Numerical Methods for Non-smooth Optimization on Riemannian ManifoldsPhD project
Regression of Time Series Data on Manifoldsmaster thesisD. Huybrechs, and B. Owren This thesis started during an exchange stay and is a master thesis at KU Leuven
Adaptive Regularization with Cubicsmaster thesis The code of this thesis is the Lanczos sub solver variant of the ARC solver available within Manopt.jl.
Multivariate Periodic Wavelets on the Patternmaster thesis
The nearest -stable matrix vir Riemannian Optimizationmaster thesisR. Zimmermann This thesis was conducted at SDU Odense. Sebastian was staying at NTNU for two weeks to conduct his numerical experiments in Julia.
Constraint Optimization on Manifoldsmaster thesisR. Herzog The code of this thesis was the main basis for The Augmented Lagrangian Method and The Exact Penalty Method available within Manopt.jl.
The Riemannian Frank-Wolfe Algorithmmaster thesis The code of this thesis was the basis for The Frank-Wolfe Algorithm available within Manopt.jl.
Support Vector Machines on Riemannian Manifoldsmaster thesis This thesis was awarded the NR Prisen for the best master thesis in mathematics at NTNU within the study year 2021/2022.
The Chambolle-Pock Algorithm for Geometry Labeling and Segmentation based on the Normal Vector Fieldmaster thesisR. Herzog
Geodätische Regression auf Mannigfaltigkeiten mit Nebenbedingungenmaster thesisR. Herzog
Variational Models and Primal-Dual Algorithms for Manifold-Valued Image Restorationmaster thesisG. Steidl
Analysis of Local Anisotropies and Denoising of -Valued Datamaster thesisG. Steidl
Constrained optimization on Riemannian manifolds using geodesic polygonal setsbachelor thesisR. Herzog
The Riemannian BFGS Method and its Implementation in Juliabachelor thesisR. Herzog The code is available at within Manopt.jl, see Riemannian quasi Newton Methods.
Regularized Clustering of Manifold-Valued Databachelor thesisR. Herzog
-TV-Regularisierung von rotationswertigen Datenbachelor thesisR. Hielscher
Optimization of Composite Bézier Curves on Riemannian Manifoldsbachelor thesis
An Alternating Gradient Descent Method for Geodesic Regression on symmetric Riemannian manifoldsbachelor thesis
Congruence classes of anisotropic patterns on the torus and application in the FFT-based homogenizationbachelor thesisD. Merkert, B. Simeon, and G. Steidl
Segmentation of Manifold-valued imagesbachelor thesisG. Steidl
Anisotropic Structures and Sampling Patterns for the FFT-based Numerical Homogenizationbachelor thesisD. Merkert, B. Simeon, and G. Steidl
Unsupervised Co-Segmentation with Histogram Priorsbachelor thesisG. Steidl
Entropy Regularized Wasserstein Distances and an Application in Image Segmentationbachelor thesisG. Steidl
Directional Information via Structure Tensorsbachelor thesisG. Steidl
Multivariate anisotrope Dirichlet-Wavelets zur Kantendetektion auf dem Torusbachelor thesisJ. Prestin
Die multivariate periodische Fourier- und Wavelet-Transformation auf anisotropen Musternbachelor thesisJ. Prestin
Manifold-Valued Graph Learning and Embedding Graphsspecialisation projectC. von Tychowicz, and M. Hanik
Low Rank Matrix Completionspecialisation project
The Multivariate Fast Fourier Transform on the Patternspecialisation project
Convolutions on Manifolds for Deep Learningspecialisation project
Optimization on the symplectic and the symplectic Stiefel manifoldspecialisation project The code is available at within Manifolds.jl, see The symplectic Manifold and the The symplectic Stiefel Manifold.
Bézier curves in Riemannian manifoldsstudent project
Semantic Segmentation using Fully Convolutional Networksstudent projectA. Moghiseh
Segmentation of Colour Images Using a Regularised Fuzzy C-Means Algorithmstudent project
Lösung der statischen Wärmeleitungsgleichung in der Homogenisierung auf anisotropen Gitternstudent projectD. Merkert
An Algorithm for Image Segmentation based on Optimal Transport Distancesstudent projectG. Steidl