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Joint estimation of surface normals and depth is essential for holistic 3D scene understanding, yet high-resolution prediction remains difficult due to the trade-off between preserving fine local detail and maintaining global consistency. To address this challenge, we propose the Ultra Resolution Geometry Transformer (URGT), which adapts the Visual Geometry Grounded Transformer (VGGT) into a unified multi-patch transformer for monocular high-resolution depth--normal estimation. A single high-resolution image is partitioned into patches that are augmented with coarse depth and normal priors from pre-trained models, and jointly processed in a single forward pass to predict refined geometric outputs. Global coherence is enforced through cross-patch attention, which enables long-range geometric reasoning and seamless propagation of information across patches within a shared backbone. To further enhance spatial robustness, we introduce a GridMix patch sampling strategy that probabilistically samples grid configurations during training, improving inter-patch consistency and generalization. Our method achieves state-of-the-art results on UnrealStereo4K, jointly improving depth and normal

We construct cellular resolutions for monomial ideals via discrete Morse theory. In particular, we develop an algorithm to create homogeneous acyclic matchings and we call the cellular resolutions induced from these matchings Barile-Macchia resolutions. These resolutions are minimal for edge ideals of weighted oriented forests and (most) cycles. As a result, we provide recursive formulas for graded Betti numbers and projective dimension. Furthermore, we compare Barile-Macchia resolutions to those created by Batzies and Welker and some well-known simplicial resolutions. Under certain assumptions, whenever the above resolutions are minimal, so are Barile-Macchia resolutions.

Let $X$ be a variety with a stratification $\mathcal{S}$ into smooth locally closed subvarieties such that $X$ is locally a product along each stratum (e.g., a symplectic singularity). We prove that assigning to each open subset $U \subset X$ the set of isomorphism classes of locally projective crepant resolutions of $U$ defines an $\mathcal{S}$-constructible sheaf of sets. Thus, for each stratum $S$ and basepoint $s \in S$, the fundamental group acts on the set of germs of projective crepant resolutions at $s$, leaving invariant the germs extending to the entire stratum. Global locally projective crepant resolutions correspond to compatible such choices for all strata. For example, if the local projective crepant resolutions are unique, they automatically glue uniquely. We give criteria for a locally projective crepant resolution $ρ: \tilde X \to X$ to be globally projective. We show that the sheafification of the presheaf $U \mapsto \text{Pic}(ρ^{-1}(U)/U)$ of relative Picard classes is also constructible. The resolution is globally projective only if there exist local relatively ample bundles whose classes glue to a global section of this sheaf. The obstruction to lifting this s

In this paper, we present a unique multi-functional super-resolution instrument, the SuperNANO system, which integrates real-time super-resolution imaging with direct laser nanofabrication capabilities. Central to the func-tionality of the SuperNANO system is its capacity for simultaneous nanoimaging and nanopatterning, enabling the creation of anti-counterfeiting markings and precision cutting with exceptional accuracy. The SuperNANO system, featuring a unibody superlens objective, achieves a resolution ranging from 50 to 320 nm. We showcase the instrument's versatility through its application in generating high-security anti-counterfeiting features on an aluminum film. These 'invisible' security features, which are nanoscale in dimension, can be crafted with arbi-trary shapes at designated locations. Moreover, the system's precision is further evidenced by its ability to cut silver nanowires to a minimum width of 50 nm. The integrated imaging and fabricating functions of the Su-perNANO make it a pivotal tool for a variety of applications, including nano trapping, sensing, cutting, weld-ing, drilling, signal enhancement, detection, and nano laser treatment.

The emergence of ultra-wideband (UWB) and high-throughput signals has necessitated advancements in data sampling technologies1. Sub-Nyquist sampling methods, such as the modulated wideband converter (MWC) and compressed auto-correlation spectrum sensing (CCS), address the limitations of traditional analog-to-digital converters (ADCs) by capturing signals below the Nyquist rate. However, these methods face challenges like spectral leakage and complex hardware requirements. This paper proposes a novel super-resolution generalized eigenvalue method that integrates the matrix pencil method with the Chinese Remainder Theorem (CRT) to enhance signal processing capabilities within a true sub-Nyquist framework3. This approach aims to improve frequency resolution and accuracy in high-frequency signal extraction, with potential applications in telecommunications, radar, and medical imaging.

