Andreas Weinmann

Martin Storath, Andreas Weinmann, Jürgen Frikel et al.

We propose a new algorithmic approach to the non-smooth and non-convex Potts problem (also called piecewise-constant Mumford-Shah problem) for inverse imaging problems. We derive a suitable splitting into specific subproblems that can all be solved efficiently. Our method does not require a priori knowledge on the gray levels nor on the number of segments of the reconstruction. Further, it avoids anisotropic artifacts such as geometric staircasing. We demonstrate the suitability of our method for joint image reconstruction and segmentation. We focus on Radon data, where we in particular consider limited data situations. For instance, our method is able to recover all segments of the Shepp-Logan phantom from $7$ angular views only. We illustrate the practical applicability on a real PET dataset. As further applications, we consider spherical Radon data as well as blurred data.

Martin Storath, Andreas Weinmann, Michael Unser

We consider $L^1$-TV regularization of univariate signals with values on the real line or on the unit circle. While the real data space leads to a convex optimization problem, the problem is non-convex for circle-valued data. In this paper, we derive exact algorithms for both data spaces. A key ingredient is the reduction of the infinite search spaces to a finite set of configurations, which can be scanned by the Viterbi algorithm. To reduce the computational complexity of the involved tabulations, we extend the technique of distance transforms to non-uniform grids and to the circular data space. In total, the proposed algorithms have complexity $\mathscr{O}(KN)$ where $N$ is the length of the signal and $K$ is the number of different values in the data set. In particular, the complexity is $\mathscr{O}(N)$ for quantized data. It is the first exact algorithm for TV regularization with circle-valued data, and it is competitive with the state-of-the-art methods for scalar data, assuming that the latter are quantized.

Miroslav Bačák, Ronny Bergmann, Gabriele Steidl et al.

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 were successfully applied for real-valued images, we introduce the second order difference and the corresponding variational models for manifold data, which up to now only existed for cyclic data. The approach requires a combination of techniques from numerical analysis, convex optimization and differential geometry. First, we establish a suitable definition of absolute second order differences for signals and images with values in a manifold. Employing this definition, we introduce a variational denoising model based on first and second order differences in the manifold setup. In order to minimize the corresponding functional, we develop an algorithm using an inexact cyclic proximal point algorithm. We propose an efficient strategy for the computation of the corresponding proximal mappings in symmetric spaces utilizing the machinery of Jacobi fields. For the n-sphere and the manifold of symmetric positive definite matrices, we demonstrate the performance of our algorithm in practice. We prove the convergence of the proposed exact and inexact variant of the cyclic proximal point algorithm in Hadamard spaces. These results which are of interest on its own include, e.g., the manifold of symmetric positive definite matrices.

Vanessa Suessle, Mimi Arandjelovic, Ammie K. Kalan et al.

The manual processing and analysis of videos from camera traps is time-consuming and includes several steps, ranging from the filtering of falsely triggered footage to identifying and re-identifying individuals. In this study, we developed a pipeline to automatically analyze videos from camera traps to identify individuals without requiring manual interaction. This pipeline applies to animal species with uniquely identifiable fur patterns and solitary behavior, such as leopards (Panthera pardus). We assumed that the same individual was seen throughout one triggered video sequence. With this assumption, multiple images could be assigned to an individual for the initial database filling without pre-labeling. The pipeline was based on well-established components from computer vision and deep learning, particularly convolutional neural networks (CNNs) and scale-invariant feature transform (SIFT) features. We augmented this basis by implementing additional components to substitute otherwise required human interactions. Based on the similarity between frames from the video material, clusters were formed that represented individuals bypassing the open set problem of the unknown total population. The pipeline was tested on a dataset of leopard videos collected by the Pan African Programme: The Cultured Chimpanzee (PanAf) and achieved a success rate of over 83% for correct matches between previously unknown individuals. The proposed pipeline can become a valuable tool for future conservation projects based on camera trap data, reducing the work of manual analysis for individual identification, when labeled data is unavailable.

