A5026483039- Medical Image Segmentation Techniques
- Adversarial Robustness in Machine Learning
- Image and Signal Denoising Methods
- Anomaly Detection Techniques and Applications
- Medical Imaging Techniques and Applications
- Topological and Geometric Data Analysis
- Neural Networks and Applications
- Sparse and Compressive Sensing Techniques
- Point processes and geometric inequalities
- Gaussian Processes and Bayesian Inference
- Advanced Differential Geometry Research
- Fault Detection and Control Systems
- Advanced Mathematical Modeling in Engineering
- Advanced Neural Network Applications
- Image and Object Detection Techniques
- Ultrasound Imaging and Elastography
- Advanced MRI Techniques and Applications
- Advanced Vision and Imaging
- Elasticity and Material Modeling
- Mathematical Biology Tumor Growth
- AI in cancer detection
- Advanced Numerical Analysis Techniques
- Mathematical Inequalities and Applications
- Stochastic Gradient Optimization Techniques
- Domain Adaptation and Few-Shot Learning
Friedrich-Alexander-Universität Erlangen-Nürnberg
2019-2024
University of Münster
2010-2018
École Nationale Supérieure d'Ingénieurs de Caen
2014-2015
GREYC
2014-2015
Centre National de la Recherche Scientifique
2014-2015
University Hospital Münster
2014
In this paper we introduce a new family of partial difference operators on graphs and study equations involving these operators. This covers local variational $p$-Laplacian, $\infty$-Laplacian, nonlocal $p$-Laplacian with gradient terms, used in morphology based the differential equation. We analyze corresponding parabolic equation which enables us to interpolate adaptively between diffusion-based filtering morphological filtering, i.e., erosion dilation. Then, consider elliptic its...
Graph-based methods have been proposed as a unified framework for discrete calculus of local and nonlocal image processing in the recent years. In order to translate variational models partial differential equations graph, certain operators investigated successfully applied real-world applications involving graph models. So far has limited real- vector-valued functions on Euclidean domains. this paper we generalize model case manifold-valued data. We introduce basic needed formulate discuss...
Abstract This paper introduces a new notion of Fenchel conjugate, which generalizes the classical conjugation to functions defined on Riemannian manifolds. We investigate its properties, e.g., Fenchel–Young inequality and characterization convex subdifferential using analogue Fenchel–Moreau Theorem. These properties conjugate are employed derive primal-dual optimization algorithm prove convergence for case Hadamard manifolds under appropriate assumptions. Numerical results illustrate...
In this work, we present an alternative formulation of the higher eigenvalue problem associated to infinity Laplacian, which opens door for numerical approximation eigenfunctions. A rigorous analysis is performed show equivalence new traditional one. Subsequently, consistent monotone schemes approximate ground states and eigenfunctions on grids. We prove that our method converges (up a subsequence) viscosity solution problem, perform experiments investigate theoretical conjectures compute...
Segmentation is an essential task in ultrasound image analysis. Recently, the trend literature towards incorporation of high-level information, e.g., shape priors, since many low-level segmentation techniques suffer from characteristics medical images, i.e., speckle noise, scattering artifacts, and shadowing effects. However, majority these works implicitly assume additive Gaussian noise model although a strong deviation this assumption well known, impact correct physical modeling not...
Migrating cells can serve as probes for determining tissue properties in live embryos.
The vulnerability of deep neural networks to small and even imperceptible perturbations has become a central topic in learning research. Although several sophisticated defense mechanisms have been introduced, most were later shown be ineffective. However, reliable evaluation model robustness is mandatory for deployment safety-critical scenarios. To overcome this problem we propose simple yet effective modification the gradient calculation state-of-the-art first-order adversarial attacks....
In recent years new application areas have emerged in which one aims to capture the geometry of objects by means three-dimensional point clouds. Often obtained data consist a dense sampling object's surface, containing many redundant 3D points. These unnecessary samples lead high computational effort subsequent processing steps. Thus, cloud sparsification or compression is often applied as preprocessing step. The two standard methods compress clouds are random subsampling and approximation...
Computer-assisted processing and interpretation of medical ultrasound images is one the most challenging tasks within image analysis. Physical phenomena in ultrasonographic images, e.g., characteristic speckle noise shadowing effects, make majority standard methods from analysis non optimal. Furthermore, validation adapted computer vision proves to be difficult due missing ground truth information. There no widely accepted software phantom community existing phantoms are not exible enough...
We propose a learning framework based on stochastic Bregman iterations, also known as mirror descent, to train sparse neural networks with an inverse scale space approach. derive baseline algorithm called LinBreg, accelerated version using momentum, and AdaBreg, which is Bregmanized generalization of the Adam algorithm. In contrast established methods for training proposed family algorithms constitutes regrowth strategy that solely optimization-based without additional heuristics. Our starts...
Abstract The aim of this paper is to revisit the definition differential operators on hypergraphs, which are a natural extension graphs in systems based interactions beyond pairs. In particular, we focus Laplacian and p -Laplace for oriented unoriented their basic properties, variational structure, scale spaces. We illustrate that diffusion equations hypergraphs possible models different applications such as information flow social networks or image processing. Moreover, spectral analysis...