Recently, the methods based on implicit neural representations have shown excellent capabilities for arbitrary-scale super-resolution (ASSR). Although these methods represent the features of an image by generating latent codes, these latent codes are difficult to adapt for different magnification factors of super-resolution, which seriously affects their performance. Addressing this, we design Multi-Scale Implicit Transformer (MSIT), consisting of an Multi-scale Neural Operator (MSNO) and Multi-Scale Self-Attention (MSSA). Among them, MSNO obtains multi-scale latent codes through feature enhancement, multi-scale characteristics extraction, and multi-scale characteristics merging. MSSA further enhances the multi-scale characteristics of latent codes, resulting in better performance. Furthermore, to improve the performance of network, we propose the Re-Interaction Module (RIM) combined with the cumulative training strategy to improve the diversity of learned information for the network. We have systematically introduced multi-scale characteristics for the first time in ASSR, extensive experiments are performed to validate the effectiveness of MSIT, and our method achieves state-of-th

We study how the energy and momentum resolution of angle-resolved photoemission spectroscopy (ARPES) affects the linewidth, Fermi crossing, velocity, and curvature of the measured band structure. Based on the fact that the resolution smooths out the spectra, acting as a low-pass filter, we develop an iterative simulation scheme that compensates for resolution effects and allows the fundamental physical parameters to be accurately extracted. By simulating a parabolic band structure of Fermi-liquid quasiparticles, we show that this method works for an energy resolution up to 100 meV and a momentum resolution equal to twice the energy resolution scaled by the Fermi velocity. Our analysis acquires particular relevance in the hard and soft x-ray regimes, where a degraded resolution limits the accuracy of the extracted physical parameters, making it possible to study how the electronic excitations are modified when the ARPES probing depth increases beyond the surface.

Spatial resolution in optical microscopy has traditionally been treated as a fixed parameter of the optical system. Here, we present an approach to enhance transverse resolution in beam-scanned optical coherence tomography (OCT) beyond its aberration-free resolution limit, without any modification to the optical system. Based on the theorem of invariance of information capacity, resolution-enhanced (RE)-OCT navigates the exchange of information between resolution and signal-to-noise ratio (SNR) by exploiting efficient noise suppression via coherent averaging and a simple computational bandwidth expansion procedure. We demonstrate a resolution enhancement of 1.5 times relative to the aberration-free limit while maintaining comparable SNR in silicone phantom. We show that RE-OCT can significantly enhance the visualization of fine microstructural features in collagen gel and ex vivo mouse brain. Beyond RE-OCT, our analysis in the spatial-frequency domain leads to an expanded framework of information capacity and resolution in coherent imaging that contributes new implications to the theory of coherent imaging. RE-OCT can be readily implemented on most OCT systems worldwide, immediatel

The optical resolution of a digital camera is one of its most crucial parameters with broad relevance for consumer electronics, surveillance systems, remote sensing, or medical imaging. However, resolution is physically limited by the optics and sensor characteristics. In addition, practical and economic reasons often stipulate the use of out-dated or low-cost hardware. Super-resolution is a class of retrospective techniques that aims at high-resolution imagery by means of software. Multi-frame algorithms approach this task by fusing multiple low-resolution frames to reconstruct high-resolution images. This work covers novel super-resolution methods along with new applications in medical imaging.

Digital Rock Imaging is constrained by detector hardware, and a trade-off between the image field of view (FOV) and the image resolution must be made. This can be compensated for with super resolution (SR) techniques that take a wide FOV, low resolution (LR) image, and super resolve a high resolution (HR), high FOV image. The Enhanced Deep Super Resolution Generative Adversarial Network (EDSRGAN) is trained on the Deep Learning Digital Rock Super Resolution Dataset, a diverse compilation 12000 of raw and processed uCT images. The network shows comparable performance of 50% to 70% reduction in relative error over bicubic interpolation. GAN performance in recovering texture shows superior visual similarity compared to SRCNN and other methods. Difference maps indicate that the SRCNN section of the SRGAN network recovers large scale edge (grain boundaries) features while the GAN network regenerates perceptually indistinguishable high frequency texture. Network performance is generalised with augmentation, showing high adaptability to noise and blur. HR images are fed into the network, generating HR-SR images to extrapolate network performance to sub-resolution features present in the H

An algorithm for the detection of overlapping natural communities in networks was proposed by Lancichinetti, Fortunato, and Kertesz (LFK) last year. The LFK algorithm constructs natural communities of (in principle) all nodes of a graph by maximising the local fitness of communities. The resulting modules can overlap. The generation of communities can easily be repeated for many values of resolution; thus allowing different views on the network at different resolutions. We implemented the main idea of the LFK algorithm---to generate natural communities of each node of a network---in a different way. We start with a value of the resolution parameter that is high enough for each node to be its own natural community. As soon as the resolution is reduced, each node acquires other nodes as members of its community, i.e. natural communities grow. For each community found at a certain resolution level we calculate the next lower resolution where a node is added. After adding a node to a community of a seed node we check whether it is also the natural community of a node that we have already analysed. In this case, we can stop expanding the seed node's community. We tested our algorithm on