Wolfgang Erb, Andreas Weinmann, Mandy Ahlborg et al.

Magnetic particle imaging (MPI) is a promising new in-vivo medical imaging modality in which distributions of super-paramagnetic nanoparticles are tracked based on their response in an applied magnetic field. In this paper we provide a mathematical analysis of the modeled MPI operator in the univariate situation. We provide a Hilbert space setup, in which the MPI operator is decomposed into simple building blocks and in which these building blocks are analyzed with respect to their mathematical properties. In turn, we obtain an analysis of the MPI forward operator and, in particular, of its ill-posedness properties. We further get that the singular values of the MPI core operator decrease exponentially. We complement our analytic results by some numerical studies which, in particular, suggest a rapid decay of the singular values of the MPI operator.

Thomas März, Andreas Weinmann

We contribute to the mathematical modeling and analysis of magnetic particle imaging which is a promising new in-vivo imaging modality. Concerning modeling, we develop a structured decomposition of the imaging process and extract its core part which we reveal to be common to all previous contributions in this context. The central contribution of this paper is the development of reconstruction formulae for MPI in 2D and 3D. Until now, in the multivariate setup, only time consuming measurement approaches are available, whereas reconstruction formulae are only available in 1D. The 2D and the 3D (describing the real world) reconstruction formulae which we derive here are significantly different from the 1D situation -- in particular there is no Dirac property in dimensions greater than one when the particle sizes approach zero. As a further result of our analysis, we conclude that the reconstruction problem in MPI is severely ill-posed. Finally, we obtain a model-based reconstruction algorithm.

Ben Isselmann, Dilara Göksu, Heinz Neumann et al.

Background: Task-specific microscopy datasets are often small, making it difficult to train deep learning models that learn robust features. While self-supervised learning (SSL) has shown promise through pretraining on large, domain-specific datasets, generalizability across datasets with differing staining protocols and channel configurations remains underexplored. We investigated the generalizability of SSL models pretrained on ImageNet-1k and HPA FOV, evaluating their embeddings on OpenCell with and without fine-tuning, two channel-mismatch strategies, and varying fine-tuning data fractions. We additionally analyzed single-cell embeddings on a labeled OpenCell subset. Result: DINO-based ViT backbones pretrained on HPA FOV or ImageNet-1k transfer well to OpenCell even without fine-tuning. The HPA FOV-pretrained model achieved the highest zero-shot performance (macro $F_1$ 0.822 $\pm$ 0.007). Fine-tuning further improved performance to 0.860 $\pm$ 0.013. At the single-cell level, the HPA single-cell-pretrained model achieved the highest k-nearest neighbor performance across all neighborhood sizes (macro $F_1$ $\geq$ 0.796). Conclusion: SSL methods like DINO, pretrained on large domain-relevant datasets, enable effective use of deep learning features for fine-tuning on small, task-specific microscopy datasets.

Vladyslav Polushko, Alexander Jenal, Jens Bongartz et al.

Floods are an increasingly common global threat, causing emergencies and severe damage to infrastructure. During crises, organisations such as the World Food Programme use remotely sensed imagery, typically obtained through drones, for rapid situational analysis to plan life-saving actions. Computer Vision tools are needed to support task force experts on-site in the evaluation of the imagery to improve their efficiency and to allocate resources strategically. We introduce the BlessemFlood21 dataset to stimulate research on efficient flood detection tools. The imagery was acquired during the 2021 Erftstadt-Blessem flooding event and consists of high-resolution and georeferenced RGB-NIR images. In the resulting RGB dataset, the images are supplemented with detailed water masks, obtained via a semi-supervised human-in-the-loop technique, where in particular the NIR information is leveraged to classify pixels as either water or non-water. We evaluate our dataset by training and testing established Deep Learning models for semantic segmentation. With BlessemFlood21 we provide labeled high-resolution RGB data and a baseline for further development of algorithmic solutions tailored to flood detection in RGB imagery.

