$ \DeclareMathOperator{\arccosh}{arccosh} \DeclareMathOperator*{\argmin}{arg\,min} \DeclareMathOperator{\Exp}{Exp} \newcommand{\geo}[2]{\gamma_{\overset{\frown}{#1,#2}}} \newcommand{\geoS}{\gamma} \newcommand{\geoD}[2]{\gamma_} \newcommand{\geoL}[2]{\gamma(#2; #1)} \newcommand{\gradM}{\nabla_{\M}} \newcommand{\gradMComp}[1]{\nabla_{\M,#1}} \newcommand{\Grid}{\mathcal G} \DeclareMathOperator{\Log}{Log} \newcommand{\M}{\mathcal M} \newcommand{\N}{\mathcal N} \newcommand{\mat}[1]{\mathbf{#1}} \DeclareMathOperator{\prox}{prox} \newcommand{\PT}[3]{\mathrm{PT}_{#1\to#2}#3} \newcommand{\R}{\mathbb R} \newcommand{\SPD}[1]{\mathcal{P}(#1)} \DeclareMathOperator{\Tr}{Tr} \newcommand{\tT}{\mathrm{T}} \newcommand{\vect}[1]{\mathbf{#1}} $

Publications

You can read any abstract clicking on and access the BibTeX code at . If there is a freely available (preprint) version, it is linked with . The links to the official article page of the corresponding journal page using the Digital Object Identifier. Accompanying code is indicated by a link to the corresponding repository, e. g. , or . Furthermore an external link might be available.

Preprints

  1. Publication illustration image
    Bergmann, R and Gousenbourger, P-Y (2018). A variational model for data fitting on manifolds by minimizing the acceleration of a Bézier curve
  2. Publication illustration image
    Bergmann, R and Herzog, R (2018). Intrinsic formulation of KKT conditions and constraint qualifications on smooth manifolds

Journal Papers

2018

  1. Publication illustration image
    Bergmann, R, Fitschen, J H, Persch, J and Steidl, G (2018). Priors with coupled first and second order differences for manifold-valued image processing. Journal of Mathematical Imaging and Vision accepted, online first
  2. Publication illustration image
    Bergmann, R and Merkert, D (2018). FFT-based homogenization on periodic anisotropic translation invariant spaces. Applied and Computational Harmonic Analysis. Available online, in press.
  3. Publication illustration image
    Bergmann, R and Merkert, D (2018). A framework for FFT-based homogenization on anisotropic lattices. Computers & Mathematics with Applications. 76 125–40
  4. Publication illustration image
    Bergmann, R and Tenbrinck, D (2018). A graph framework for manifold-valued data. SIAM Journal on Imaging Sciences. 11 325–60

2017

  1. Publication illustration image
    Bergmann, R, Fitschen, J H, Persch, J and Steidl, G (2017). Iterative multiplicative filters for data labeling. International Journal of Computer Vision. 123 435–53

2016

  1. Publication illustration image
    Bergmann, R and Weinmann, A (2016). A second order TV-type approach for inpainting and denoising higher dimensional combined cyclic and vector space data. Journal of Mathematical Imaging and Vision. 55 401–27
  2. Publication illustration image
    Bačák, M, Bergmann, R, Steidl, G and Weinmann, A (2016). A second order non-smooth variational model for restoring manifold-valued images. SIAM Journal on Scientific Computing. 38 A567–A597
  3. Publication illustration image
    Bergmann, R, Persch, J and Steidl, G (2016). A parallel Douglas–Rachford algorithm for minimizing ROF-like functionals on images with values in symmetric Hadamard manifolds. SIAM Journal on Imaging Sciences. 9 901–37
  4. Publication illustration image
    Bergmann, R, Chan, R H, Hielscher, R, Persch, J and Steidl, G (2016). Restoration of manifold-valued images by half-quadratic minimization. Inverse Problems and Imaging. 10 281–304

2015

  1. Publication illustration image
    Bergmann, R and Prestin, J (2015). Multivariate periodic wavelets of de la Vallée Poussin type. Journal of Fourier Analysis and Applications. 21 342–69

2014

  1. Publication illustration image
    Bergmann, R, Laus, F, Steidl, G and Weinmann, A (2014). Second order differences of cyclic data and applications in variational denoising. SIAM Journal on Imaging Sciences. 7 2916–53

2013

  1. Publication illustration image
    Bergmann, R (2013). The fast Fourier transform and fast wavelet transform for patterns on the torus. Applied and Computational Harmonic Analysis. 35 39–51

Peer-reviewed Conference Proceedings

2017

  1. Publication illustration image
    Bergmann, R and Merkert, D (2017). Approximation of periodic PDE solutions with anisotropic translation invariant spaces. 2017 International Conference on Sampling Theory and Applications (SampTA). 396–9
  2. Publication illustration image
    Bergmann, R, Fitschen, J H, Persch, J and Steidl, G (2017). Infimal Convolution Coupling of First and Second Order Differences on Manifold-Valued Images. Scale Space and Variational Methods in Computer Vision: 6th International Conference, SSVM 2017, Kolding, Denmark, June 4-8, 2017, Proceedings. Springer International Publishing, Cham. 447–59
  3. Publication illustration image
    Bergmann, R and Tenbrinck, D (2017). Nonlocal inpainting of manifold-valued data on finite weighted graphs. Geometric Science of Information – 3rd Conference on Geometric Science of Information. Springer International Publishing, Cham. 604–12
  4. Publication illustration image
    Bergmann, R (2017). MVIRT, A toolbox for manifold-valued image restoration. IEEE International Conference on Image Processing, IEEE ICIP 2017, Beijing, China, September 17–20, 2017

2015

  1. Publication illustration image
    Bergmann, R and Weinmann, A (2015). Inpainting of cyclic data using first and second order differences. Energy Minimization Methods in Computer Vision and Pattern Recognition, 10th International Conference on, EMMCVPR 2015, Hong Kong. Springer. 155–68
  2. Publication illustration image
    Oezguen, N, Schubert, K J, Bergmann, R, Bennewitz, R and Strauss, D J (2015). Relating tribological stimuli to somatosensory electroencephalographic responses. Engineering in Medicine and Biology Society (EMBC), 37th Annual International Conference of the IEEE. 8115–8

2014

  1. Publication illustration image
    Bergmann, R and Prestin, J (2014). Multivariate anisotropic interpolation on the torus. Approximation Theory XIV: San Antonio 2013. 27–44

Theses

  1. Publication illustration image
    Bergmann, R (2013). Translationsinvariante Räume Multivariater Anisotroper Funktionen Auf Dem Torus. Dissertation. Universität zu Lübeck in german. Similarily: Shaker Verlag, ISBN 978-3844022667, 2013.
  2. Publication illustration image
    Bergmann, R (2009). Interaktive Und Automatisierte Hypergraphenvisualisierung Mittels NURBS-Kurven. Diploma thesis. Universität zu Lübeck In german.

Miscellaneous

  1. Publication illustration image
    Bergmann, R, Laus, F, Persch, J and Steidl, G (2017). Manifold-valued Image Processing. Siam News. 50 1&3