On this page, I keep track of the talks I gave and keep slides for at least a similar talk. Some might even include a recording of the talk or links to external further sources.

Organizer

• Young Researchers Minisymposium “YR3 Local and nonlocal methods for processing manifold and point cloud data” at the Jahrestagung der Gesellschaft für angewandte Mathematik und Mechanik 2017, March 6—10, Weimar, Germany (together with Daniel Tenbrinck).
• Workshop on manifold-valued image processing, December 1st, 2016, Technische Universität Kaiserslautern, Germany (together with Gabriele Steidl).

Selected Talks

• MVIRT – A Toolbox for Manifold-valued Image Restoration IEEE International Conference on Image Processing (ICIP) 2017, September 17—20, 2017 Bejing, China Invited talk within the Special Session “Trends in Statistical Analysis of Manifold-Valued Data – Theory and Applications to Imaging”, supported by a DAAD conference travel grant
  In many real life application measured data takes its values on Riemannian manifolds. For the special case of the Euclidean space this setting includes the classical grayscale and color images. Like these classical images, manifold-valued data might suffer from measurement errors in form of noise or missing data. In this talk we present the manifold-valued image restoration toolbox (MVIRT) that provides implementations of classical image processing tasks. Based on recent developments in variational methods for manifold-valued image processing methods, like total variation regularization, the toolbox provides easy access to work with these algorithms. The toolbox is implemented in Matlab, open source, and easily extendible, e.g. with own manifolds, noise models or further algorithms. This paper introduces the main mathematical methods as well as numerical examples.
• Second Order TV-Type Regularization Methods for Manifold-Valued Images SIAM Conference of Imaging Sciences 2016, May 23—26, 2016 Albuquerque, NM, USA Invited talk within the Minisymposium I on “Inversion on Non-linear Image Formation Models”, supported by a DAAD conference travel grant.
  In many real world situations, measured data is noisy and nonlinear, i.e., the data is given as values in a certain manifold. Examples are Interferometric Synthetic Aperture Radar (InSAR) images or the hue channel of HSV, where the entries are phase-valued, directions in \(\mathbb R^n\), which are data given on \(\mathbb S^{n-1}\), and diffusion tensor magnetic resonance imaging (DT-MRI), where the obtained pixel of the image are symmetric positive definite matrices.
  
  In this talk we extend the recently introduced total variation model on manifolds by a second order TV type model. We first introduce second order differences on manifolds in a sound way using the induced metric on Riemannian manifolds. By avoiding a definition involving tangent bundles, this definition allows for a minimization employing the inexact cyclic proximal point algorithm, where the proximal maps can be computed using Jacobian fields. The algorithm is then applied to several examples on the aforementioned manifolds to illustrate the efficiency of the algorithm.
  
  This is joint work with M. Bačák, J. Persch, G. Steidl, and A. Weinmann.
• A Second Order Non-smooth Variational Model for Restoring Manifold-valued images 25th Rhein-Main Arbeitskreis – Mathematics of Computation, July 10, 2015, Darmstadt, Germany Invited talk
  In many real world situations, measured data is noisy and nonlinear, i.e., the data is given as values in a certain manifold. Examples are InSAR images and the hue channel of HSV, where the entries are phase-valued, directions in \(R^n\), which are data given on \(S^{n-1}\), and diffusion tensor magnetic resonance imaging, where the obtained data items are symmetric positive definite matrices.
• A Graph Framework for Manifold-valued Data 87^thAnnual Meeting of the International Association of Applied Mathematics and Mechanics (Gesellschaft für angewandte Mathematik und Mechanik, GAMM), March 6—10, 2017 Weimar & Ilmenau A talk within the Session 21 on Image processing

Talks

2018

• A Variational Model for Data Fitting on Manifolds by Minimizing the Acceleration of a Bézier Curve Mecklenburg Workshop – Approximation Methods and Fast Algorithms, September 10—14, 2018 Hasenwinkel, Germany
  Fitting a smooth curve to data points $d_0,\dots,d_n$ lying on a Riemannian manifold $\mathcal M$ and associated with real-valued parameters $t_0,\dots,t_n$ is a common problem in applications like wind field approximation, rigid body motion interpolation, or sphere-valued data analysis. The resulting curve should strike a balance between data proximity and a smoothing regularization constraint.
  