Akshaya Srinivasan, Xiaoyin Cheng, Jianming Yi et al.

Hybrid quantum-classical machine learning offers a promising direction for advancing automated quality control in industrial settings. In this study, we investigate two hybrid quantum-classical approaches for classifying defects in aluminium TIG welding images and benchmarking their performance against a conventional deep learning model. A convolutional neural network is used to extract compact and informative feature vectors from weld images, effectively reducing the higher-dimensional pixel space to a lower-dimensional feature space. Our first quantum approach encodes these features into quantum states using a parameterized quantum feature map composed of rotation and entangling gates. We compute a quantum kernel matrix from the inner products of these states, defining a linear system in a higher-dimensional Hilbert space corresponding to the support vector machine (SVM) optimization problem and solving it using a Variational Quantum Linear Solver (VQLS). We also examine the effect of the quantum kernel condition number on classification performance. In our second method, we apply angle encoding to the extracted features in a variational quantum circuit and use a classical optimizer for model training. Both quantum models are tested on binary and multiclass classification tasks and the performance is compared with the classical CNN model. Our results show that while the CNN model demonstrates robust performance, hybrid quantum-classical models perform competitively. This highlights the potential of hybrid quantum-classical approaches for near-term real-world applications in industrial defect detection and quality assurance.

Tamara R. Lenhard, Andreas Weinmann, Hichem Snoussi et al.

Robust long-term tracking of drone is a critical requirement for modern surveillance systems, given their increasing threat potential. While detector-based approaches typically achieve strong frame-level accuracy, they often suffer from temporal inconsistencies caused by frequent detection dropouts. Despite its practical relevance, research on RGB-based drone tracking is still limited and largely reliant on conventional motion models. Meanwhile, foundation models like SAMURAI have established their effectiveness across other domains, exhibiting strong category-agnostic tracking performance. However, their applicability in drone-specific scenarios has not been investigated yet. Motivated by this gap, we present the first systematic evaluation of SAMURAI's potential for robust drone tracking in urban surveillance settings. Furthermore, we introduce a detector-augmented extension of SAMURAI to mitigate sensitivity to bounding-box initialization and sequence length. Our findings demonstrate that the proposed extension significantly improves robustness in complex urban environments, with pronounced benefits in long-duration sequences - especially under drone exit-re-entry events. The incorporation of detector cues yields consistent gains over SAMURAI's zero-shot performance across datasets and metrics, with success rate improvements of up to +0.393 and FNR reductions of up to -0.475.

Vladyslav Gapyak, Thomas März, Andreas Weinmann

Model-based reconstruction approaches for the medical imaging modality Magnetic Particle Imaging (MPI) are typically based on the Langevin model, which assumes instantaneous alignment of the particles magnetic momenta with the applied field. Regarding the application to real data, Langevin model-based reconstruction methods require model transfer functions (MTF) obtained from calibrations to preprocess the data. There are also model-based reconstruction approaches that include relaxation effects and other particle-level dynamics. However, they are limited either to 1D or 1D-like scanning scenarios when considering real data, or are limited to simulated data in the case of multi-dimensional field-free point (FFP) MPI. Thus, fully model-based reconstructions from multi-dimensional FFP scanning data that incorporate relaxation effects without using an MTF have not yet been demonstrated. In this work, we incorporate relaxation effects by considering a multi-dimensional Debye model and provide reconstruction formulae. In particular, we show that the Debye model-based signal is the response of a linear time-invariant system with exponential memory applied to a Langevin model-based signal. We provide a reconstruction algorithm for the introduced multi-dimensional Debye model. To this end, we devise a relaxation adaption step. For the resulting relaxation-adapted Debye signal, we show that it can be expressed by the well-studied MPI core operator derived from the Langevin theory. This results in a three-stage algorithm with low additional cost over the Langevin model, as the relaxation adaption scales linearly in the input data. We provide numerical results for the proposed algorithmic approach. In particular, we obtain fully model-based reconstructions from real 2D MPI data without involving any specific MTF analogous to the Langevin model case.

