15 results on '"Martin Burger"'
Search Results
2. Resolution-Invariant Image Classification Based on Fourier Neural Operators
- Author
-
Samira Kabri, Tim Roith, Daniel Tenbrinck, and Martin Burger
- Published
- 2023
- Full Text
- View/download PDF
3. Nonlinear spectral image fusion
- Author
-
Daniel Cremers, Carola-Bibiane Schönlieb, Martin Burger, Raz Z. Nossek, Martin Benning, Guy Gilboa, and Michael Möller
- Subjects
FOS: Computer and information sciences ,Poisson image editing ,Computer science ,Computer Vision and Pattern Recognition (cs.CV) ,G.1.6 ,Computer Science - Computer Vision and Pattern Recognition ,G.1.8 ,G.1.3 ,02 engineering and technology ,Image editing ,35P30, 62H35, 65M70, 94A08 ,computer.software_genre ,01 natural sciences ,Regularization (mathematics) ,Image (mathematics) ,FOS: Mathematics ,0202 electrical engineering, electronic engineering, information engineering ,Image fusion ,Computer vision ,Mathematics - Numerical Analysis ,0101 mathematics ,Multiscale methods ,Feature detection (computer vision) ,I.4.0 ,Image composition ,business.industry ,I.4.5 ,Numerical Analysis (math.NA) ,Total variation regularization ,Total variation denoising ,010101 applied mathematics ,Face (geometry) ,Computer Science::Computer Vision and Pattern Recognition ,Nonlinear spectral decomposition ,020201 artificial intelligence & image processing ,Artificial intelligence ,business ,computer - Abstract
In this paper we demonstrate that the framework of nonlinear spectral decompositions based on total variation (TV) regularization is very well suited for image fusion as well as more general image manipulation tasks. The well-localized and edge-preserving spectral TV decomposition allows to select frequencies of a certain image to transfer particular features, such as wrinkles in a face, from one image to another. We illustrate the effectiveness of the proposed approach in several numerical experiments, including a comparison to the competing techniques of Poisson image editing, linear osmosis, wavelet fusion and Laplacian pyramid fusion. We conclude that the proposed spectral TV image decomposition framework is a valuable tool for semi- and fully-automatic image editing and fusion., 13 pages, 9 figures, submitted to SSVM conference proceedings 2017
- Published
- 2017
- Full Text
- View/download PDF
4. Continuum Modeling of Biological Network Formation
- Author
-
Giacomo Albi, Jan Haskovec, Peter A. Markowich, Martin Burger, and Matthias Schlottbom
- Subjects
non-convex optimization ,Mesoscopic physics ,Partial differential equation ,Discretization ,010102 general mathematics ,Mathematical analysis ,Relaxation (iterative method) ,Biological Network ,01 natural sciences ,Finite element method ,numerical modeling ,reaction-diffusion equations ,Biological Network, numerical modeling, reaction-diffusion equations, non-convex optimization ,0103 physical sciences ,Reaction–diffusion system ,0101 mathematics ,010306 general physics ,Continuum Modeling ,Randomness ,Mathematics - Abstract
We present an overview of recent analytical and numerical results for the elliptic–parabolic system of partial differential equations proposed by Hu and Cai, which models the formation of biological transportation networks. The model describes the pressure field using a Darcy type equation and the dynamics of the conductance network under pressure force effects. Randomness in the material structure is represented by a linear diffusion term and conductance relaxation by an algebraic decay term. We first introduce micro- and mesoscopic models and show how they are connected to the macroscopic PDE system. Then, we provide an overview of analytical results for the PDE model, focusing mainly on the existence of weak and mild solutions and analysis of the steady states. The analytical part is complemented by extensive numerical simulations. We propose a discretization based on finite elements and study the qualitative properties of network structures for various parameter values.
