Search Results (85)

Artificial intelligence technologies, particularly machine learning and computer vision, are being increasingly utilized to preserve, restore, and create immersive virtual experiences with cultural artifacts and sites, thus aiding in conserving cultural heritage and making it accessible to a global audience. This paper examines the performance of Generative Adversarial Networks (GAN), especially Style-Based Generator Architecture (StyleGAN), as a deep learning approach for producing realistic images of Egyptian monuments. We used Sigmoid loss for Language–Image Pre-training (SigLIP) as a unique image–text alignment system to guide monument generation through semantic elements. We also studied truncation methods to regulate the generated image noise and identify the most effective parameter settings based on architectural representation versus diverse output creation. An improved discriminator design that combined noise addition with squeeze-and-excitation blocks and a modified MinibatchStdLayer produced 27.5% better Fréchet Inception Distance performance than the original discriminator models. Moreover, differential evolution for latent-space optimization reduced alignment mistakes during specific monument construction tasks by about 15%. We checked a wide range of truncation values from 0.1 to 1.0 and found that somewhere between 0.4 and 0.7 was the best range because it allowed for good accuracy while retaining many different architectural elements. Our findings indicate that specific model optimization strategies produce superior outcomes by creating better-quality and historically correct representations of diverse Egyptian monuments. Thus, the developed technology may be instrumental in generating educational and archaeological visualization assets while adding virtual tourism capabilities. Full article

A study is made of linear isometries on Fréchet spaces for which the metric is given in terms of a sequence of seminorms. This establishes sufficient conditions on the growth of the function that defines the metric in terms of the seminorms to ensure that a linear operator preserving the metric also preserves each of these seminorms. As an application, characterizations are given of the isometries on various spaces including those of holomorphic functions on complex domains and continuous functions on open sets, extending the Banach–Stone theorem to surjective and nonsurjective cases. Full article

The synthesis of realistic fog in images is critical for applications such as autonomous navigation, augmented reality, and visual effects. Traditional methods based on Koschmieder’s law or GAN-based image translation typically assume homogeneous fog distributions and rely on oversimplified scattering models, limiting their physical realism. In this paper, we propose a physics-driven approach to fog synthesis by discretizing the Radiative Transfer Equation (RTE). Our method models spatially inhomogeneous fog and anisotropic multi-scattering, enabling the generation of structurally consistent and perceptually plausible fog effects. To evaluate performance, we construct a dataset of real-world foggy, cloudy, and sunny images and compare our results against both Koschmieder-based and GAN-based baselines. Experimental results show that our method achieves a lower Fréchet Inception Distance ($-10\%$ vs. Koschmieder, $-42\%$ vs. CycleGAN) and a higher Pearson correlation ($+4\%$ and $+21\%$, respectively), highlighting its superiority in both feature space and structural fidelity. These findings highlight the potential of RTE-based fog synthesis for physically consistent image augmentation under challenging visibility conditions. However, the method’s practical deployment may be constrained by high memory requirements due to tensor-based computations, which must be addressed for large-scale or real-time applications. Full article

Plant-parasiticnematodes represent a significant biosecurity threat in cross-border plant quarantine, necessitating precise identification for effective border control. While DL models have demonstrated success in nematode image classification based on morphological features, the limited availability of high-quality samples and the species-specific nature of nematodes result in insufficient training data, which constrains model performance. Although generative models have shown promise in data augmentation, they often struggle to balance morphological fidelity and phenotypic diversity. This paper proposes a novel few-shot data augmentation framework based on a morphology-constrained latent diffusion model, which, for the first time, integrates morphological constraints into the latent diffusion process. By geometrically parameterizing nematode morphology, the proposed approach enhances topological fidelity in the generated images and addresses key limitations of traditional generative models in controlling biological shapes. This framework is designed to augment nematode image datasets and improve classification performance under limited data conditions. The framework consists of three key components: First, we incorporate a fine-tuning strategy that preserves the generalization capability of model in few-shot settings. Second, we extract morphological constraints from nematode images using edge detection and a moving least squares method, capturing key structural details. Finally, we embed these constraints into the latent space of the diffusion model, ensuring generated images maintain both fidelity and diversity. Experimental results demonstrate that our approach significantly enhances classification accuracy. For imbalanced datasets, the Top-1 accuracy of multiple classification models improved by 7.34–14.66% compared to models trained without augmentation, and by 2.0–5.67% compared to models using traditional data augmentation. Additionally, when replacing up to 25% of real images with generated ones in a balanced dataset, model performance remained nearly unchanged, indicating the robustness and effectiveness of the method. Ablation experiments demonstrate that the morphology-guided strategy achieves superior image quality compared to both unconstrained and edge-based constraint methods, with a Fréchet Inception Distance of 12.95 and an Inception Score of 1.21 ± 0.057. These results indicate that the proposed method effectively balances morphological fidelity and phenotypic diversity in image generation. Full article