Patrick Bauer, Marius Schwinning, Florian Renk et al.

The European Space Agency (ESA), driven by its ambitions on planned lunar missions with the Argonaut lander, has a profound interest in reliable crater detection, since craters pose a risk to safe lunar landings. This task is usually addressed with automated crater detection algorithms (CDA) based on deep learning techniques. It is non-trivial due to the vast amount of craters of various sizes and shapes, as well as challenging conditions such as varying illumination and rugged terrain. Therefore, we propose a deep-learning CDA based on the OWLv2 model, which is built on a Vision Transformer, that has proven highly effective in various computer vision tasks. For fine-tuning, we utilize a manually labeled dataset fom the IMPACT project, that provides crater annotations on high-resolution Lunar Reconnaissance Orbiter Camera Calibrated Data Record images. We insert trainable parameters using a parameter-efficient fine-tuning strategy with Low-Rank Adaptation, and optimize a combined loss function consisting of Complete Intersection over Union (CIoU) for localization and a contrastive loss for classification. We achieve satisfactory visual results, along with a maximum recall of 94.0% and a maximum precision of 73.1% on a test dataset from IMPACT. Our method achieves reliable crater detection across challenging lunar imaging conditions, paving the way for robust crater analysis in future lunar exploration.

Tamara R. Lenhard, Andreas Weinmann, Kai Franke et al.

Developing robust drone detection systems is often constrained by the limited availability of large-scale annotated training data and the high costs associated with real-world data collection. However, leveraging synthetic data generated via game engine-based simulations provides a promising and cost-effective solution to overcome this issue. Therefore, we present SynDroneVision, a synthetic dataset specifically designed for RGB-based drone detection in surveillance applications. Featuring diverse backgrounds, lighting conditions, and drone models, SynDroneVision offers a comprehensive training foundation for deep learning algorithms. To evaluate the dataset's effectiveness, we perform a comparative analysis across a selection of recent YOLO detection models. Our findings demonstrate that SynDroneVision is a valuable resource for real-world data enrichment, achieving notable enhancements in model performance and robustness, while significantly reducing the time and costs of real-world data acquisition. SynDroneVision will be publicly released upon paper acceptance.

Ben Isselmann, Dilara Göksu, Andreas Weinmann

Task-specific microscopy datasets are often too small to train deep learning models that learn robust feature representations. Self-supervised learning (SSL) can mitigate this by pretraining on large unlabeled datasets, but it remains unclear how well such representations transfer across microscopy domains with different staining protocols and channel configurations. We investigate the cross-domain transferability of DINO-pretrained Vision Transformers for protein localization on the OpenCell dataset. We generate image embeddings using three DINO backbones pretrained on ImageNet-1k, the Human Protein Atlas (HPA), and OpenCell, and evaluate them by training a supervised classification head on OpenCell labels. All pretrained models transfer well, with the microscopy-specific HPA-pretrained model achieving the best performance (mean macro $F_1$-score = 0.8221 $\pm$ 0.0062), slightly outperforming a DINO model trained directly on OpenCell (0.8057 $\pm$ 0.0090). These results highlight the value of large-scale pretraining and indicate that domain-relevant SSL representations can generalize effectively to related but distinct microscopy datasets, enabling strong downstream performance even when task-specific labeled data are limited.

Vladyslav Gapyak, Corinna Rentschler, Thomas März et al.