- Published
- 2017
- Full Text
- View/download PDF
5. First Order Algorithms in Variational Image Processing
- Author
-
Martin Burger, Gabriele Steidl, and Alex Sawatzky
- Subjects
Sequence ,Efficient algorithm ,Regular polygon ,Structure (category theory) ,Image processing ,02 engineering and technology ,First order ,030218 nuclear medicine & medical imaging ,03 medical and health sciences ,0302 clinical medicine ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Algorithm ,Mathematics - Abstract
The success of non-smooth variational models in image processing is heavily based on efficient algorithms. Taking into account the specific structure of the models as sum of different convex terms, splitting algorithms are an appropriate choice. Their strength consists in the splitting of the original problem into a sequence of smaller proximal problems which are easy and fast to compute.
- Published
- 2016
- Full Text
- View/download PDF
6. Bregman Distances in Inverse Problems and Partial Differential Equations
- Author
-
Martin Burger
- Subjects
Mathematical optimization ,Partial differential equation ,Numerical analysis ,010102 general mathematics ,Structure (category theory) ,Image processing ,010103 numerical & computational mathematics ,Bregman divergence ,Inverse problem ,01 natural sciences ,Nonlinear system ,Development (topology) ,Applied mathematics ,0101 mathematics ,Mathematics - Abstract
The aim of this paper is to provide an overview of recent development related to Bregman distances outside its native areas of optimization and statistics. We discuss approaches in inverse problems and image processing based on Bregman distances, which have evolved to a standard tool in these fields in the last decade. Moreover, we discuss related issues in the analysis and numerical analysis of nonlinear partial differential equations with a variational structure. For such problems Bregman distances appear to be of similar importance, but are currently used only in a quite hidden fashion. We try to work out explicitly the aspects related to Bregman distances, which also lead to novel mathematical questions and may also stimulate further research in these areas.
- Published
- 2016
- Full Text
- View/download PDF
7. Infimal Convolution Regularisation Functionals of $$\mathrm {BV}$$ and $$\mathrm {L}^{p}$$ Spaces. The Case $$p=\infty $$
- Author
-
Carola-Bibiane Schönlieb, Evangelos Papoutsellis, Martin Burger, Konstantinos Papafitsoros, University of Münster, Weierstraß-Institut für Angewandte Analysis und Stochastik = Weierstrass Institute for Applied Analysis and Stochastics [Berlin] (WIAS), Forschungsverbund Berlin e.V. (FVB) (FVB), Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO), Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), University of Cambridge [UK] (CAM), Lorena Bociu, Jean-Antoine Désidéri, Abderrahmane Habbal, and TC 7
- Subjects
Discrete mathematics ,Total variation ,Denoising ,Staircasing ,Infimal convolution ,010103 numerical & computational mathematics ,01 natural sciences ,$$\mathrm {L}^{\infty }$$ norm ,General family ,010101 applied mathematics ,Combinatorics ,Norm (mathematics) ,[INFO]Computer Science [cs] ,Piecewise affine ,0101 mathematics ,Mathematics - Abstract
International audience; In this paper we analyse an infimal convolution type regularisation functional called $$\mathrm {TVL}^{\infty }$$, based on the total variation ($$\mathrm {TV}$$) and the $$\mathrm {L}^{\infty }$$ norm of the gradient. The functional belongs to a more general family of $$\mathrm {TVL}^{p}$$ functionals ($$1
- Published
- 2016
- Full Text
- View/download PDF
8. Regularization with Sparse Vector Fields: From Image Compression to TV-type Reconstruction
- Author
-
Joana Sarah Grah, Eva-Maria Brinkmann, and Martin Burger
- Subjects
business.industry ,Inpainting ,Regularization (mathematics) ,Edge detection ,Image (mathematics) ,Feature (computer vision) ,Computer Science::Computer Vision and Pattern Recognition ,Compression (functional analysis) ,Computer vision ,Artificial intelligence ,business ,Algorithm ,Laplace operator ,Image compression ,Mathematics - Abstract
This paper introduces a novel variational approach for image compression motivated by recent PDE-based approaches combining edge detection and Laplacian inpainting. The essential feature is to encode the image via a sparse vector field, ideally concentrating on a set of measure zero. An equivalent reformulation of the compression approach leads to a variational model resembling the ROF-model for image denoising, hence we further study the properties of the effective regularization functional introduced by the novel approach and discuss similarities to TV and TGV functionals. Moreover we computationally investigate the behaviour of the model with sparse vector fields for compression in particular for high resolution images and give an outlook towards denoising.
