Gaussian Function Research Articles

Multi-Source Image Fusion Based on BEMD and Region Sharpness Guidance Region Overlapping Algorithm

Multi-focal image and multi-modal image fusion technology can fully take advantage of different sensors or different times, retaining the image feature information and improving the image quality. A multi-source image fusion algorithm based on bidimensional empirical mode decomposition (BEMD) and a region sharpness-guided region overlapping algorithm are studied in this article. Firstly, source images are decomposed into multi-layer bidimensional intrinsic mode functions (BIMFs) and residuals from high-frequency layer to low-frequency layer by BEMD. Gaussian bidimensional intrinsic mode functions (GBIMFs) are obtained by applying Gaussian filtering operated on BIMF and calculating the sharpness value of segmented regions using an improved weighted operator based on the Tenengrad function, which is the key to comparison selection and fusion. Then, the GBIMFs and residuals selected by sharpness comparison strategy are fused by the region overlapping method, and the stacked layers are weighted to construct the final fusion image. Finally, based on qualitative evaluation and quantitative evaluation indicators, the proposed algorithm is compared with six typical image fusion algorithms. The comparison results show that the proposed algorithm can effectively capture the feature information of images in different states and reduce the redundant information.

Simulation of Time-Sequence Operation Considering DC Utilization Hours of New Energy Base in Desert and Gobi Area

Direct current power transmission is a crucial method for consuming new energy in desert and Gobi regions. Given the issue of the inefficient use of transmission channels, this study develops a simulation model for the operational time sequence of new energy bases in these areas. The model integrates factors such as hours of DC power transmission, environmental impacts, economic considerations, and operational flexibility. Initially, the model addresses the significant variability and unpredictability of wind and solar energy in these regions by introducing an analysis method combining Gaussian Kernel Density Estimation (GKDE) with a Gaussian Mixture Model (GMM). Subsequently, a flexible DC power transmission operational model is formulated, taking into account different DC transmission modes. The model’s efficiency is enhanced by employing the Dung Beetle Optimization algorithm with nondominated sorting to minimize variable ranges and expedite solution times. The model’s effectiveness is demonstrated through a simulation applied to a new energy base in Gansu Province, Northwest China, confirming its validity.

STNMDA: A Novel Model for Predicting Potential Microbe-Drug Associations with Structure-Aware Transformer

Introduction: Microbes are intimately involved in the physiological and pathological processes of numerous diseases. There is a critical need for new drugs to combat microbe-induced diseases in clinical settings. Predicting potential microbe-drug associations is, therefore, essential for both disease treatment and novel drug discovery. However, it is costly and time-consuming to verify these relationships through traditional wet lab approaches. Methods: We proposed an efficient computational model, STNMDA, that integrated a StructureAware Transformer (SAT) with a Deep Neural Network (DNN) classifier to infer latent microbedrug associations. The STNMDA began with a “random walk with a restart” approach to construct a heterogeneous network using Gaussian kernel similarity and functional similarity measures for microorganisms and drugs. This heterogeneous network was then fed into the SAT to extract attribute features and graph structures for each drug and microbe node. Finally, the DNN classifier calculated the probability of associations between microbes and drugs. Results: Extensive experimental results showed that STNMDA surpassed existing state-of-the-art models in performance on the MDAD and aBiofilm databases. In addition, the feasibility of STNMDA in confirming associations between microbes and drugs was demonstrated through case validations. Conclusion: Hence, STNMDA showed promise as a valuable tool for future prediction of microbedrug associations.

A fourth-order kernel for improving numerical accuracy and stability in Eulerian SPH for fluids and total Lagrangian SPH for solids