Objective: Magnetic particle imaging (MPI) is an emerging medical imaging modality which has gained increasing interest in recent years. Among the benefits of MPI are its high temporal resolution, and that the technique does not expose the specimen to any kind of ionizing radiation. It is based on the non-linear response of magnetic nanoparticles to an applied magnetic field. From the electric signal measured in receive coils, the particle concentration has to be reconstructed. Due to the ill-posedness of the reconstruction problem, various regularization methods have been proposed for reconstruction ranging from early stopping methods, via classical Tikhonov regularization and iterative methods to modern machine learning approaches. In this work, we contribute to the latter class: we propose a plug-and-play approach based on a generic zero-shot denoiser with an $\ell^1$-prior. Approach: We validate the reconstruction parameters of the method on a hybrid dataset and compare it with the baseline Tikhonov, DIP and the previous PP-MPI, which is a plug-and-play method with denoiser trained on MPI-friendly data. Main results: We offer a quantitative and qualitative evaluation of the zero-shot plug-and-play approach on the 3D Open MPI dataset. Moreover, we show the quality of the approach with different levels of preprocessing of the data. Significance: The proposed method employs a zero-shot denoiser which has not been trained for the MPI task and therefore saves the cost for training. Moreover, it offers a method that can be potentially applied in future MPI contexts.

Vladyslav Gapyak, Thomas März, Andreas Weinmann

Magnetic Particle Imaging (MPI) is a promising tomographic technique for visualizing the spatio-temporal distribution of superparamagnetic nanoparticles, with applications ranging from cancer detection to real-time cardiovascular monitoring. Traditional MPI reconstruction relies on either time-consuming calibration (measured system matrix) or model-based simulation of the forward operator. Recent developments have shown the applicability of Chebyshev polynomials to multi-dimensional Lissajous Field-Free Point (FFP) scans. This method is bound to the particular choice of sinusoidal scanning trajectories. In this paper, we present the first reconstruction on real 2D MPI data with a trajectory-independent model-based MPI reconstruction algorithm. We further develop the zero-shot Plug-and-Play (PnP) algorithm of the authors -- with automatic noise level estimation -- to address the present deconvolution problem, leveraging a state-of-the-art denoiser trained on natural images without retraining on MPI-specific data. We evaluate our method on the publicly available 2D FFP MPI dataset ``MPIdata: Equilibrium Model with Anisotropy", featuring scans of six phantoms acquired using a Bruker preclinical scanner. Moreover, we show reconstruction performed on custom data on a 2D scanner with additional high-frequency excitation field and partial data. Our results demonstrate strong reconstruction capabilities across different scanning scenarios -- setting a precedent for general-purpose, flexible model-based MPI reconstruction.

David Hagens, Jan M. Knaup, Elke Hergenröther et al.

The automation of games using Deep Reinforcement Learning Strategies (DRL) is a well-known challenge in AI research. While for feature extraction in a video game typically the whole image is used, this is hardly practical for many real world games. Instead, using a smaller game state reducing the dimension of the parameter space to include essential parameters only seems to be a promising approach. In the game of Foosball, a compact and comprehensive game state description consists of the positional shifts and rotations of the figures and the position of the ball over time. In particular, velocities and accelerations can be derived from consecutive time samples of the game state. In this paper, a figure detection system to determine the game state in Foosball is presented. We capture a dataset containing the rotations of the rods which were measured using accelerometers and the positional shifts were derived using traditional Computer Vision techniques (in a laboratory setting). This dataset is utilized to train Convolutional Neural Network (CNN) based end-to-end regression models to predict the rotations and shifts of each rod. We present an evaluation of our system using different state-of-the-art CNNs as base architectures for the regression model. We show that our system is able to predict the game state with high accuracy. By providing data for both black and white teams, the presented system is intended to provide the required data for future developments of Imitation Learning techniques w.r.t. to observing human players.

Tim Selig, Thomas März, Martin Storath et al.