In this study, we discuss the semilocal convergence analysis of a fourth-order iterative method in Banach spaces. We assume the Fréchet derivative satisfies the Lipschitz continuity condition, obtains suitable recurrence relations, and determines the domain of convergence under appropriate initial estimates. In addition, the uniqueness domain for the solution and the error bounds are obtained. Next, several numerical examples, one which includes a Chandrasekhar integral equation, are carried out to apply the theoretical findings for semilocal convergence. Then, a final overview is provided. Full article

One of the methods for studying the solvability of infinite systems of integral or differential equations is the application of various fixed-point theorems to operators acting in appropriate functional Banach spaces. This method is fairly well developed, frequently used, and effective in many situations. However, there are cases in which certain infinite systems of differential equations arise—linked to the modeling of significant real-world phenomena—where this method, based on situating considerations within Banach spaces, fails and cannot be applied. In this paper, we propose a slightly different approach, which involves conducting the analysis within appropriate functional Fréchet spaces. We discuss the fundamental properties of these spaces and formulate compactness criteria. The main result of this paper is a positive answer, using the proposed method, to an open problem concerning the modeling of a stochastic birth-and-death process, as formulated in one of the cited publications. The most important conclusion is that the presented computational technique, based on functional Fréchet spaces, can be regarded as a more effective alternative to methods based on Banach spaces. Full article

This study presents a comprehensive analysis of the semilocal convergence properties of a high-order iterative scheme designed to solve nonlinear equations in Banach spaces. The investigation is carried out under the assumption that the first derivative of the associated nonlinear operator adheres to a generalized Lipschitz-type condition, which broadens the applicability of the convergence analysis. Furthermore, the research demonstrates that, under an additional mild assumption, the proposed scheme achieves a remarkable ninth-order rate of convergence. This high-order convergence result significantly contributes to the theoretical understanding of iterative schemes in infinite-dimensional settings. Beyond the theoretical implications, the results also have practical relevance, particularly in the context of solving complex systems of equations and integral equations that frequently arise in applied mathematics, physics, and engineering disciplines. Overall, the findings provide valuable insights into the behavior and efficiency of advanced iterative schemes in Banach space frameworks. The comparative analysis with existing schemes also demonstrates that the ninth-order iterative scheme achieves faster convergence in most cases, particularly for smaller radii. Full article

In this paper, we study three kinds of dentabilities and present their important applications in the geometric theory of Banach spaces. First, the relations between weak-denting points and extreme points are established. Moreover, we characterize strong convex spaces and weakly locally uniformly smooth spaces by using weakly locally uniform dentability. Finally, we provide some important applications of $stron{g}^{\ast }$ dentability in Fréchet-smooth Banach spaces while investigating the density of $stron{g}^{\ast }$ points in dual Banach spaces. Full article

The Banach Gelfand Triple $(S_0,L^2,S_0^{\prime })$ consists of the Feichtinger algebra $S_0\left(R^d\right)$ as a space of test functions, the dual space $S_0^{\prime }\left(R^d\right)$, known as the space of mild distributions, and the intermediate Hilbert space $L^2\left(R^d\right)$. This Gelfand Triple is very useful for the description of mathematical problems in the area of time-frequency analysis, but also for classical Fourier analysis and engineering applications. Because the involved spaces are Banach spaces, we speak of a Banach Gelfand Triple, in contrast to the widespread concept of rigged Hilbert spaces, which usually involve nuclear Frechet spaces. Still, both concepts serve very similar purposes. Based on the manifold properties of $S_0\left(R^d\right)$, it has found applications in the derivation of mathematical statements related to Gabor Analysis but also in providing an alternative and more lucid description of classical results, such as the Shannon sampling theory, with a potential to renew the way how Fourier and time-frequency analysis, but also signal processing courses for engineers (or physicists and mathematicians) could be taught in the future. In the present study, we will demonstrate that one could choose a relatively large variety of similar Banach Gelfand Triples, even if one wants to include key properties such as Fourier invariance (an extended version of Plancherel’s Theorem). Some of them appeared naturally in the literature. It turns out, that $S_0\left(R^d\right)$ is the smallest member of this family. Consequently $S_0^{\prime }\left(R^d\right)$ is the largest dual space among all these spaces, which may be one of the reasons for its universal usefulness. This article provides a study of the basic properties following from a short list of relatively simple assumptions and gives a list of non-trivial examples satisfying these basic axioms. Full article