  In this talk we present a variational model to fit a composite Bézier curve to the set of data points $d_0,\dots,d_n$ on a Riemannian manifold $\mathcal M$. The resulting curve is obtained in such a way that its mean squared acceleration is minimal in addition to remaining close the data points. We approximate the acceleration by discretizing the squared second order derivative along the curve. We derive a closed-form, numerically stable and efficient algorithm to compute the gradient of a Bézier curve on manifolds with respect to its control points. This gradient can be expressed as a concatenation of so called adjoint Jacobi fields. Several examples illustrate the capabilities of this approach both for interpolation and approximation.
• Variational Methods for Manifold-valued image Processing Seminar “Theory and Algorithms in Data Science” at the Alan Turing Institute, September 3, 2018, London, United Kingdom Invited talk and a week of research stay with M. Cucuringu and Hemant Tyagi.
  In many real life scenarios measured data appears as values from a Riemannian manifold. For example in interferometric Synthetic Aperture Radar (InSAR) data is given as a phase, in electron backscattered diffraction (EBSD) as data items being from a quotient of the orientation group SO(3), and in diffusion tensor magnetic resonance imaging (DT-MRI) the measured data are symmetric positive definite matrices. These data items are often measured on a pixel grid like usual images and they also suffer from the same measurement errors like noisy or incompleteness.Hence there is a need to perform image processing tasks like denoising, inpainting or segmentation on these manifold-valued images. Recently the ROF-Model for TV regularization has been transferred to the setting of manifold-valued images to perform such image processing tasks.
  
  In this talk we present methods and algorithms to compute the TV regularization for manifold-valued images efficiently using variational methods. We present generalizations to second order models, and to the case, where the data is not given on a pixel grid, for example when dealing with nonlocal methods.
• A parallel Douglas-Rachford Algorithm for Data on Hadamard Manifolds 23rd International Symposium on Mathematical Programming, July 1—6, 2018 Bordeaux, France Invited talk within the Session “Riemannian Geometry in Optimization for Learning” organized by N. Boumal.
  In many applications like DT-MRI or a data set of multivariate Gaussian distributions. Since these measurements suffer from errors or even loss of data, we aim to transfer image processing methods to manifold-valued data. In this talk we present a parallel Douglas-Rachford algorithm for manifold-valued data and proof its convergence to a minimizer for Hadamard manifolds of constant curvature. We illustrate the algorithm using the total variation regularization or ROF model and demonstrate the performance within the Manifold-Valued Image Restoration Toolbox (MVIRT).
• Nonlocal Inpainting of Manifold-valued Data on Finite Weighted Graphs SIAM Conference of Imaging Science 2018, June 5—8, 2018 Bologna, Italy Invited talk within the Session Minisymposium #31 “Variational Approaches for Regularizing Nonlinear Geometric Data”
  When dealing with manifold-valued data one faces the same challenging processing tasks as, e.g., in classical imaging. In this talk we consider image inpainting for manifold-valued data in which missing information have to be filled in suitably. We present a generalization of the graph infinity-Laplacian to manifold-valued data based on the min-max characterization of the local discrete Lipschitz constant. We derive a numerical scheme to solve the obtained manifold-valued infinity-Laplace equation and inpaint missing data.
• The Graph-Infinity Laplacian for Manifold-valued Data 88^thAnnual Meeting of the International Association of Applied Mathematics and Mechanics (Gesellschaft für angewandte Mathematik und Mechanik, GAMM), March 19—23, 2018 Munich, Germany
  Due to recent technological advances in the development of modern sensors new imaging modalities have emerged for which the acquired data values are given on a Riemannian manifold, e.g., in phase values in InSAR imaging or when dealing with diffusion tensors in DT-MRI. Furthermore, to process not only rectangular domains and regular grids, graphs can be employed to model both data on arbitrary (sampled) manifolds as well as nonlocal vicinity.
  
