Space of Shells 
May 12th, 2016  SIAM Conference on Mathematical Aspects of Material Sciences, Philadelphia, USA Timediscrete geodesic calculus in the space of shells 
January 28th, 2016  Oberwolfach Workshop on Mathematical Imaging and Surface Processing, Oberwolfach, Germany Riemannian Splines in the Space of Shells 
July 11th, 2014  Symposium on Geometry Processing in Cardiff, Wales Exploring the Geometry in the Space of Shells 
August 19th, 2013  EMMCVPR Conference in Lund, Sweden Discrete Geodesic Regression in Shape Space 
July 18th, 2013  European Conference on Computational Optimization 2013 in Chemnitz, Germny Discrete Geodesic Calculus in the Space of Thin Shells 
March 20th, 2013  GAMM Annual Meeting in Novi Sad, Serbia Discrete Geodesic Calculus in the Space of Thin Shells 
Sep 11th, 2012  Conference on Scientific Computing Algoritmy 2012 in Podbanske, Slovakia Timediscrete Geodesics in the Space of Shells 
July 18th, 2012  Symposium on Geometry Processing in Tallinn, Estonia Timediscrete Geodesics in the Space of Shells 
March 29th, 2012  Workshop Navigating the Space of Surfaces in Bonn, Germany Timediscrete Geodesics in the Space of Shells 
March 28th, 2012  GAMM Annual Meeting in Darmstadt, Germany Timediscrete Geodesics in the Space of Shells 
Winter term 2017/18:  Seminar on Shape spaces and shape representations 
Summer term 2017:  Lecture course on Geometry Processing and Discrete Shells 
Assistant for Algorithmische Mathematik II given by Prof. Dr. A. Eberle and Prof. Dr. A. Umschmajew.  
Winter term 2016/17:  Assistant for Ingenieurmathematik III given by Dr. Martin Lenz 
Summer term 2016:  Assistant for Ingenieurmathematik II given by Dr. Martin Lenz 
Winter term 2015/16:  Computer lab for Einführung in die Grundlagen der Numerik given by Prof. Martin Rumpf 
Summer term 2015:  Tutorial and computer lab for Algorithmische Mathematik II given by Prof. Martin Rumpf 
Winter term 2014/15:  Assistant for Ingenieurmathematik I given by Dr. Antje Kiesel 
Summer term 2014:  Assistant for Ingenieurmathematik II given by Dr. Martin Lenz 
Winter term 2013/14:  Organizing Seminar on Modeling and Simulation with PDEs given by Prof. Martin Rumpf and Dr. Peter Hornung 
Summer term 2013:  Computer lab Numerical Methods for Thin Elastic Sheets with Ricardo Perl 
Winter term 2012/13:  Assistant for Numerical Algorithms with Benedict Geihe 