Computed tomography from a low radiation dose (LDCT) is challenging due to high noise in the projection data. Popular approaches for LDCT image reconstruction are two-stage methods, typically consisting of the filtered backprojection (FBP) algorithm followed by a neural network for LDCT image enhancement. Two-stage methods are attractive for their simplicity and potential for computational efficiency, typically requiring only a single FBP and a neural network forward pass for inference. However, the best reconstruction quality is currently achieved by unrolled iterative methods (Learned Primal-Dual and ItNet), which are more complex and thus have a higher computational cost for training and inference. We propose a method combining the simplicity and efficiency of two-stage methods with state-of-the-art reconstruction quality. Our strategy utilizes a neural network pretrained for Gaussian noise removal from natural grayscale images, fine-tuned for LDCT image enhancement. We call this method FBP-DTSGD (Domain and Task Shifted Gaussian Denoisers) as the fine-tuning is a task shift from Gaussian denoising to enhancing LDCT images and a domain shift from natural grayscale to LDCT images. An ablation study with three different pretrained Gaussian denoisers indicates that the performance of FBP-DTSGD does not depend on a specific denoising architecture, suggesting future advancements in Gaussian denoising could benefit the method. The study also shows that pretraining on natural images enhances LDCT reconstruction quality, especially with limited training data. Notably, pretraining involves no additional cost, as existing pretrained models are used. The proposed method currently holds the top mean position in the LoDoPaB-CT challenge.

Tamara R. Lenhard, Andreas Weinmann, Tobias Koch

Drone detection in visually complex environments remains challenging due to background clutter, small object scale, and camouflage effects. While generic object detectors like YOLO exhibit strong performance in low-texture scenes, their effectiveness degrades in cluttered environments with low object-background separability. To address these limitations, this work presents an enhanced iteration of YOLO-FEDER FusionNet -- a detection framework that integrates generic object detection with camouflage object detection techniques. Building upon the original architecture, the proposed iteration introduces systematic advancements in training data composition, feature fusion strategies, and backbone design. Specifically, the training process leverages large-scale, photo-realistic synthetic data, complemented by a small set of real-world samples, to enhance robustness under visually complex conditions. The contribution of intermediate multi-scale FEDER features is systematically evaluated, and detection performance is comprehensively benchmarked across multiple YOLO-based backbone configurations. Empirical results indicate that integrating intermediate FEDER features, in combination with backbone upgrades, contributes to notable performance improvements. In the most promising configuration -- YOLO-FEDER FusionNet with a YOLOv8l backbone and FEDER features derived from the DWD module -- these enhancements lead to a FNR reduction of up to 39.1 percentage points and a mAP increase of up to 62.8 percentage points at an IoU threshold of 0.5, compared to the initial baseline.

Vladyslav Polushko, Damjan Hatic, Ronald Rösch et al.

Floods cause serious problems around the world. Responding quickly and effectively requires accurate and timely information about the affected areas. The effective use of Remote Sensing images for accurate flood detection requires specific detection methods. Typically, Deep Neural Networks are employed, which are trained on specific datasets. For the purpose of river flood detection in RGB imagery, we use the BlessemFlood21 dataset. We here explore the use of different augmentation strategies, ranging from basic approaches to more complex techniques, including optical distortion. By identifying effective strategies, we aim to refine the training process of state-of-the-art Deep Learning segmentation networks.

Vanessa Suessle, Marco Heurich, Colleen T. Downs et al.

The bilateral asymmetry of flanks of animals with visual body marks that uniquely identify an individual, complicates tasks like population estimations. Automatically generated additional information on the visible side of the animal would improve the accuracy for individual identification. In this study we used transfer learning on popular CNN image classification architectures to train a flank predictor that predicts the visible flank of quadruped mammalian species in images. We automatically derived the data labels from existing datasets originally labeled for animal pose estimation. We trained the models in two phases with different degrees of retraining. The developed models were evaluated in different scenarios of different unknown quadruped species in known and unknown environments. As a real-world scenario, we used a dataset of manually labeled Eurasian lynx (Lynx lynx) from camera traps in the Bavarian Forest National Park to evaluate the model. The best model, trained on an EfficientNetV2 backbone, achieved an accuracy of 88.70 % for the unknown species lynx in a complex habitat.

Michael Doell, Dominik Kuehn, Vanessa Suessle et al.

