Thomas Richter

Stefan Frei, Thomas Richter, Thomas Wick

In this work, we describe a simple finite element approach that is able to resolve weak discontinuities in interface problems accurately. The approach is based on a fixed patch mesh consisting of quadrilaterals, that will stay unchanged independent of the position of the interface. Inside the patches we refine once more, either in eight triangles or in four quadrilaterals, in such a way that the interface is locally resolved. The resulting finite element approach can be considered a fitted finite element approach. In our practical implementation, we do not construct this fitted mesh, however. Instead, the local degrees of freedom are included in a parametric way in the finite element space, or to be more precise in the local mappings between a reference patch and the physical patches. We describe the implementation in the open source C++ finite element library deal.II in detail and present two numerical examples to illustrate the performance of the approach. Finally, detailed studies of the behavior of iterative linear solvers complement this work.

Srivatsa Prativadibhayankaram, Thomas Richter, Heiko Sparenberg et al.

Deep learning based image compression has gained a lot of momentum in recent times. To enable a method that is suitable for image compression and subsequently extended to video compression, we propose a novel deep learning model architecture, where the task of image compression is divided into two sub-tasks, learning structural information from luminance channel and color from chrominance channels. The model has two separate branches to process the luminance and chrominance components. The color difference metric CIEDE2000 is employed in the loss function to optimize the model for color fidelity. We demonstrate the benefits of our approach and compare the performance to other codecs. Additionally, the visualization and analysis of latent channel impulse response is performed.

Johan Hoffman, Bärbel Holm, Thomas Richter

We present a locally adapted parametric finite element method for interface problems. For this adapted finite element method we show optimal convergence for elliptic interface problems with a discontinuous diffusion parameter. The method is based on the adaption of macro elements where a local basis represents the interface. The macro elements are independent of the interface and can be cut by the interface. A macro element which is a triangle in the triangulation is divided into four subtriangles. On these subtriangles, the basis functions of the macro element are interpreted as linear functions. The position of the vertices of these subtriangles is determined by the location of the interface in the case a macro element is cut by the interface. Quadrature is performed on the subtriangles via transformations to a reference element. Due to the locality of the method, its use is well suited on distributed architectures.

Mohsen Jenadeleh, Jon Sneyers, Davi Lazzarotto et al.

High dynamic range (HDR) and wide color gamut (WCG) technologies significantly improve color reproduction compared to standard dynamic range (SDR) and standard color gamuts, resulting in more accurate, richer, and more immersive images. However, HDR increases data demands, posing challenges for bandwidth efficiency and compression techniques. Advances in compression and display technologies require more precise image quality assessment, particularly in the high-fidelity range where perceptual differences are subtle. To address this gap, we introduce AIC-HDR2025, the first such HDR dataset, comprising 100 test images generated from five HDR sources, each compressed using four codecs at five compression levels. It covers the high-fidelity range, from visible distortions to compression levels below the visually lossless threshold. A subjective study was conducted using the JPEG AIC-3 test methodology, combining plain and boosted triplet comparisons. In total, 34,560 ratings were collected from 151 participants across four fully controlled labs. The results confirm that AIC-3 enables precise HDR quality estimation, with 95\% confidence intervals averaging a width of 0.27 at 1 JND. In addition, several recently proposed objective metrics were evaluated based on their correlation with subjective ratings. The dataset is publicly available.

Shihan Guo, Thomas Richter

We propose a hybrid method, the Neural Enrichment Finite Element Method (NEFEM), designed for problems involving strong oscillations or interface problems with weak discontinuities. This method is based on the stable generalized finite element method (SGFEM) framework, wherein neural networks (NNs) are introduced as enrichment functions for adaptivity, and the Ritz functional is applied for the training process. This works makes two main contributions. First, the method constructs local subspaces with superior approximation properties, significantly reducing the required number of degrees of freedom (DoFs). Second, minimal \emph{a priori} knowledge is required to define enrichment functions, as the NNs evolve heuristically during training. Furthermore, for smooth problems, we provide a residual-based error estimator and prove both its reliability and efficiency. For interface problems, a theoretical analysis on the optimal convergence of the SGFEM is studied, notably without imposing additional regularity assumptions. These analytic results guide the network architecture design and training strategies. The performance and effectiveness of the proposed method is validated through several numerical experiments.

Medard Govoeyi, Thomas Richter

Physics-Informed Neural Networks (PINNs) are mesh-free approaches for the numerical approximation of partial differential equations, where a neural network is trained by minimizing a loss function derived from the governing equations and boundary conditions. The Deep Ritz method can be interpreted as a particular variational form of a PINN, where the loss corresponds to the minimization of an energy functional associated with a symmetric positive definite problem. In this work, we study the approximation of the Laplace equation using both the classical PINN formulation and its variational counterpart, the Deep Ritz method, with the objective of accurately estimating prescribed goal functionals. When standard sampling strategies, such as uniform or loss-based sampling, are employed during training, the convergence of the functional error and the attained minimal functional value can be slow. To address this issue, we introduce a functional-oriented importance sampling strategy that can be applied to both PINNs and the Deep Ritz method. The key ingredient is the construction of a reliable and accurate estimator for the error in a given quantity of interest. This estimator is derived using concepts from the Dual Weighted Residual (DWR) framework and is implemented entirely within the neural network setting. It is then used to adaptively guide the sampling of training points in the computational domain, focusing computational effort on regions that have the strongest influence on the functional value. Numerical experiments demonstrate that the proposed adaptive sampling strategy significantly accelerates the convergence of the functional error and improves the minimization of the target functional during training for both PINN and Deep Ritz formulations.

Srivatsa Prativadibhayankaram, Mahadev Prasad Panda, Thomas Richter et al.