The error of smoothed particle hydrodynamics (SPH) using a kernel for particle-based approximation mainly arises from smoothing and integration errors. The choice of the kernel significantly impacts numerical accuracy, stability and computational efficiency. Currently, the most popular kernels, such as B-spline, truncated Gaussian (for compact support), and Wendland kernels, have 2nd-order smoothing errors, and the Wendland kernel has become mainstream in the SPH community due to its stability and accuracy. Since the particle distribution after relaxation can achieve fast convergence of integration error with respect to support radius, it is logical to choose kernels with higher-order smoothing error to improve the numerical accuracy. In this paper, the error of the 4th-order Laguerre-Wendland kernel proposed by Litvinov et al. [1] is revisited, and another 4th-order truncated Laguerre-Gauss kernel is further analyzed and considered to replace the widely used Wendland kernel. The proposed kernel has the following three properties: One is that it avoids the pair-instability problem during the relaxation process, unlike the original truncated Gaussian kernel, and achieves much less relaxation residue than the Wendland and Laguerre-Wendland kernels; One is the truncated compact support size is the same as the non-truncated one of the Wendland kernel, which leads to both kernels' comparably computational efficiency; Another is that the truncation error of this kernel is much less than that of the Wendland kernel. Furthermore, a comprehensive set of 2D and 3D benchmark cases on Eulerian SPH for fluid dynamics and total Lagrangian SPH for solid dynamics validate the considerably improved numerical accuracy of the truncated Laguerre-Gauss kernel without introducing extra computational effort.

Agricultural path detection systems using Canny-edge detection and Hough transform

Navigation is one of the crucial aspects of automation technology within the field of agriculture, such as robotics systems or autonomous agricultural vehicles. Despite many navigation systems having been developed for agricultural land, due to their high development and component costs, these systems are difficult to access for farmers or organizations with limited capital. In this study, the Canny-edge detection and Hough transform methods are implemented in a path detection system on agricultural land to find an alternative, cost-effective navigation system for autonomous farming robots or vehicles. The system is tested on ground-level view images, which are captured from a low perspective and under three different lighting conditions. The testing and experimentation process involves adjusting the parameters of the Canny-edge detection and Hough transform methods for different lighting conditions. Subsequently, an evaluation is conducted using Intersection over Union to obtain the best accuracy results, followed by fine-tuning of the canny-edge detection and Hough transform method parameters. The identified parameters, specifically a 15×15 Gaussian kernel, low threshold of 50, high threshold of 150, Hough threshold, minimum line length of 150, and maximum line gap, have been discerned as optimal for the canny-edge and Hough transform algorithms under medium lighting conditions (G=1.0). The observed efficacy of these parameter configurations suggests the method’s viability for implementation in path detection systems for agricultural vehicles or robots. This underscores its potential to deliver reliable performance and navigate seamlessly across diverse lighting scenarios within the agricultural context.

3D Reconstruction of Indoor Scenes Based on 3DGS Models

Abstract Abstract With the rapid development of computer vision and artificial intelligence technologies, indoor scene reconstruction has been more and more widely used in the fields of virtual reality, augmented reality and architectural design. In this paper, we study an indoor scene reconstruction method based on the 3DGS model, which has been widely used in computer graphics and vision processing with powerful scene representation and rendering capabilities. In this study, we optimize the 3DGS model to enhance the detail preservation and realism of the reconstruction results by adjusting the opacity of the Gaussian function. We used the Replica dataset and the self-harvested dataset for model training. Through experimental validation, the peak signal-to-noise ratio as well as the structural similarity ratio of the reconstruction results of the optimized model have an improvement effect of more than 1%, which indicates that the optimized model has a significant improvement in detail retention and realism, and the reconstructed scene performs more realistically in terms of texture details and light and shadow effects.

Spatial resolution of sea surface temperature observed by AMSR2 on GCOM-W satellite

ABSTRACT This study developed a method to evaluate the effective spatial resolution of sea surface temperature (SST) data produced from observations of a microwave radiometer on satellites. The method was applied to 7-year SST data from the Advanced Microwave Scanning Radiometer 2 (AMSR2) on the Japan Aerospace Exploration Agency’s (JAXA) Global Change Observation Mission-Water (GCOM-W) satellite. JAXA has produced three SST products from AMSR2 observations: standard SST, 10-GHz SST, and multi-band SST. They differ in spatial resolution because the frequency used to retrieve the SST has different footprint sizes, although the resolution has not been evaluated so far. We utilized high-resolution infrared SST data from the geostationary meteorological satellite Himawari-8. The Himawari SST was spatially smoothed by a Gaussian function to identify the smoothing scale that most accurately reproduces the AMSR2 SST gradient fields in the same area and time. The similarities between the Himawari and AMSR2 SST gradient fields were assessed using three metrics. The correlation coefficient provided a stable and robust estimate against the noise included in the AMSR2 SSTs. As a result, the effective resolution was estimated at 67 km for the standard SST, 52 km for the 10-GHz SST, and 63 km for the multi-band SST. These are all larger than the nominal resolution expected from the AMSR2 footprint size. The 10-GHz and multi-band SSTs had significantly higher resolutions than the standard SST.