Analyses for biodiversity monitoring based on passive acoustic monitoring (PAM) recordings is time-consuming and challenged by the presence of background noise in recordings. Existing models for sound event detection (SED) worked only on certain avian species and the development of further models required labeled data. The developed framework automatically extracted labeled data from available platforms for selected avian species. The labeled data were embedded into recordings, including environmental sounds and noise, and were used to train convolutional recurrent neural network (CRNN) models. The models were evaluated on unprocessed real world data recorded in urban KwaZulu-Natal habitats. The Adapted SED-CRNN model reached a F1 score of 0.73, demonstrating its efficiency under noisy, real-world conditions. The proposed approach to automatically extract labeled data for chosen avian species enables an easy adaption of PAM to other species and habitats for future conservation projects.

Tamara R. Lenhard, Andreas Weinmann, Stefan Jäger et al.

Predominant methods for image-based drone detection frequently rely on employing generic object detection algorithms like YOLOv5. While proficient in identifying drones against homogeneous backgrounds, these algorithms often struggle in complex, highly textured environments. In such scenarios, drones seamlessly integrate into the background, creating camouflage effects that adversely affect the detection quality. To address this issue, we introduce a novel deep learning architecture called YOLO-FEDER FusionNet. Unlike conventional approaches, YOLO-FEDER FusionNet combines generic object detection methods with the specialized strength of camouflage object detection techniques to enhance drone detection capabilities. Comprehensive evaluations of YOLO-FEDER FusionNet show the efficiency of the proposed model and demonstrate substantial improvements in both reducing missed detections and false alarms.

Lukas Kiefer, Stefania Petra, Martin Storath et al.

We consider reconstructing multi-channel images from measurements performed by photon-counting and energy-discriminating detectors in the setting of multi-spectral X-ray computed tomography (CT). Our aim is to exploit the strong structural correlation that is known to exist between the channels of multi-spectral CT images. To that end, we adopt the multi-channel Potts prior to jointly reconstruct all channels. This prior produces piecewise constant solutions with strongly correlated channels. In particular, edges are enforced to have the same spatial position across channels which is a benefit over TV-based methods. We consider the Potts prior in two frameworks: (a) in the context of a variational Potts model, and (b) in a Potts-superiorization approach that perturbs the iterates of a basic iterative least squares solver. We identify an alternating direction method of multipliers (ADMM) approach as well as a Potts-superiorized conjugate gradient method as particularly suitable. In numerical experiments, we compare the Potts prior based approaches to existing TV-type approaches on realistically simulated multi-spectral CT data and obtain improved reconstruction for compound solid bodies.

Lukas Kiefer, Martin Storath, Andreas Weinmann

Signals and images with discontinuities appear in many problems in such diverse areas as biology, medicine, mechanics, and electrical engineering. The concrete data are often discrete, indirect and noisy measurements of some quantities describing the signal under consideration. A frequent task is to find the segments of the signal or image which corresponds to finding the discontinuities or jumps in the data. Methods based on minimizing the piecewise constant Mumford-Shah functional -- whose discretized version is known as Potts functional -- are advantageous in this scenario, in particular, in connection with segmentation. However, due to their non-convexity, minimization of such functionals is challenging. In this paper we propose a new iterative minimization strategy for the multivariate Potts functional dealing with indirect, noisy measurements. We provide a convergence analysis and underpin our findings with numerical experiments.

Martin Storath, Andreas Weinmann

In this paper, we consider the sparse regularization of manifold-valued data with respect to an interpolatory wavelet/multiscale transform. We propose and study variational models for this task and provide results on their well-posedness. We present algorithms for a numerical realization of these models in the manifold setup. Further, we provide experimental results to show the potential of the proposed schemes for applications.

Martin Storath, Andreas Weinmann

In this paper, we consider the variational regularization of manifold-valued data in the inverse problems setting. In particular, we consider TV and TGV regularization for manifold-valued data with indirect measurement operators. We provide results on the well-posedness and present algorithms for a numerical realization of these models in the manifold setup. Further, we provide experimental results for synthetic and real data to show the potential of the proposed schemes for applications.