  In this talk we extend a framework for processing discrete manifold-valued data to the task of inpainting missing values, such that the inpainted area nonlocally incorporates data into the reconstruction. We discuss a generalization of the graph infinity-Laplacian to manifold-valued data based on the min-max characterization of the local discrete Lipschitz constant. Finally, we present a numerical scheme to solve the obtained manifold-valued infinity-Laplace equation.

2017

• Nonlocal Inpainting of Manifold-valued Data on Finite Weighted Graphs 3^rd Conference on Geometric Science of Information, November 7—9, 2017 Paris, France Contributed talk within the session “Optimization on Manifolds” organized by P.-A. Absil and R. Sepulchre.
  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 task of denoising has been extensively studied in the last years, there was rarely an attempt to perform image inpainting on manifold-valued data. In this paper we present a nonlocal inpainting method for manifold-valued data given on a finite weighted graph. We introduce a new graph infinity-Laplace operator based on the idea of discrete minimizing Lipschitz extensions, which we use to formulate the inpainting problem as PDE on the graph. Furthermore, we derive an explicit numerical solving scheme, which we evaluate on two classes of synthetic manifold-valued images.
• MVIRT – A Toolbox for Manifold-valued Image Restoration IEEE International Conference on Image Processing (ICIP) 2017, September 17—20, 2017 Bejing, China Invited talk within the Special Session “Trends in Statistical Analysis of Manifold-Valued Data – Theory and Applications to Imaging”, supported by a DAAD conference travel grant
  In many real life application measured data takes its values on Riemannian manifolds. For the special case of the Euclidean space this setting includes the classical grayscale and color images. Like these classical images, manifold-valued data might suffer from measurement errors in form of noise or missing data. In this talk we present the manifold-valued image restoration toolbox (MVIRT) that provides implementations of classical image processing tasks. Based on recent developments in variational methods for manifold-valued image processing methods, like total variation regularization, the toolbox provides easy access to work with these algorithms. The toolbox is implemented in Matlab, open source, and easily extendible, e.g. with own manifolds, noise models or further algorithms. This paper introduces the main mathematical methods as well as numerical examples.
• A Graph Framework for Manifold-valued Data Kolloquium angewandte Mathematik at the Institute of Computational and Applied Mathematics, WWU Münster., June 26, 2017, Münster, Germany Invited talk and research stay within the research group of B. Wirth.
  In many real-world applications measured data are not in a Euclidean vector space but rather are given on a Riemannian manifold. This is the case, e.g., when dealing with Interferometric Synthetic Aperture Radar (InSAR) data consisting of phase values or data obtained in Diffusion Tensor Magnetic Resonance Imaging (DT-MRI). In this talk we present a framework for processing discrete manifold-valued data, for which the underlying (sampling) topology is modeled by a graph. We introduce the notion of a manifold-valued differences on a graph and based on this deduce a family of manifold-valued graph operators. In particular, we introduce the graph p-Laplacian and graph infinity-Laplacian for manifold-valued data. We discuss a numerical scheme to compute a solution to the corresponding parabolic PDEs and apply this algorithm to different manifold-valued data, illustrating the diversity and flexibility of the proposed framework in denoising and inpainting applications. This is joint work with Daniel Tenbrinck (WWU Münster)
• Infimal Convolution Coupling of First and Second Order Differences on Manifold-Valued Images 6^th Internvational Conference on Scale Space and Variational Methods in Computer Vision, June 4—8, 2017 Kolding, Denmark
• Variational Models for Manifold-valued Image Processing Seminars in Mathematical Engineering of the ICTEAM at Université catolique de Louvain, March 21, 2017, Louvain-la-Neuve, Belgium Invited talk and a week of research stay with the group of P.-A. Absil.
• A Graph Framework for Manifold-valued Data 87^thAnnual Meeting of the International Association of Applied Mathematics and Mechanics (Gesellschaft für angewandte Mathematik und Mechanik, GAMM), March 6—10, 2017 Weimar & Ilmenau A talk within the Session 21 on Image processing