Design and application of a high-precision counterweighted self-calibrating surface thermometer.

In this study, a high-precision counterweight self-calibrating surface thermometer is designed to reduce human and environmental influences on a thermocouple surface thermometer during measuring. A self-weighted spring structure based on a copper substrate is designed to ensure perfect contact between the surface thermometer and the temperature source. In conjunction, a wind guard is coupled with insulating materials to optimize the thermal exchange of the surface thermometer. Subsequently, the maximum error is reduced to ±1.5 °C by system hardware optimization. However, hardware calibration alone is insufficient. Furthermore, a back propagation neural network is employed to calibrate the surface thermometer. Temperature sensor data are collected under various surface source temperatures and airflow velocities to train the neural network. Hence, the effectiveness of the proposed Gaussian function in enhancing the measurement accuracy of the surface temperature sensor is demonstrated. The results show higher stability and repeatability in temperature measurement than thermocouple-based surface thermometers. The proposed thermometer exhibits robustness against environmental and operational variability with a maximum indication error of -0.2 °C. In contrast, the maximum error of the surface thermometer is between -2.8 and -6.8 °C. Regarding repeatability, the standard deviation with the proposed device is 0.2%, highlighting its accuracy and consistency of performance. These results can mostly be attributed to the synergistic effect of clever mechanical design and software optimization, resulting in a surface thermometer with outstanding accuracy and repeatability.

A Distorted Light Field Image Correction Method Based on Improved Hough Transform

Introduction: In using a camera to take photos, due to environmental limitations, uneven lighting can cause uneven distribution of the image light field, resulting in distortion of the image background and target, blurring of details, and distorted light field images. Method: In view of this, research is conducted on the correction of distorted light field images based on the Hough transform. First, the improved Hough transform is utilized to locate the four coordinates, the matrix information of the normal image is applied to calculate the corresponding parameter amount, and then the low-frequency part of the image spectrum is removed. Finally, it uses the Gaussian function for difference, inputs the original data, and gets the correction result of the distorted light field image. Result: The research results indicate that in the practical application of the distorted light field image correction algorithm based on the Hough transform, the improved Hough transform algorithm is superior to the traditional one. Conclusion: In comparative experiments, the research algorithm outperforms the other three algorithms, with an average color restoration of 93.76% and an average signal-to-noise ratio of 54.22dB. The superiority of the research algorithm has been verified, indicating that the research method can perfectly correct distorted light field images and achieve good correction results.

Stability of the logarithmic Sobolev inequality and uncertainty principle for the Tsallis entropy

We consider the stability of the functional inequalities concerning the entropy functional. For the Boltzmann–Shannon entropy, the logarithmic Sobolev inequality holds as a lower bound of the entropy by the Fisher information, and the Heisenberg uncertainty principle follows from combining it with the Shannon inequality. The optimizer for these inequalities is the Gauss function, which is a fundamental solution to the heat equation. In the fields of statistical mechanics and information theory, the Tsallis entropy is known as a one-parameter extension of the Boltzmann–Shannon entropy, and the Wasserstein gradient flow of it corresponds to the quasilinear diffusion equation. We consider the improvement and stability of the optimizer for the logarithmic Sobolev inequality related to the Tsallis entropy. Furthermore, we show the stability results of the uncertainty principle concerning the Tsallis entropy.

