The SFB/TRR 109 "Discretization in Geometry and Dynamics" has been funded by the Deutsche Forschungsgemeinschaft e.V. (DFG) since 2012.
The project is a collaboration between:
- the Technische Universität Berlin as lead university,
- the Technische Universität München as partner university,
- and individual scientists from
The central goal of the SFB/Transregio is to pursue research on the discretization of differential geometry and dynamics. In both fields of mathematics, the objects under investigation are usually governed by differential equations. Generally, the term "discretization" refers to any procedure that turns a differential equation into difference equations involving only finitely many variables, whose solutions approximate those of the differential equation.
The common idea of our research in geometry and dynamics is to find and investigate discrete models that exhibit properties and structures characteristic of the corresponding smooth geometric objects and dynamical processes. If we refine the discrete models by decreasing the mesh size they will of course converge in the limit to the conventional description via differential equations. But in addition, the important characteristic qualitative features should be captured even at the discrete level, independent of the continuous limit. The resulting discretizations constitutes a fundamental mathematical theory, which incorporates the classical analog in the continuous limit.
The SFB/Transregio brings together scientists from the fields of geometry and dynamics, to join forces in tackling the numerous problems raised by the challenge of discretizing their respective disciplines.
New film featuring the work of the SFB
- 22.06.2018, 12:00 - 13:00
12:00 - 13:00
Inversions in Lie geometry,
- 26.06.2018, 13:30 - 14:00
13:30 - 14:00
Introduction to the talk "Constraint-based Point Set Denoising" ,
- 26.06.2018, 14:15 - 15:15
14:15 - 15:15
Constraint-based Point Set Denoising,
Marting Skrodzki (FU Berlin)
- In many applications, point set surfaces are acquired by 3D scanners. During this process, noise and outliers are inevitable. For a high fidelity surface reconstruction from a noisy point set, a feature preserving point set denoising operation has to be performed to remove noise and outliers from the input point set. We introduce an anisotropic point set denoising algorithm in the normal voting tensor framework. The method consists of three different stages that are iteratively applied: in the first stage, noisy vertex normals are processed using a vertex-based normal voting tensor and binary eigenvalues optimization. In the second stage, feature points are categorized into corners, edges, and surface patches using a weighted covariance matrix, which is computed based on the processed vertex normals. In the last stage, vertex positions are updated using restricted quadratic error metrics. Finally, we show our method to be robust and comparable to state-of-the-art methods in experiments
Current Guests and Visitors
- Prof. Dr. Bernd Sturmfels as Einstein Visiting Fellow at TU Berlin (01.05.2015 - 31.07.2020)
- Prof. Dr. Francisco Santos as Einstein Visiting Fellow at FU Berlin (01.04.2016 - 31.03.2019)
- Prof. Dr. Peter Schröder as Einstein Visiting Fellow at TU Berlin (01.03.2018 - 28.02.2021)
- Prof. Dr. Steffen Rohde as Guest Professor at TU Berlin (30.03.2018 - 26.06.2018)
- Prof. Dr. Wolfgang K. Schief as Guest Professor at TU Berlin (09.06.2018 - 17.07.2018)
- Associate Prof. Shimpei Kobayashi as Visitor at TU Berlin (15.06.2018 - 14.08.2018)
Forthcoming Guests and Visitors
- Roman Prosanov as Visitor at TU Berlin (16.07.2018 - 20.07.2018)
- Associate Prof. Shimpei Kobayashi as Visitor at TU München (15.08.2018 - 21.09.2018)