16 citations · 19 across the 12 of their papers we have counts for
13 papers
A modified Riemannian Levenberg-Marquardt Algorithm for robust or constraint optimization on manifolds
Mateusz Baran, Ronny Bergmann
We extend the Levenberg-Marquardt method on Riemannian manifolds to a robust variant that allows to tackle problems from applications where outliers are to be expected. We formally…
A Riemannian quasi-Newton algorithm for optimization with Euclidean bounds
Mateusz Baran, Ronny Bergmann, Patryk Przybysz
We propose a Riemannian limited-memory BFGS method for optimization problems with Euclidean bounds. The method combines a limited-memory quasi-Newton update in the tangent space wi…
Procrustes Problems on Random Matrices
Hajg Jasa, Ronny Bergmann, Christian Kümmerle +2
Meaningful comparison between sets of observations often necessitates alignment or registration between them, and the resulting optimization problems range in complexity from those…
Newton's method for nonlinear mappings into vector bundles Part II: Application to variational problems
Laura Weigl, Ronny Bergmann, Anton Schiela
We consider the solution of variational equations on manifolds by Newton's method. These problems can be expressed as root finding problems for mappings from infinite dimensional m…
The Intrinsic Riemannian Proximal Gradient Method for Convex Optimization
Ronny Bergmann, Hajg Jasa, Paula John +1
We consider a class of (possibly strongly) geodesically convex optimization problems on Hadamard manifolds, where the objective function splits into the sum of a smooth and a possi…
Total Generalized Variation of the Normal Vector Field and Applications to Mesh Denoising
Lukas Baumgärtner, Ronny Bergmann, Roland Herzog +2
We propose a novel formulation for the second-order total generalized variation (TGV) of the normal vector on an oriented, triangular mesh embedded in . The normal vector is…
p-Laplacians for Manifold-valued Hypergraphs
Jo Andersson Stokke, Ronny Bergmann, Martin Hanik +1
Hypergraphs extend traditional graphs by enabling the representation of N-ary relationships through higher-order edges. Akin to a common approach of deriving graph Laplacians, we d…
The Intrinsic Riemannian Proximal Gradient Method for Nonconvex Optimization
Ronny Bergmann, Hajg Jasa, Paula John +1
We consider the proximal gradient method on Riemannian manifolds for functions that are possibly not geodesically convex. Starting from the forward-backward-splitting, we define an…
Two Models for Surface Segmentation using the Total Variation of the Normal Vector
Manuel Weiß, Lukas Baumgärtner, Laura Weigl +3
We consider the problem of surface segmentation, where the goal is to partition a surface represented by a triangular mesh. The segmentation is based on the similarity of the norma…
Nonlinear Fenchel Conjugates
Anton Schiela, Roland Herzog, Ronny Bergmann
The classical concept of Fenchel conjugation is tailored to extended real-valued functions defined on linear spaces. In this paper we generalize this concept to functions defined o…
The Riemannian Convex Bundle Method
Ronny Bergmann, Roland Herzog, Hajg Jasa
We introduce the convex bundle method to solve convex, non-smooth optimization problems on Riemannian manifolds of bounded sectional curvature. Each step of our method is based on…
Mesh Denoising and Inpainting using the Total Variation of the Normal and a Shape Newton Approach
Lukas Baumgärtner, Ronny Bergmann, Roland Herzog +3
We present a novel approach to denoising and inpainting problems for surface meshes. The purpose of these problems is to remove noise or fill in missing parts while preserving impo…
A Graph Framework for Manifold-valued Data
Ronny Bergmann, Daniel Tenbrinck
Graph-based methods have been proposed as a unified framework for discrete calculus of local and nonlocal image processing methods in the recent years. In order to translate variat…