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We present a novel technique by which highly-segmented electrostatic configurations can be solved. The Robin Hood method is a matrix-inversion algorithm optimized for solving high density boundary element method (BEM) problems. We…

Depth refinement aims to infer high-resolution depth with fine-grained edges and details, refining low-resolution results of depth estimation models. The prevailing methods adopt tile-based manners by merging numerous patches, which lacks…

Here we present exact, stationary, parametric solutions to the Schr\"odinger--Poisson system. We confront two images: on one hand, we draw on the homotopy analysis method which leads us to a nonlinear integral scheme. Indeed, this approach…

We present a method for obtaining qualitatively accurate grain boundary plane distributions (GBPD) for textured microstructures using a stereological calculation applied to two-dimensional electron backscatter diffraction (EBSD) orientation…

Homological algebra techniques can be found in almost all modern areas of mathematics. Many interesting problems in mathematics can be formulated, computed, or can find their equivalence in terms of Ext-groups. For instance, important…

Materials characterization using electron backscatter diffraction (EBSD) requires indexing the orientation of the measured region from Kikuchi patterns. The quality of Kikuchi patterns can degrade due to pattern overlaps arising from two or…

Automated segmentation of the fetal head in ultrasound images is critical for prenatal monitoring. However, achieving robust segmentation remains challenging due to the poor quality of ultrasound images and the lack of annotated data.…

Many inverse problems have to deal with complex, evolving and often not exactly known geometries, e.g. as domains of forward problems modeled by partial differential equations. This makes it desirable to use methods which are robust with…

Understanding the orientation of geological structures is crucial for analyzing the complexity of the Earths' subsurface. For instance, information about geological structure orientation can be incorporated into local anisotropic…

The identification of repeating patterns in discrete grids is rudimentary within symbolic reasoning, algorithm synthesis and structural optimization across diverse computational domains. Although statistical approaches targeting noisy data…

Ambipolar diffusion is a process occurring in partially ionised astrophysical systems that imparts a complicated mathematical and physical nature to Ohm's law. The numerical codes that solve the magnetohydrodynamic (MHD) equations have to…

In this paper, we investigate a new extragradient algorithm for solving pseudomonotone equilibrium problems on Hadamard manifolds. The algorithm uses a variable stepsize which is updated at each iteration and based on some previous…

This paper presents a novel approach for denoising Electron Backscatter Diffraction (EBSD) patterns using diffusion models. We propose a two-stage training process with a UNet-based architecture, incorporating an auxiliary regression head…

Despite advancements in electron backscatter diffraction (EBSD) detector speeds, the acquisition rates of 4-Dimensional (4D) EBSD data, i.e., a collection of 2-dimensional (2D) diffraction maps for every position of a convergent electron…

Frequency domain spectroscopy allows an experimenter to establish optical properties of solids in a wide frequency band including the technically challenging 10 THz region, and in other bands enables metrological comparison between…

This paper proposes a novel approach to image deblurring and digital zooming using sparse local models of image appearance. These models, where small image patches are represented as linear combinations of a few elements drawn from some…

In pseudo integrable systems diffractive scattering caused by wedges and impurities can be described within the framework of Geometric Theory of Diffraction (GDT) in a way similar to the one used in the Periodic Orbit Theory of Diffraction…

We introduce a novel reflection-mode diffraction tomography technique that enables simultaneous recovery of forward and backward scattering information for high-resolution 3D refractive index reconstruction. Our technique works by imaging a…

We present the development of extended diffraction tomography, a new approach to the solution of the linear seismic waveform inversion problem. This method has several appealing features, such as the use of arbitrary depth-dependent…

This paper introduces a novel boundary integral approach of shape uncertainty quantification for the Helmholtz scattering problem in the framework of the so-called parametric method. The key idea is to construct an integration grid whose…