We propose the structure and color based learned image codec (SLIC) in which the task of compression is split into that of luminance and chrominance. The deep learning model is built with a novel multi-scale architecture for Y and UV channels in the encoder, where the features from various stages are combined to obtain the latent representation. An autoregressive context model is employed for backward adaptation and a hyperprior block for forward adaptation. Various experiments are carried out to study and analyze the performance of the proposed model, and to compare it with other image codecs. We also illustrate the advantages of our method through the visualization of channel impulse responses, latent channels and various ablation studies. The model achieves Bjøntegaard delta bitrate gains of 7.5% and 4.66% in terms of MS-SSIM and CIEDE2000 metrics with respect to other state-of-the-art reference codecs.

Konstantin Schmidt, Thomas Richter

First Order Motion Model is a generative model that animates human heads based on very little motion information derived from keypoints. It is a promising solution for video communication because first it operates at very low bitrate and second its computational complexity is moderate compared to other learning based video codecs. However, it has strong limitations by design. Since it generates facial animations by warping source-images, it fails to recreate videos with strong head movements. This works concentrates on one specific kind of head movements, namely head rotations. We show that replacing the Jacobian transformations in FOMM by a global rotation helps the system to perform better on items with head-rotations while saving 40% to 80% of bitrate on P-frames. Moreover, we apply state-of-the-art normalization techniques to the discriminator to stabilize the adversarial training which is essential for generating visually appealing videos. We evaluate the performance by the learned metics LPIPS and DISTS to show the success our optimizations.

Ayman A. Ameen, Thomas Richter, André Kaup

Current learned image compression models typically exhibit high complexity, which demands significant computational resources. To overcome these challenges, we propose an innovative approach that employs hierarchical feature extraction transforms to significantly reduce complexity while preserving bit rate reduction efficiency. Our novel architecture achieves this by using fewer channels for high spatial resolution inputs/feature maps. On the other hand, feature maps with a large number of channels have reduced spatial dimensions, thereby cutting down on computational load without sacrificing performance. This strategy effectively reduces the forward pass complexity from \(1256 \, \text{kMAC/Pixel}\) to just \(270 \, \text{kMAC/Pixel}\). As a result, the reduced complexity model can open the way for learned image compression models to operate efficiently across various devices and pave the way for the development of new architectures in image compression technology.

Ayman A. Ameen, Thomas Richter, André Kaup

Current image compression models often require separate models for each quality level, making them resource-intensive in terms of both training and storage. To address these limitations, we propose an innovative approach that utilizes latent variables from pre-existing trained models (such as the Stable Diffusion Variational Autoencoder) for perceptual image compression. Our method eliminates the need for distinct models dedicated to different quality levels. We employ overfitted learnable functions to compress the latent representation from the target model at any desired quality level. These overfitted functions operate in the latent space, ensuring low computational complexity, around $25.5$ MAC/pixel for a forward pass on images with dimensions $(1363 \times 2048)$ pixels. This approach efficiently utilizes resources during both training and decoding. Our method achieves comparable perceptual quality to state-of-the-art learned image compression models while being both model-agnostic and resolution-agnostic. This opens up new possibilities for the development of innovative image compression methods.

Srivatsa Prativadibhayankaram, Mahadev Prasad Panda, Jürgen Seiler et al.

In this work, we present a comparison between color spaces namely YUV, LAB, RGB and their effect on learned image compression. For this we use the structure and color based learned image codec (SLIC) from our prior work, which consists of two branches - one for the luminance component (Y or L) and another for chrominance components (UV or AB). However, for the RGB variant we input all 3 channels in a single branch, similar to most learned image codecs operating in RGB. The models are trained for multiple bitrate configurations in each color space. We report the findings from our experiments by evaluating them on various datasets and compare the results to state-of-the-art image codecs. The YUV model performs better than the LAB variant in terms of MS-SSIM with a Bjøntegaard delta bitrate (BD-BR) gain of 7.5\% using VTM intra-coding mode as the baseline. Whereas the LAB variant has a better performance than YUV model in terms of CIEDE2000 having a BD-BR gain of 8\%. Overall, the RGB variant of SLIC achieves the best performance with a BD-BR gain of 13.14\% in terms of MS-SSIM and a gain of 17.96\% in CIEDE2000 at the cost of a higher model complexity.

Wilhelm Hasselbring, Sören Henning, Björn Latte et al.

The visions and ideas of Industry 4.0 require a profound interconnection of machines, plants, and IT systems in industrial production environments. This significantly increases the importance of software, which is coincidentally one of the main obstacles to the introduction of Industry 4.0. Lack of experience and knowledge, high investment and maintenance costs, as well as uncertainty about future developments cause many small and medium-sized enterprises hesitating to adopt Industry 4.0 solutions. We propose Industrial DevOps as an approach to introduce methods and culture of DevOps into industrial production environments. The fundamental concept of this approach is a continuous process of operation, observation, and development of the entire production environment. This way, all stakeholders, systems, and data can thus be integrated via incremental steps and adjustments can be made quickly. Furthermore, we present the Titan software platform accompanied by a role model for integrating production environments with Industrial DevOps. In two initial industrial application scenarios, we address the challenges of energy management and predictive maintenance with the methods, organizational structures, and tools of Industrial DevOps.

Alessandro Artusi, Thomas Richter, Touradj Ebrahimi et al.

In this lecture note, we describe high dynamic range (HDR) imaging systems; such systems are able to represent luminances of much larger brightness and, typically, also a larger range of colors than conventional standard dynamic range (SDR) imaging systems. The larger luminance range greatly improve the overall quality of visual content, making it appears much more realistic and appealing to observers. HDR is one of the key technologies of the future imaging pipeline, which will change the way the digital visual content is represented and manipulated today.