With the advancement of agricultural automation, the demand for road recognition and understanding in agricultural machinery autonomous driving systems has significantly increased. To address the scarcity of instance segmentation data for rural roads and rural unstructured scenes, particularly the lack of support for high-resolution and fine-grained classification, a 20-class instance segmentation dataset was constructed, comprising 10,062 independently annotated instances. An improved StyleGAN2-ADA data augmentation method was proposed to generate higher-quality image data. This method incorporates a decoupled mapping network (DMN) to reduce the coupling degree of latent codes in W-space and integrates the advantages of convolutional networks and transformers by designing a convolutional coupling transfer block (CCTB). The core cross-shaped window self-attention mechanism in the CCTB enhances the network’s ability to capture complex contextual information and spatial layouts. Ablation experiments comparing the improved and original StyleGAN2-ADA networks demonstrate significant improvements, with the inception score (IS) increasing from 42.38 to 77.31 and the Fréchet inception distance (FID) decreasing from 25.09 to 12.42, indicating a notable enhancement in data generation quality and authenticity. In order to verify the effect of data enhancement on the model performance, the algorithms Mask R-CNN, SOLOv2, YOLOv8n, and OneFormer were tested to compare the performance difference between the original dataset and the enhanced dataset, which further confirms the effectiveness of the improved module. Full article

We investigate the well-posedness of an initial boundary value problem for the Kelvin–Voigt–Brinkman–Forchheimer equations with memory and variable viscosity under a non-homogeneous Dirichlet boundary condition. A theorem about the global-in-time existence and uniqueness of a strong solution of this problem is proved under some smallness requirements on the size of the model data. For obtaining this result, we used a new technique, which is based on the operator treatment of the initial boundary value problem with the consequent application of an abstract theorem about the local unique solvability of an operator equation containing an isomorphism between Banach spaces with two kind perturbations: bounded linear and differentiable nonlinear having a zero Fréchet derivative at a zero element. Our work extends the existing frameworks of mathematical analysis and understanding of the dynamics of non-Newtonian fluids in porous media. Full article

The safety of ships during nighttime navigation has always been a major concern. With the widespread application of technologies such as intelligent recognition, intelligent detection, and unmanned ship navigation at night, nighttime maritime light pollution has significantly affected the effectiveness of these intelligent technologies and navigation safety. Therefore, effectively eliminating nighttime maritime light pollution has become an urgent challenge that needs to be addressed. This paper presents a model based on spatial frequency blocks (SFBs) to solve the problem of light pollution in nighttime sea images. The model includes ResNet-50, an encoder, a decoder, and a discriminator. To enable the model to better remove the influence of light pollution, this study designs a method of first detecting the light pollution area and then removing it. It extracts image information from the space–frequency domain to help eliminate light pollution and retain more image information. The experimental results show that on the nighttime light pollution dataset, the Peak Signal-to-Noise Ratio (PSNR) of the model is improved to 24.91 compared to the current state-of-the-art image restoration model, while the Frechet inception distance (FID) is reduced to 64.85. At the same time, in the real night environment, the model can better remove light pollution to recover the original nighttime information. It has excellent performance and provides a certain reference value for advancing the safety of nighttime maritime navigation. Full article

Symmetry and anti-symmetry appear naturally in the study of systems of nonlinear equations resulting from numerous fields. The solutions of such equations can be obtained in analytical form only in some special situations. Therefore, algorithms or iterative schemes are mostly studied, which approximate the solution. In particular, Jarratt-like methods were introduced with convergence order at least six in Euclidean spaces. We study the methods in the Banach-space setting. Semilocal convergence is studied to obtain the ball containing the solution. The local convergence analysis is performed without the help of the Taylor series with relaxed differentiability assumptions. Our assumptions for obtaining the convergence order are independent of the solution; earlier studies used assumptions involving the solution for local convergence analysis. We compare the methods numerically with similar-order methods and also study the dynamics. Full article

We propose an anime style transfer model to generate anime faces from human face images. We improve the model by modifying the normalization function to obtain more feature information. To make the face feature position of the anime face similar to the human face, we propose facial landmark loss to calculate the error between the generated image and the real human face image. To avoid obvious color deviation in the generated images, we introduced perceptual color loss into the loss function. In addition, due to the lack of reasonable metrics to evaluate the quality of the animated images, we propose the use of Fréchet anime inception distance to calculate the distance between the distribution of the generated animated images and the real animated images in high-dimensional space, so as to understand the quality of the generated animated images. In the user survey, up to 74.46% of users think that the image produced by the proposed method is the best compared with other models. Also, the proposed method reaches a score of 126.05 for Fréchet anime inception distance. Our model performs the best in both user studies and FAID, showing that we have achieved better performance in human visual perception and model distribution. According to the experimental results and user feedback, our proposed method can generate results with better quality compared to existing methods. Full article

Addressing the challenge of limited samples arising from the difficulty and high cost of pavement crack, image collecting and labeling, along with the inadequate ability of traditional data augmentation methods to enhance sample feature space, we propose VDCrackGAN, a generative adversarial network combining VAE and DCGAN, specifically tailored for pavement crack data augmentation. Furthermore, spectral normalization is incorporated to enhance the stability of network training, and the self-attention mechanism Swin Transformer is integrated into the network to further improve the quality of crack generation. Experimental outcomes reveal that in comparison to the baseline DCGAN, VDCrackGAN achieves notable improvements of 13.6% and 26.4% in the Inception Score (IS) and Fréchet Inception Distance (FID) metrics, respectively. Full article