- Published
- 2015
- Full Text
- View/download PDF
9. Spectral Representations of One-Homogeneous Functionals
- Author
-
Martin Burger, Michael Moeller, Guy Gilboa, and Lina Eckardt
- Subjects
Parseval's identity ,Pure mathematics ,Hilbert space ,Regular polygon ,02 engineering and technology ,Eigenfunction ,01 natural sciences ,Scale space ,010101 applied mathematics ,symbols.namesake ,Fourier transform ,Wavelet ,Norm (mathematics) ,0202 electrical engineering, electronic engineering, information engineering ,symbols ,020201 artificial intelligence & image processing ,0101 mathematics ,Mathematics - Abstract
This paper discusses a generalization of spectral representations related to convex one-homogeneous regularization functionals, e.g. total variation or \(\ell ^1\)-norms. Those functionals serve as a substitute for a Hilbert space structure (and the related norm) in classical linear spectral transforms, e.g. Fourier and wavelet analysis. We discuss three meaningful definitions of spectral representations by scale space and variational methods and prove that (nonlinear) eigenfunctions of the regularization functionals are indeed atoms in the spectral representation. Moreover, we verify further useful properties related to orthogonality of the decomposition and the Parseval identity.
- Published
- 2015
- Full Text
- View/download PDF
10. Optimal Control of Self-Consistent Classical and Quantum Particle Systems
- Author
-
René Pinnau, Marcisse Fouego, Sebastian Rau, and Martin Burger
- Subjects
Classical capacity ,Physics ,Quantum dynamics ,Quantum process ,Quantum operation ,Quantum algorithm ,Statistical physics ,Quantum dissipation ,Amplitude damping channel ,Quantum chaos - Abstract
We study optimal control problems for self-consistent interacting classical and quantum particle systems from the analytical and numerical point of view. This involves microscopic as well as macroscopic quantum models, which have two main features in common: The control enters in a bilinear manner into the partial differential equations and in all models particle interaction takes place via a self-consistent electrostatic potential. This special model structure appears in many different types of applications, like quantum semiconductor devices, optimal quantum control or biomedical applications and it is used to construct fast optimization algorithms.
- Published
- 2014
- Full Text
- View/download PDF
11. Registration of Noisy Images via Maximum A-Posteriori Estimation
- Author
-
Daniel Tenbrinck, Martin Burger, Sebastian Suhr, and Jan Modersitzki
- Subjects
Statistical noise ,business.industry ,Computer science ,Dynamic imaging ,Physics::Medical Physics ,ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION ,Image registration ,Imaging phantom ,Synthetic data ,Noise ,Robustness (computer science) ,Computer Science::Computer Vision and Pattern Recognition ,Maximum a posteriori estimation ,Computer vision ,Artificial intelligence ,business - Abstract
Biomedical image registration faces challenging problems induced by the image acquisition process of the involved modality. A common problem is the omnipresence of noise perturbations. A low signal-to-noise ratio – like in modern dynamic imaging with short acquisition times – may lead to failure or artifacts in standard image registration techniques. A common approach to deal with noise in registration is image presmoothing, which may however result in bias or loss of information. A more reasonable alternative is to directly incorporate statistical noise models into image registration. In this work we present a general framework for registration of noise perturbed images based on maximum a-posteriori estimation. This leads to variational registration inference problems with data fidelities adapted to the noise characteristics, and yields a significant improvement in robustness under noise impact and parameter choices. Using synthetic data and a popular software phantom we compare the proposed model to conventional methods recently used in biomedical imaging and discuss its potential advantages.