2016

• A Second Order Non-smooth Variational Model for Restoring Manifold-valued Image Mecklenburg Workshop – Approximation Methods and Data Analysis, September 5—9, 2016 Hasenwinkel, Germany
• Second Order TV-Type Regularization Methods for Manifold-Valued Images SIAM Conference of Imaging Sciences 2016, May 23—26, 2016 Albuquerque, NM, USA Invited talk within the Minisymposium I on “Inversion on Non-linear Image Formation Models”, supported by a DAAD conference travel grant.
  In many real world situations, measured data is noisy and nonlinear, i.e., the data is given as values in a certain manifold. Examples are Interferometric Synthetic Aperture Radar (InSAR) images or the hue channel of HSV, where the entries are phase-valued, directions in \(\mathbb R^n\), which are data given on \(\mathbb S^{n-1}\), and diffusion tensor magnetic resonance imaging (DT-MRI), where the obtained pixel of the image are symmetric positive definite matrices.
  
  In this talk we extend the recently introduced total variation model on manifolds by a second order TV type model. We first introduce second order differences on manifolds in a sound way using the induced metric on Riemannian manifolds. By avoiding a definition involving tangent bundles, this definition allows for a minimization employing the inexact cyclic proximal point algorithm, where the proximal maps can be computed using Jacobian fields. The algorithm is then applied to several examples on the aforementioned manifolds to illustrate the efficiency of the algorithm.
  
  This is joint work with M. Bačák, J. Persch, G. Steidl, and A. Weinmann.
• A Second Order Non-smooth Variational Model for Restoring Manifold-valued Image Seminar AG Imaging at the Imaging Workgroup, Institute of Computational and Applied Mathematics, May 11, 2016, Münster, Germany Invited talk and a week research stay with D. Tenbrinck.
  In many real world situations, measured data is noisy and nonlinear, i.e., the data is given as values in a certain manifold or on a submanifold of the euclidean space the measurements are taken in. Examples are InSAR images and the hue channel of HSV, where the entries are phase-valued, directions in \(\mathbb R n\), which are data given on sphere \(\mathbb S^{n−1}\), and diffusion tensor magnetic resonance imaging, where the obtained data items are symmetric positive definite \(3\times 3\) matrices. In this talk we extend the recently introduced total variation model on manifolds by a second order TV type model. We first introduce second order differences on manifolds in a sound way using the induced metric on Riemannian manifolds. By avoiding a definition involving tangent bundles, this definition allows for a minimization employing the inexact cyclic proximal point algorithm, where the proximal maps can be computed using Jacobian fields. The algorithm is then applied to several examples on the aforementioned manifolds to illustrate the efficiency of the algorithm.
• A Second Order Non-smooth Variational Model for Restoring Manifold-valued images 37^th Northern German Colloquium on Applied Analysis and Numerical Mathematics, April 22—23, 2016 Lübeck, Germany
• A Second Order Non-smooth Variational Model for Restoring Manifold-valued images 86^thAnnual Meeting of the International Association of Applied Mathematics and Mechanics (Gesellschaft für angewandte Mathematik und Mechanik, GAMM), March 7—11, 2016 Braunschweig, Germany Invited talk within the Young Researchers Minisymposium YR 3 “Dedicated regularization for variational image processing”