Superpixel segmentation has recently seen important progress benefiting from the advances in differentiable deep learning. However, the very high-resolution superpixel segmentation still remains challenging due to the expensive memory and computation cost, making the current advanced superpixel networks fail to process. In this paper, we devise Patch Calibration Networks (PCNet), aiming to efficiently and accurately implement high-resolution superpixel segmentation. PCNet follows the principle of producing high-resolution output from low-resolution input for saving GPU memory and relieving computation cost. To recall the fine details destroyed by the down-sampling operation, we propose a novel Decoupled Patch Calibration (DPC) branch for collaboratively augment the main superpixel generation branch. In particular, DPC takes a local patch from the high-resolution images and dynamically generates a binary mask to impose the network to focus on region boundaries. By sharing the parameters of DPC and main branches, the fine-detailed knowledge learned from high-resolution patches will be transferred to help calibrate the destroyed information. To the best of our knowledge, we make the f

Fluorescence microscopy is an important and extensively utilised tool for imaging biological systems. However, the image resolution that can be obtained has a limit as defined through the laws of diffraction. Demand for improved resolution has stimulated research into developing methods to image beyond the diffraction limit based on far-field fluorescence microscopy techniques. Rapid progress is being made in this area of science with methods emerging that enable fluorescence imaging in the far-field to possess a resolution well beyond the diffraction limit. This review outlines developments in far-field fluorescence methods which enable ultrahigh resolution imaging and application of these techniques to biology. Future possible trends and directions in far-field fluorescence imaging with ultrahigh resolution are also outlined.

The present study is concerned with large-eddy simulations (LES) of supersonic jet flows. The work addresses, in particular, the simulation of a perfectly expanded free jet flow with an exit Mach number of 1.4 and an exit temperature equal to the ambient temperature. Calculations are performed using a nodal discontinuous Galerkin method. The present effort studies the effects of mesh and polynomial refinement on the solution. The present calculations consider computational meshes and polynomial orders such that the number of degrees of freedom (DOFs) in the solution ranges from 50 to 410 million. Mean velocity results and root mean square (RMS) values of velocity fluctuations indicate a better agreement with experimental data as the resolution is increased. The generated data provide a good understanding of the effects of increasing the discretization refinement for LES calculations of jet flows. The present results can guide future simulations of similar flow configurations.

The paper deals with the resolution of third and fourth degree equations by means of radicals. It is a survey of some historical details about this fundamental problem. Moreover, it explains practical methods for the resolution of third and fourth degree equation through the algebraic side and we introduce some results about the equations of greater degree. Mathematicians and complex numbers and the results of rules of calculations as well as having completed the theory of equations model Mathematics in different historical and chronological contexts at several levels of research. The subject would join a reference auditorium for authors, teachers and students at a time when the context of collocation favors algebraic equations and radical solutions.

This article shall serve as a quick reference for somebody who needs precise information on concepts and results related to resolution of singularities. As such, it is more a technical manual than a bedtime story. Topics which are covered: Singular and regular points of varieties and schemes; various definitions of blowups and their mutual relations; properties of blowups; transforms of varieties, schemes and ideals; exceptional divisors; Cartier and normal crossings divisors; transversality; hypersurfaces of maximal contact; flags; coefficient ideals; resolution invariants; order of ideals; Hilbert-Samuel function; semicontinuity; various resolution statements; characteristic zero resolution; characteristic p phenomena. The text is complemented with lots of illustrating examples.

Anaphora resolution is envisaged in this paper as part of the reference resolution process. A general open architecture is proposed, which can be particularized and configured in order to simulate some classic anaphora resolution methods. With the aim of improving pronoun resolution, the system takes advantage of elementary cues about characters of the text, which are represented through a particular data structure. In its most robust configuration, the system uses only a general lexicon, a local morpho-syntactic parser and a dictionary of synonyms. A short comparative corpus analysis shows that narrative texts are the most suitable for testing such a system.

Visual-only speech recognition is dependent upon a number of factors that can be difficult to control, such as: lighting; identity; motion; emotion and expression. But some factors, such as video resolution are controllable, so it is surprising that there is not yet a systematic study of the effect of resolution on lip-reading. Here we use a new data set, the Rosetta Raven data, to train and test recognizers so we can measure the affect of video resolution on recognition accuracy. We conclude that, contrary to common practice, resolution need not be that great for automatic lip-reading. However it is highly unlikely that automatic lip-reading can work reliably when the distance between the bottom of the lower lip and the top of the upper lip is less than four pixels at rest.

Ultra-high resolution image segmentation has raised increasing interests in recent years due to its realistic applications. In this paper, we innovate the widely used high-resolution image segmentation pipeline, in which an ultra-high resolution image is partitioned into regular patches for local segmentation and then the local results are merged into a high-resolution semantic mask. In particular, we introduce a novel locality-aware context fusion based segmentation model to process local patches, where the relevance between local patch and its various contexts are jointly and complementarily utilized to handle the semantic regions with large variations. Additionally, we present the alternating local enhancement module that restricts the negative impact of redundant information introduced from the contexts, and thus is endowed with the ability of fixing the locality-aware features to produce refined results. Furthermore, in comprehensive experiments, we demonstrate that our model outperforms other state-of-the-art methods in public benchmarks. Our released codes are available at: https://github.com/liqiokkk/FCtL.