Piotr Swierczynski

Jianyu Wen, Jun Xie, Feng Chen et al.

In this paper, we present Self-DACE++, an improved unsupervised and lightweight framework for Low-Light Image Enhancement (LLIE), building upon our previous Self-Reference Deep Adaptive Curve Estimation (Self-DACE). To better address the trade-off between computational efficiency and restoration quality, Self-DACE++ introduces enhanced Adaptive Adjustment Curves (AACs). These curves, governed by minimal trainable parameters, flexibly adjust the dynamic range while preserving the color fidelity, structural integrity, and naturalness of the enhanced images. To achieve an extremely lightweight architecture without sacrificing performance, we propose a randomized order training strategy coupled with a network fusion mechanism, which compresses the model into an efficient iterative inference structure. Furthermore, we formulate a physics-grounded objective function based on Retinex theory and incorporate a dedicated denoising module to effectively estimate and suppress latent noise in dark regions. Extensive qualitative and quantitative evaluations on multiple real-world benchmark datasets demonstrate that Self-DACE++ outperforms existing state-of-the-art methods, delivering superior enhancement quality with real-time inference capability. The code is available at https://github.com/John-Wendell/Self-DACE.

Piotr Swierczynski, Barbara Wohlmuth

The presence of corners in the computational domain, in general, reduces the regularity of solutions of parabolic problems and diminishes the convergence properties of the finite element approximation introducing a so-called "pollution effect". Standard remedies based on mesh refinement around the singular corner result in very restrictive stability requirements on the time-step size when explicit time integration is applied. In this article, we introduce and analyse the energy-corrected finite element method for parabolic problems, which works on quasi-uniform meshes, and, based on it, create fast explicit time discretisation. We illustrate these results with extensive numerical investigations not only confirming the theoretical results but also showing the flexibility of the method, which can be applied in the presence of multiple singular corners and a three-dimensional setting. We also propose a fast explicit time-stepping scheme based on a piecewise cubic energy-corrected discretisation in space completed with mass-lumping techniques and numerically verify its efficiency.

Jianyu Wen, Chenhao Wu, Tong Zhang et al.

In this paper, we propose a 2-stage low-light image enhancement method called Self-Reference Deep Adaptive Curve Estimation (Self-DACE). In the first stage, we present an intuitive, lightweight, fast, and unsupervised luminance enhancement algorithm. The algorithm is based on a novel low-light enhancement curve that can be used to locally boost image brightness. We also propose a new loss function with a simplified physical model designed to preserve natural images' color, structure, and fidelity. We use a vanilla CNN to map each pixel through deep Adaptive Adjustment Curves (AAC) while preserving the local image structure. Secondly, we introduce the corresponding denoising scheme to remove the latent noise in the darkness. We approximately model the noise in the dark and deploy a Denoising-Net to estimate and remove the noise after the first stage. Exhaustive qualitative and quantitative analysis shows that our method outperforms existing state-of-the-art algorithms on multiple real-world datasets.

Leaf Jiang, Matthew Holzel, Bernhard Kaplan et al.

High-resolution (5MP+) stereo vision systems are essential for advancing robotic capabilities, enabling operation over longer ranges and generating significantly denser and accurate 3D point clouds. However, realizing the full potential of high-angular-resolution sensors requires a commensurately higher level of calibration accuracy and faster processing -- requirements often unmet by conventional methods. This study addresses that critical gap by processing 5MP camera imagery using a novel, advanced frame-to-frame calibration and stereo matching methodology designed to achieve both high accuracy and speed. Furthermore, we introduce a new approach to evaluate real-time performance by comparing real-time disparity maps with ground-truth disparity maps derived from more computationally intensive stereo matching algorithms. Crucially, the research demonstrates that high-pixel-count cameras yield high-quality point clouds only through the implementation of high-accuracy calibration.

Leaf Jiang, Matthew Holzel, Bernhard Kaplan et al.

This study derives analytical expressions for the depth and range error of fisheye stereo vision systems as a function of object distance, specifically accounting for accuracy at large angles.

Stefan Dohr, Christian Kahle, Sergejs Rogovs et al.

We study the numerical approximation of linear-quadratic optimal control problems subject to the fractional Laplace equation with its spectral definition. We compute an approximation of the state equation using a discretization of the Balakrishnan formula that is based on a finite element discretization in space and a sinc quadrature approximation of the additionally involved integral. A tailored approach for the numerical solution of the resulting linear systems is proposed. Concerning the discretization of the optimal control problem we consider two schemes. The first one is the variational approach, where the control set is not discretized, and the second one is the fully discrete scheme where the control is discretized by piecewise constant functions. We derive finite element error estimates for both methods and illustrate our results by numerical experiments.

Ustim Khristenko, Laura Scarabosio, Piotr Swierczynski et al.

We consider the generation of samples of a mean-zero Gaussian random field with Matérn covariance function. Every sample requires the solution of a differential equation with Gaussian white noise forcing, formulated on a bounded computational domain. This introduces unwanted boundary effects since the stochastic partial differential equation is originally posed on the whole $\mathbb{R}^d$, without boundary conditions. We use a window technique, whereby one embeds the computational domain into a larger domain, and postulates convenient boundary conditions on the extended domain. To mitigate the pollution from the artificial boundary it has been suggested in numerical studies to choose a window size that is at least as large as the correlation length of the Matérn field. We provide a rigorous analysis for the error in the covariance introduced by the window technique, for homogeneous Dirichlet, homogeneous Neumann, and periodic boundary conditions. We show that the error decays exponentially in the window size, independently of the type of boundary condition. We conduct numerical experiments in 1D and 2D space, confirming our theoretical results.