2015

• A Second Order Non-smooth Variational Model for Restoring Manifold-valued images Variational Methods for Dynamic Inverse Problems and imaging, September 28—30, 2015 Münster, Germany
• A Second Order Non-smooth Variational Model for Restoring Manifold-valued images 25th Rhein-Main Arbeitskreis – Mathematics of Computation, July 10, 2015, Darmstadt, Germany Invited talk
  In many real world situations, measured data is noisy and nonlinear, i.e., the data is given as values in a certain manifold. Examples are InSAR images and the hue channel of HSV, where the entries are phase-valued, directions in \(R^n\), which are data given on \(S^{n-1}\), and diffusion tensor magnetic resonance imaging, where the obtained data items are symmetric positive definite matrices.
• The anisotropic Strang-Fix conditions Mecklenburger Workshop – Approximation Methods and Function Spaces, March 16—20, 2015 Hasenwinkel, Germany
• Second Order Differences for Combined Cyclic and Vector Space Data and their Application to Denoising and Inpainting Cambridge Image Analysis seminars, March 4, 2015, Cambridge, United Kingdom Invited talk and a week research stay with J. Lellmann
• Inpainting and Denoising of Cyclic Data Using First and Second Order Differences Seminar of the Institute of Computational Biology, Helmholtzzentrum München, February 18, 2015, Munich, Germany Invited talk and research stay with M. Bačák and A. Weinmann
• Inpainting of Cyclic Data using First and Second Order Differences 10th International Conference on Energy Minimizing Methods in Computer Vision and Pattern Recognition, January 13—16, 2015 Hong Kong, China
  Cyclic data arise in various image and signal processing applications such as interferometric synthetic aperture radar, electroencephalogram data analysis, and color image restoration in HSV or LCh spaces. In this paper we introduce a variational inpainting model for cyclic data which utilizes our definition of absolute cyclic second order differences. Based on analytical expressions for the proximal mappings of these differences we propose a cyclic proximal point algorithm (CPPA) for minimizing the corresponding functional. We choose appropriate cycles to implement this algorithm in an efficient way. We further introduce a simple strategy to initialize the unknown inpainting region. Numerical results both for synthetic and real-world data demonstrate the performance of our algorithm.

2014

• Second Order Differences of Cyclic Data and Applications in Variational Denoising Deutsch-französischer Workshop Mathematische Bildverarbeitung, October 6—8, 2014 Fraunhofer ITWM, Kaiserslautern, Germany
• Second Order Differences of Cyclic Data and Applications in Variational Denoising Mathematical Image Processing and Phase Retrieval, September 1—3, 2014 Göttingen, Germany
• Second Order Differences of Cyclic Data and Application to Variational Denoising Seminar of the Institute of Computational Biology, Helmholtzzentrum München, May 14, 2014, Munich, Germany Invited talk and research stay with A. Weinmann
• Multivariate anisotrope Interpolation auf dem Torus Mecklenburger Workshop – Approximationsmethoden und schnelle Algorithmen, March 17—20, 2014 Hasenwinkel, Germany
• Multivariate Anisotropic periodic Wavelets 85^thAnnual Meeting of the International Association of Applied Mathematics and Mechanics (Gesellschaft für angewandte Mathematik und Mechanik, GAMM), March 10—14, 2014 Erlangen, Germany

2013

• Multivariate Anisotropic Wavelets on the Torus Workshop on Advances in Image Processing, September 30—October 2, 2013 Anweiler am Trifels, Germany
• Multivariate anisotrope Wavelets auf dem Torus Mecklenburger Workshop — Approximationsmethoden und schnelle Algorithmen, June 20—23, 2013 Hasenwinkel, Germany
• Multivariate anisotrope Wavelets auf dem Torus 32. Norddeutsches Kolloquium über angewandte Analysis und Numerische Mathematik, May 3—4, 2013 Clausthal, Germany
• Die multivariate anisotropen Wavelet-Transformation auf dem Torus Kolloquiumsvortrag, Image Processing and Data Analysis Group, April 8, 2013, Kaiserslautern, Germany

2012

• The multivariate anisotropic Wavelet Transform on the Torus Workshop on Mathematics for Life Sciences, September 3—14, 2012 Kiev, Ukraine