- Published
- 2014
- Full Text
- View/download PDF
12. Level Set and PDE Based Reconstruction Methods in Imaging
- Author
-
Martin Burger, Stanley Osher, Martin Rumpf, and Andrea Mennucci
- Subjects
Level set (data structures) ,business.industry ,Computer science ,Pattern recognition ,Artificial intelligence ,business ,Reconstruction method - Published
- 2013
- Full Text
- View/download PDF
13. EM-TV Methods for Inverse Problems with Poisson Noise
- Author
-
Thomas Kosters, Christoph Brune, Frank Wübbeling, Alex Sawatzky, and Martin Burger
- Subjects
symbols.namesake ,Signal processing ,Computer science ,Discrete Poisson equation ,symbols ,Shot noise ,Deconvolution ,Bregman divergence ,Total variation denoising ,Inverse problem ,Poisson distribution ,Algorithm - Abstract
We address the task of reconstructing images corrupted by Poisson noise, which is important in various applications such as fluorescence microscopy (Dey et al., 3D microscopy deconvolution using Richardson-Lucy algorithm with total variation regularization, 2004), positron emission tomography (PET; Vardi et al., J Am Stat Assoc 80:8–20, 1985), or astronomical imaging (Lanteri and Theys, EURASIP J Appl Signal Processing 15:2500–2513, 2005). Here we focus on reconstruction strategies combining the expectation-maximization (EM) algorithm and total variation (TV) based regularization, and present a detailed analysis as well as numerical results. Recently extensions of the well known EM/Richardson-Lucy algorithm received increasing attention for inverse problems with Poisson data (Dey et al., 3D microscopy deconvolution using Richardson-Lucy algorithm with total variation regularization, 2004; Jonsson et al., Total variation regularization in positron emission tomography, 1998; Panin et al., IEEE Trans Nucl Sci 46(6):2202–2210, 1999). However, most of these algorithms for regularizations like TV lead to convergence problems for large regularization parameters, cannot guarantee positivity, and rely on additional approximations (like smoothed TV). The goal of this lecture is to provide accurate, robust and fast EM-TV based methods for computing cartoon reconstructions facilitating post-segmentation and providing a basis for quantification techniques. We illustrate also the performance of the proposed algorithms and confirm the analytical concepts by 2D and 3D synthetic and real-world results in optical nanoscopy and PET.
- Published
- 2013
- Full Text
- View/download PDF
14. A Guide to the TV Zoo
- Author
-
Martin Burger and Stanley Osher
- Subjects
Computer science ,Total variation minimization ,Image processing ,Variation (game tree) ,Total variation denoising ,Inverse problem ,Bregman divergence ,Data science ,Field (computer science) ,Task (project management) - Abstract
Total variation methods and similar approaches based on regularizations with l 1-type norms (and seminorms) have become a very popular tool in image processing and inverse problems due to peculiar features that cannot be realized with smooth regularizations. In particular total variation techniques had particular success due to their ability to realize cartoon-type reconstructions with sharp edges. Due to an explosion of new developments in this field within the last decade it is a difficult task to keep an overview of the major results in analysis, the computational schemes, and the application fields. With these lectures we attempt to provide such an overview, of course biased by our major lines of research. We are focusing on the basic analysis of total variation methods and the extension of the original ROF-denoising model due various application fields. Furthermore we provide a brief discussion of state-of-the art computational methods and give an outlook to applications in different disciplines.
- Published
- 2013
- Full Text
- View/download PDF
15. Computing Nonlinear Eigenfunctions via Gradient Flow Extinction
- Author
-
Martin Burger, Daniel Tenbrinck, and Leon Bungert
- Subjects
Work (thermodynamics) ,Computation ,02 engineering and technology ,Eigenfunction ,01 natural sciences ,010101 applied mathematics ,Nonlinear system ,Extinction (optical mineralogy) ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,020201 artificial intelligence & image processing ,0101 mathematics ,Balanced flow ,Clustering coefficient ,Mathematics - Abstract
In this work we investigate the computation of nonlinear eigenfunctions via the extinction profiles of gradient flows. We analyze a scheme that recursively subtracts such eigenfunctions from given data and show that this procedure yields a decomposition of the data into eigenfunctions in some cases as the 1-dimensional total variation, for instance. We discuss results of numerical experiments in which we use extinction profiles and the gradient flow for the task of spectral graph clustering as used, e.g., in machine learning applications.
- Full Text
- View/download PDF
Catalog
Discovery Service for Jio Institute Digital Library
For full access to our library's resources, please sign in.