A novel meshless radial basis reproducing kernel particle approach for 3D thermo-mechanical analysis of mushy zone phase-change problems

This paper presents a three-dimensional thermo-elastoplastic computational model for the analysis of phase change problems involving the mushy zone. The model utilizes a novel meshless radial basis reproducing kernel particle approach, incorporating a high-order kernel that integrates Gaussian and cosine functions. An energy balance equation for the entire domain is formulated using the effective heat capacity method, based on the enthalpy formulation. The governing equations are discretized using the Galerkin weak form to compute thermal residual stresses, with essential boundary conditions enforced through the penalty method. Plastic deformation is characterized using the von Mises criterion with isotropic hardening, and the strain term resulting from temperature-dependent material properties is incorporated into the incremental solution process. Determination of the plastic strain increment is based on the Prandtl–Reuss flow rule. The accuracy and efficiency of the proposed meshless approach were rigorously evaluated through numerical examples encompassing two- and three-dimensional problems. The computational results were compared against available analytical and validated numerical solutions. This comprehensive assessment substantiated the robustness and precision of the developed technique. The case studies presented elucidate the capacity of the novel meshless model to effectively predict temperature distributions and residual stress fields within mushy zone phase change phenomena, accommodating both regular and irregular geometries under various boundary conditions. Notably, the model demonstrated consistent stability and high accuracy across the spectrum of simulated scenarios, thus underscoring its potential as a valuable tool for investigating complex phase change processes.

Video-based subtle vibration measurement in the presence of large motions

Recently, phase-based methods offer precise measurement of subtle vibrations from videos but face challenges when dealing with moving objects. This paper introduces a novel video-based method for measuring subtle vibrations in the presence of large motions. It employs complex steerable filters to capture phase variations at each pixel, extracting a composite motion signal. Based on the differences in acceleration characteristics between subtle vibrations and large motions, a band-passed acceleration filter is designed to separate them, relying only on limited prior knowledge of the frequency band. The filter design minimizes passband attenuation using a genetic algorithm for iterative parameter optimization. By further incorporating a Gaussian amplitude kernel, we suppress large-amplitude nonlinear motion interference and extract subtle vibrations with acceleration characteristics. Both simulation experiments and real-world tests demonstrate that this method outperforms state-of-the-art techniques in terms of accuracy, providing a more effective approach for measuring subtle vibrations in moving objects.

Mainardi smoothing homotopy method for solving nonlinear optimal control problems

This paper proposes a new type of smoothing homotopy method for solving general nonlinear optimal control problems via the indirect method, leveraging the Mainardi kernel as the smoothing kernel. The Mainardi kernel is firstly derived from the fundamental solution of the time-fractional diffusion-wave equation, representing a generalized form of the Gaussian kernel. By altering the fractional derivative order, the kernel can seamlessly switch between non-Gaussian and Gaussian forms. Then, parts of the two-point boundary value problems are convolved with the smoothing kernel, and the resulting surrogates are incorporated into the necessary conditions, replacing the terminal state and costate variables. The homotopy process is used for the smoothing parameter: increasing this parameter enhances the smoothing effect, simplifying the homotopy problems, while a parameter value of zero implies no smoothing, reverting to the original problems. Additionally, explicit expressions for the Mainardi kernel at specific derivative orders are derived, avoiding the inefficiencies associated with fractional derivatives. Simulation examples demonstrate that the proposed method offers significant advantages in flexibility and convergence compared to the traditional Gaussian smoothing homotopy method.

Measuring the pose repeatability accuracy of the industrial robot end-effector based on the ISSA-IGCF-IHT method

Abstract Industrial robots play an essential role in intelligent manufacturing. The pose repeatability accuracy of the end effector is an important indicator of the robot's precision operations ability. So, it is essential to measure the pose repeatability accuracy of the end effector. However, most of the existing measurement methods have problems such as cumbersome measurement processes and difficulty realizing multi-point measurements of large spaces. Considering the shortcomings of the existing methods, a theoretical model of the robot end effector’s pose repeatability accuracy measurement is proposed in this paper. Based on the theoretical model, a new method based on an improved sparrow search algorithm-improved Gaussian curve fitting-improved Hough transform (ISSA-IGCF-IHT) algorithm is proposed to measure the Industrial robot end effector’s pose repeatability accuracy. The experimental results show that the position measurement error after compensation is ±1.5μm, and the angle measurement error after compensation is ±2arcsec. We can conclude that the Industrial robot end effector’s pose repeatability accuracy measurement is achieved using the proposed method. The authors' main contribution is that the proposed method’s measurement process is simple and it can achieve multi-point measurement in large spaces. It provides a reference for measuring and evaluating the Industrial robot end effector’s pose repeatability accuracy.