2011

• Die multivariate periodische Wavelet-Transformation 32. Norddeutsches Kolloquium über angewandte Analysis und Numerische Mathematik, May 27—28, 2011 Institut für Mathematik, Universität Osnabrück, Osnabrück
  Für periodische Wavelets im eindimensionalen Fall ist seit Mitte der 1990er Jahre eine umfassende Theorie bekannt. Dieser Vortrag stellt die multivariate Verallgemeinerung vor. Ausgehend von anisotropen gleichmäßigen Mustern auf dem $d$-dimensionalen Torus wird eine diskrete Fourier-Transformation definiert. Dies führt zu diskreten Frequenzmengen – die erzeugende Gruppe –, die bestimmte Richtungen bevorzugen und trotzdem schnelle Algorithmen ermöglichen. Dazu ist es notwendig, eine bestimmte Anordnung der Musterpunkte, sowie der erzeugenden Gruppe, zu finden. Die darauf aufbauende Wavelet-Zerlegung wird für den Spezialfall einer dyadischen Zerlegung präsentiert. Sie zerlegt einen Raum von Translaten in zwei zueinander orthogonale Unterräume mit jeweils halber Dimension des Ursprungsraumes. Auch hier ist eine schnelle Implementierung möglich, wenn man für die Elemente der erzeugenden Gruppe eine entsprechende Anordnung wählt.
• Multivariate translationsinvariante Räume 21. Rhein-Ruhr Workshop, February 11, 2011, Königswinter, Germany
• Multivariate Periodic Function Spaces Sparse Representations and Efficitent Sensing of Data, February 3, 2011, Dagstuhl Seminar, Dagstuhl, Germany

2009

• Drawing Hypergraphs using NURBS curves Presentation of my diploma thesis, September 16, 2009, TU Bergakademie Freiberg, Freiberg, Germany

Other Conferences

Mathematics and Image Analysis 2018 (MIA 2018),

January 15—17, 2018, Berlin, Germany.

Rhein-Main-Arbeitskreis Mathematics of Computation,

July 7, 2017, Mannheim, Germany.

Workshop: Shape, Images and Optimization,

February 28—March 3, 2017, Münster, Germany.

Project Meeting of the Marie Curie Inital Training Network Scheme: INTREPID Forensics,

February 5, 2016, Leicester, United Kingdom.

Summer School on Applied Analysis 2015,

September 21—25, 2015, Chemnitz, Germany.

5^th International Conference on Scale Space and Variational Methods in Computer Vision (SSVM 2013),

May 30—June 4, 2015, Bordeaux, France.

Workshop “Optimisation Géométrique sur les Variétés”,

November 21, 2014, Paris, France.

Colloquium Commemorating Bernd Fischer,

October 10, 2014, Lübeck, Gemany.

Summer School on Applied Analysis 2014,

September 22—26, 2014, Chemnitz, Germany.

Mathematik in Medizin und Lebenswissenschaften,

May 1, 2014, Lübeck, Germany, Meeting on occasion of the 20^th birthday of the Institute of Mathematics at the University of Lübeck..

Rhein-Main-Arbeitskreis Mathematics of Computation,

February 7, 2014, Marburg, Germany.

Summer School on Applied Analysis 2013,

September 23—27, 2013, Chemnitz, Germany.

Summer School on Applied Analysis 2012,

September 24—28, 2012, Chemnitz, Germany.

33. Norddeutsches Kolloquium über Angewandte Analysis und Numerische Mathematik,

May 4—5, 2012, Rostock, Germany.

22. Rhein-Rhuhr-Workshop,

February 3—4, 2012, Bestwig, Germany.

28th GAMM-Seminar Leipzig on Analysis and Numerical Methods in Higher Dimension,

January 16—18, 2012, Leipzig, Germany.

Summer School on Applied Analysis 2011,

September 26—30, 2011, Chemnitz, Germany.

1^st Workshop: A Computational Approach to Harmonic Analysis,

August 22—26, 2011, Marburg, Germany.

From Abstract to Computational Harmonic Analysis,

June 13—19, 2011, Strobl, Austria.

Summer School on Applied Analysis 2010,

October 4—8, 2010, Chemnitz, Germany.

20. Rhein-Rhuhr-Workshop,

February 12—13, 2010, Burg Gemen, Germany.