In various applications in science and engineering, the data do not take values in a vector space but in a nonlinear space such as a manifold. Examples are circle and sphere-valued data as appearing in SAR imaging and the space of positive matrices with the Fisher-Rao metric, which is the underlying data space for Diffusion Tensor Imaging. Many recent, successful methods for processing geometric data rely on variational approaches, i.e., the minimization of an energy functional. In this mini-symposium, we aim at bringing together researches with different areas of expertise, who share interest in variational approaches for geometric data.

Metamorphosis and Schild's Ladder for One-Dimensional Shapes with Applications to the Classification of Cardiac Stem Cells

Rene Vidal (Johns Hopkins University)

Averaging positive-definite matrices

Pierre-Antoine Absil (University of Louvain)

Curvature Regularization on Manifolds

Benedikt Wirth (Universität Münster)

Unsupervised Label Learning on Manifolds by Spatially Regularized Geometric Assignment

Artjom Zern (Universität Heidelberg)

A variational approach for Multi-Angle TIRF Microscopy

Vincent Duval (INRIA)

Variational approximation of data in manifolds using Geometric Finite Elements

Hanne Hardering (TU Dresden)

Edge-Parallel Inference with Graphical Models Using Wasserstein Messages and Geometric Assignment

Ruben Hühnerbein (Universität Heidelberg)

Total generalized variation for manifold-valued data

Martin Holler (École Polytechnique, Université Paris Saclay)

Geodesic Interpolation in the Space of Images

Alexander Effland (Universität Bonn)

Functional-Analytic Questions in Measure-Valued Variational Problems

Thomas Vogt (Universität Lübeck)

Nonlocal inpainting of manifold-valued data on finite weighted graphs

Ronny Bergmann (Technische Universität Chemnitz)

Curvature Regularization with Adaptive Discretization of Measures

Ulrich Hartleif (Universität Münster)

Organizers:

Martin Holler (École Polytechnique, Université Paris Saclay)

Martin Storath (Universität Heidelberg)

Andreas Weinmann (Hochschule Darmstadt)

Keywords:

geometric data, manifold, regularization, variational methods