Numerical investigation of bimodal tip clearance effect on the lift-drag and flow characteristics of a hydrofoil

Tip leakage flow has adverse effect on energy conversion of the hydraulic machinery. The new tip clearance structure based on Bimodal Gaussian function is designed to reduce tip leakage vortex. The effects of bimodal structure with different amplitudes and arrangement positions on lift-drag and flow characteristics are studied. The results show that the maximum rise of the lift-drag ratio reaches 5.88% when the bimodal structure amplitude is equal to the tip clearance size. The bimodal structure reduces the outflow velocity at the peak and forms a smooth streamline, which weakens the entrainment with the mainstream. The location of the bimodal structure far away from leading edge helps to produce smooth streamlines and make the flow field smoother, and reduces the area of high turbulent kinetic energy region near leading edge and in tip clearance outflow region significantly. The arrangement position of bimodal structure close to leading edge can produce a low-speed zone or a recirculation zone in the mainstream, which can block the mainstream flow and reduce the energy characteristics of the hydrofoil.

Investigating the missing-wedge problem in small-angle X-ray scattering tensor tomography across real and reciprocal space.

Small-angle-scattering tensor tomography is a technique for studying anisotropic nanostructures of millimetre-sized samples in a volume-resolved manner. It requires the acquisition of data through repeated tomographic rotations about an axis which is subjected to a series of tilts. The tilt that can be achieved with a typical setup is geometrically constrained, which leads to limits in the set of directions from which the different parts of the reciprocal space map can be probed. Here, we characterize the impact of this limitation on reconstructions in terms of the missing wedge problem of tomography, by treating the problem of tensor tomography as the reconstruction of a three-dimensional field of functions on the unit sphere, represented by a grid of Gaussian radial basis functions. We then devise an acquisition scheme to obtain complete data by remounting the sample, which we apply to a sample of human trabecular bone. Performing tensor tomographic reconstructions of limited data sets as well as the complete data set, we further investigate and validate the missing wedge problem by investigating reconstruction errors due to data incompleteness across both real and reciprocal space. Finally, we carry out an analysis of orientations and derived scalar quantities, to quantify the impact of this missing wedge problem on a typical tensor tomographic analysis. We conclude that the effects of data incompleteness are consistent with the predicted impact of the missing wedge problem, and that the impact on tensor tomographic analysis is appreciable but limited, especially if precautions are taken. In particular, there is only limited impact on the means and relative anisotropies of the reconstructed reciprocal space maps.

A combination of improved spline-kernelled chirplet transform and multi-synchrosqueezing technique for analyzing nonstationary signals and structural instantaneous frequency identification

To improve the accuracy of structural instantaneous frequency (IF) identified by the spline-kernelled chirplet transform, a combination of an improved spline-kernelled chirplet transform and a multi-synchrosqueezing technique is proposed for analyzing nonstationary signals and structural IF identification in this paper. Firstly, an improved spline-kernelled chirplet transform (ISCT) is put forward by introducing a three parameter Gaussian window function for an existing spline-kernelled chirplet transform. These three parameters are successfully obtained through an optimization algorithm and the energy concentration measure (CM). Then, combined with a multi-synchrosqueezing technique, a so-called improved multi-synchrosqueezing spline-kernelled chirplet transform (IMSSSCT) approach is further presented to improve the time–frequency energy concentration. Finally, the accuracy and practicability of the proposed IMSSSCT method are validated by analytical signals, a single-degree-of-freedom Duffing system, a three-layer shear frame, as well as a cantilever beam experiment. The research results indicate that the IMSSSCT technique can effectively and accurately identify the IFs of nonlinear and time-varying structures.

