95 citations · 482 across the 27 of their papers we have counts for
27 papers
Multivariate Hermite interpolation of manifold-valued data
Ralf Zimmermann, Ronny Bergmann
In this paper, we propose two methods for multivariate Hermite interpolation of manifold-valued functions. On the one hand, we approach the problem via computing suitable weighted…
Total Generalized Variation for Piecewise Constant Functions on Triangular Meshes with Applications in Imaging
Lukas Baumgärtner, Ronny Bergmann, Roland Herzog +2
We propose a novel discrete concept for the total generalized variation (TGV), which has originally been derived to reduce the staircasing effect in classical total variation (TV)…
The difference of convex algorithm on Hadamard manifolds
Ronny Bergmann, Orizon P. Ferreira, Elianderson M. Santos +1
In this paper, we propose a Riemannian version of the difference of convex algorithm (DCA) to solve a minimization problem involving the difference of convex (DC) function. We esta…
First- and Second-Order Analysis for Optimization Problems with Manifold-Valued Constraints
Ronny Bergmann, Roland Herzog, Julián Ortiz López +1
We consider optimization problems with manifold-valued constraints. These generalize classical equality and inequality constraints to a setting in which both the domain and the cod…
Manifolds.jl: An Extensible Julia Framework for Data Analysis on Manifolds
Seth D. Axen, Mateusz Baran, Ronny Bergmann +1
We present the Julia package Manifoldsjl, providing a fast and easy-to-use library of Riemannian manifolds and Lie groups. This package enables working with data defined on a Ri…
Fenchel Duality and a Separation Theorem on Hadamard Manifolds
Maurício Silva Louzeiro, Ronny Bergmann, Roland Herzog
In this paper, we introduce a definition of Fenchel conjugate and Fenchel biconjugate on Hadamard manifolds based on the tangent bundle. Our definition overcomes the inconvenience…
Discrete Total Variation of the Normal Vector Field as Shape Prior with Applications in Geometric Inverse Problems
Ronny Bergmann, Marc Herrmann, Roland Herzog +2
An analogue of the total variation prior for the normal vector field along the boundary of piecewise flat shapes in 3D is introduced. A major class of examples are triangulated sur…
Fenchel Duality Theory and A Primal-Dual Algorithm on Riemannian Manifolds
Ronny Bergmann, Roland Herzog, Maurício Silva Louzeiro +2
This paper introduces a new notion of a Fenchel conjugate, which generalizes the classical Fenchel conjugation to functions defined on Riemannian manifolds. We investigate its prop…
Total Variation of the Normal Vector Field as Shape Prior
Ronny Bergmann, Marc Herrmann, Roland Herzog +2
An analogue of the total variation prior for the normal vector field along the boundary of smooth shapes in 3D is introduced. The analysis of the total variation of the normal vect…
Recent Advances in Denoising of Manifold-Valued Images
Ronny Bergmann, Friederike Laus, Johannes Persch +1
Modern signal and image acquisition systems are able to capture data that is no longer real-valued, but may take values on a manifold. However, whenever measurements are taken, no…
A variational model for data fitting on manifolds by minimizing the acceleration of a Bézier curve
Ronny Bergmann, Pierre-Yves Gousenbourger
We derive a variational model to fit a composite Bézier curve to a set of data points on a Riemannian manifold. The resulting curve is obtained in such a way that its mean squared…
Intrinsic formulation of KKT conditions and constraint qualifications on smooth manifolds
Ronny Bergmann, Roland Herzog
Karush-Kuhn-Tucker (KKT) conditions for equality and inequality constrained optimization problems on smooth manifolds are formulated. Under the Guignard constraint qualification, l…
Priors with Coupled First and Second Order Differences for Manifold-Valued Image Processing
Ronny Bergmann, Jan Henrik Fitschen, Johannes Persch +1
Recently variational models with priors involving first and second order derivatives resp. differences were successfully applied for image restoration. There are several ways to in…
Approximation of Periodic PDE Solutions with Anisotropic Translation Invariant Spaces
Ronny Bergmann, Dennis Merkert
We approximate the quasi-static equation of linear elasticity in translation invariant spaces on the torus. This unifies different FFT-based discretisation methods into a common fr…
Nonlocal Inpainting of Manifold-valued Data on Finite Weighted Graphs
Ronny Bergmann, Daniel Tenbrinck
Recently, there has been a strong ambition to translate models and algorithms from traditional image processing to non-Euclidean domains, e.g., to manifold-valued data. While the t…
FFT-based homogenization on periodic anisotropic translation invariant spaces
Ronny Bergmann, Dennis Merkert
In this paper we derive a discretisation of the equation of quasi-static elasticity in homogenization in form of a variational formulation and the so-called Lippmann-Schwinger equa…
A Framework for FFT-based Homogenization on Anisotropic Lattices
Ronny Bergmann, Dennis Merkert
In order to take structural anisotropies of a given composite and different shapes of its unit cell into account, we generalize the Basic Scheme in Homogenization by Moulinec and S…
Iterative Multiplicative Filters for Data Labeling
Ronny Bergmann, Jan Henrik Fitschen, Johannes Persch +1
Based on an idea in [4] we propose a new iterative multiplicative filtering algorithm for label assignment matrices which can be used for the supervised partitioning of data. Start…
A Parallel Douglas Rachford Algorithm for Minimizing ROF-like Functionals on Images with Values in Symmetric Hadamard Manifolds
Ronny Bergmann, Johannes Persch, Gabriele Steidl
We are interested in restoring images having values in a symmetric Hadamard manifold by minimizing a functional with a quadratic data term and a total variation like regularizing t…
A Second Order Non-Smooth Variational Model for Restoring Manifold-Valued Images
Miroslav Bačák, Ronny Bergmann, Gabriele Steidl +1
We introduce a new non-smooth variational model for the restoration of manifold-valued data which includes second order differences in the regularization term. While such models we…
Restoration of Manifold-Valued Images by Half-Quadratic Minimization
Ronny Bergmann, Raymond H. Chan, Ralf Hielscher +2
The paper addresses the generalization of the half-quadratic minimization method for the restoration of images having values in a complete Riemannian manifold. We recall the half-q…
A Second Order TV-type Approach for Inpainting and Denoising Higher Dimensional Combined Cyclic and Vector Space Data
Ronny Bergmann, Andreas Weinmann
In this paper we consider denoising and inpainting problems for higher dimensional combined cyclic and linear space valued data. These kind of data appear when dealing with nonline…
Inpainting of Cyclic Data using First and Second Order Differences
Ronny Bergmann, Andreas Weinmann
Cyclic data arise in various image and signal processing applications such as interferometric synthetic aperture radar, electroencephalogram data analysis, and color image restorat…
Second Order Differences of Cyclic Data and Applications in Variational Denoising
Ronny Bergmann, Gabriele Steidl, Friederike Laus +1
In many image and signal processing applications, as interferometric synthetic aperture radar (SAR), electroencephalogram (EEG) data analysis or color image restoration in HSV or L…