Denis Fortun, Martin Storath, Dennis Rickert et al.

Current algorithmic approaches for piecewise affine motion estimation are based on alternating motion segmentation and estimation. We propose a new method to estimate piecewise affine motion fields directly without intermediate segmentation. To this end, we reformulate the problem by imposing piecewise constancy of the parameter field, and derive a specific proximal splitting optimization scheme. A key component of our framework is an efficient one-dimensional piecewise-affine estimator for vector-valued signals. The first advantage of our approach over segmentation-based methods is its absence of initialization. The second advantage is its lower computational cost which is independent of the complexity of the motion field. In addition to these features, we demonstrate competitive accuracy with other piecewise-parametric methods on standard evaluation benchmarks. Our new regularization scheme also outperforms the more standard use of total variation and total generalized variation.

Martin Kiechle, Martin Storath, Andreas Weinmann et al.

Features that capture well the textural patterns of a certain class of images are crucial for the performance of texture segmentation methods. The manual selection of features or designing new ones can be a tedious task. Therefore, it is desirable to automatically adapt the features to a certain image or class of images. Typically, this requires a large set of training images with similar textures and ground truth segmentation. In this work, we propose a framework to learn features for texture segmentation when no such training data is available. The cost function for our learning process is constructed to match a commonly used segmentation model, the piecewise constant Mumford-Shah model. This means that the features are learned such that they provide an approximately piecewise constant feature image with a small jump set. Based on this idea, we develop a two-stage algorithm which first learns suitable convolutional features and then performs a segmentation. We note that the features can be learned from a small set of images, from a single image, or even from image patches. The proposed method achieves a competitive rank in the Prague texture segmentation benchmark, and it is effective for segmenting histological images.

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 nonlinear color spaces such as HSV, and they can be obtained by changing the space domain of, e.g., an optical flow field to polar coordinates. For such nonlinear data spaces, we develop algorithms for the solution of the corresponding second order total variation (TV) type problems for denoising, inpainting as well as the combination of both. We provide a convergence analysis and we apply the algorithms to concrete problems.

Andreas Weinmann, Laurent Demaret, Martin Storath

Mumford-Shah and Potts functionals are powerful variational models for regularization which are widely used in signal and image processing; typical applications are edge-preserving denoising and segmentation. Being both non-smooth and non-convex, they are computationally challenging even for scalar data. For manifold-valued data, the problem becomes even more involved since typical features of vector spaces are not available. In this paper, we propose algorithms for Mumford-Shah and for Potts regularization of manifold-valued signals and images. For the univariate problems, we derive solvers based on dynamic programming combined with (convex) optimization techniques for manifold-valued data. For the class of Cartan-Hadamard manifolds (which includes the data space in diffusion tensor imaging), we show that our algorithms compute global minimizers for any starting point. For the multivariate Mumford-Shah and Potts problems (for image regularization) we propose a splitting into suitable subproblems which we can solve exactly using the techniques developed for the corresponding univariate problems. Our method does not require any a priori restrictions on the edge set and we do not have to discretize the data space. We apply our method to diffusion tensor imaging (DTI) as well as Q-ball imaging. Using the DTI model, we obtain a segmentation of the corpus callosum.

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 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.

Andreas Weinmann, Laurent Demaret, Martin Storath

We consider total variation minimization for manifold valued data. We propose a cyclic proximal point algorithm and a parallel proximal point algorithm to minimize TV functionals with $\ell^p$-type data terms in the manifold case. These algorithms are based on iterative geodesic averaging which makes them easily applicable to a large class of data manifolds. As an application, we consider denoising images which take their values in a manifold. We apply our algorithms to diffusion tensor images, interferometric SAR images as well as sphere and cylinder valued images. For the class of Cartan-Hadamard manifolds (which includes the data space in diffusion tensor imaging) we show the convergence of the proposed TV minimizing algorithms to a global minimizer.