Missing-Mass Measurement of the 12C(K-, K+) Reaction at 1.8 GeV/c with the Superconducting Kaon Spectrometer

Abstract We performed a measurement of the inclusive missing-mass spectrum of the $^{12}$C$(K^-, K^+)$ reaction at an incident beam momentum of 1.8 GeV/c. This measurement was carried out by using the Superconducting Kaon Spectrometer (SKS) and the K1.8 beamline spectrometer at the Hadron Experimental Facility in J-PARC. From the missing-mass of the $^{12}$C$(K^-, K^+)$ reaction, the binding energy of a $\Xi ^-$ hyperon in a core $^{11}$B nucleus, $B_{\Xi ^-}$, can be calculated. Our experimental setup yielded a good energy resolution of 8.2 MeV (full width at half maximum), which allowed us to observe significant enhancements in the proximity of the $^{12}_{\Xi }$Be production threshold region. In order to extract information from the missing-mass spectrum, we employed several fitting parameters assumptions. A good agreement with the spectrum shape was obtained by adding two Gaussian functions, with the constant experimental resolution for the $\Xi$-hypernuclear states, to the background distribution. The peak positions were obtained to be $B_{\Xi ^-} = 8.9 \pm 1.4$ (stat.) $^{+3.8}_{-3.1}$ (syst.) MeV and $B_{\Xi ^-} = -2.4 \pm 1.3$ (stat.) $^{+2.8}_{-1.2}$ (syst.) MeV. Another model assumption, one Breit–Wigner function with $B_{\Xi ^-} = -2.7 \pm 2.2$ (stat.) $^{+0.5}_{-0.7}$ (syst.) MeV and $\Gamma = 4.1 \pm 2.1$ (stat.) $^{+1.2}_{-0.7}$ (syst.) MeV, also yielded a similar $\chi ^2$ value.

Changes in evaporation patterns and their impact on Climatic Water Balance and river discharges in central Poland, 1961–2020

This study investigates the changes in precipitation and evaporation patterns and their impact on Climatic Water Balance and river discharges in central Poland from 1961 to 2020. The analysis focuses on two “normal” periods, 1961–1990 and 1991–2020 (according to the World Meteorological Organization). Bartlett’s test and the Kruskal–Wallis rank sum test were used to assess the homogeneity of variances and compare distributions of analyzed variables over two “normal” periods. The probability density functions were estimated using a kernel density estimator with a Gaussian kernel function. Significant findings indicate alterations in evaporation rates and shifts in water balance dynamics. Mean evaporation increased from 530.8 to 637.9 mm, leading to a notable decrease in the mean Climatic Water Balance from 1.1 to − 107.5 mm (in the periods 1961–1990 and 1991–2020, respectively). Additionally, rivers showed reduced mean annual discharges (from 4.28 to 3.01 m3·s−1 and 1.25 to 0.87 m3·s−1, for the Zgłowiączka and Skrwa Lewa rivers, respectively). These climatic changes in central Poland have substantial implications for regional water resources, especially in spring and summer and particularly in agricultural areas, potentially exacerbating drought conditions and impacting agricultural productivity mainly in the warm half-year.

Practical time‐varying formation cooperative control for high‐order nonlinear multi‐agent systems avoiding spatial resource conflict via safety constraints

AbstractThe operation of multi‐agent systems (MAS) in space necessitates considerations for obstacle avoidance, collision prevention, and connectivity among agents. This coupling conflict, stemming from spatial resource utilization, poses a significant and non‐negligible threat to the safe operation of MAS. This article proposes a consensus control scheme for the time‐varying formation of MAS, incorporating functions for maintaining connectivity, collision avoidance, and obstacle dodging. This scheme effectively constrains the time‐varying formation tracking error within an arbitrarily small range. The considered system model takes a high‐order nonlinear form, with uncertainties and disturbances present in each order. This grants the control scheme with high generality and practicability. By employing barrier Lyapunov function to delineate the safe operational space of MAS, conflicts in spatial resource utilization are avoided. This approach simultaneously fulfills the requirements for connectivity maintenance, collision avoidance, and obstacle dodging in the safe operation of MAS. An additional rotation operator is integrated into the controller to smoothly address the “minima” problem, eliminating the need for external intervention. Gaussian radial basis function is used to estimate the nonlinear terms, uncertainties, and unknown perturbation online in the system. The stability of the MAS under the proposed control scheme is analyzed through Lyapunov function. Finally, numerical simulation results are demonstrated to explain the effectiveness of the control scheme.