Gaussian Weighted Research Articles

Dilated Spectral–Spatial Gaussian Transformer Net for Hyperspectral Image Classification

In recent years, deep learning-based classification methods for hyperspectral images (HSIs) have gained widespread popularity in fields such as agriculture, environmental monitoring, and geological exploration. This is owing to their ability to automatically extract features and deliver outstanding performance. This study provides a new Dilated Spectral–Spatial Gaussian Transformer Net (DSSGT) model. The DSSGT model incorporates dilated convolutions as shallow feature extraction units, which allows for an expanded receptive field while maintaining computational efficiency. We integrated transformer architecture to effectively capture feature relationships and generate deep fusion features, thereby enhancing classification accuracy. We used consecutive dilated convolutional layers to extract joint low-level spectral–spatial features. We then introduced Gaussian Weighted Pixel Embedding blocks, which leverage Gaussian weight matrices to transform the joint features into pixel-level vectors. By combining the features of each pixel with its neighbouring pixels, we obtained pixel-level representations that are more expressive and context-aware. The transformed vector matrix was fed into the transformer encoder module, enabling the capture of global dependencies within the input data and generating higher-level fusion features with improved expressiveness and discriminability. We evaluated the proposed DSSGT model using five hyperspectral image datasets through comparative experiments. Our results demonstrate the superior performance of our approach compared to those of current state-of-the-art methods, providing compelling evidence of the DSSGT model’s effectiveness.

A quasi-classical study in a quantum spirit of mode specificity of the H + HOD abstraction reaction.

Quantum benchmark calculations of the H + HOD abstraction reaction [B. Zhao et al., Phys. Chem. Chem. Phys., 2018, 20, 17029-17037] provide an opportunity to test approximate methods, such as quasi-classical trajectories (QCTs) with Gaussian binning. However, the large mode-specific enhancements of this reaction lead to special challenges and unphysical QCT cross-section artifacts. We propose and apply a general backward-forward-backward (BFB) trajectory procedure to avoid cross-section artifacts arising from vibrational motion delocalization of the initially prepared reactants. We also develop and apply a general hybrid weighting scheme, in which vibrationally adiabatic products receive unit weights, while vibrationally non-adiabatic products are Gaussian weighted. Motivated by examination of the product vibrational actions, the hybrid weighting is necessary to avoid large cross-section errors. These QCTs with Gaussian weighting extensions are general and are recommended for future polyatomic reaction simulations.

Implicit Continuous User Authentication for Mobile Devices based on Deep Reinforcement Learning

The predominant method for smart phone accessing is confined to methods directing the authentication by means of Point-of-Entry that heavily depend on physiological biometrics like, fingerprint or face. Implicit continuous authentication initiating to be loftier to conventional authentication mechanisms by continuously confirming users’ identities on continuing basis and mark the instant at which an illegitimate hacker grasps dominance of the session. However, divergent issues remain unaddressed. This research aims to investigate the power of Deep Reinforcement Learning technique to implicit continuous authentication for mobile devices using a method called, Gaussian Weighted Cauchy Kriging-based Continuous Czekanowski’s (GWCK-CC). First, a Gaussian Weighted Non-local Mean Filter Preprocessing model is applied for reducing the noise present in the raw input face images. Cauchy Kriging Regression function is employed to reduce the dimensionality. Finally, Continuous Czekanowski’s Classification is utilized for proficient classification between the genuine user and attacker. By this way, the proposed GWCK-CC method achieves accurate authentication with minimum error rate and time. Experimental assessment of the proposed GWCK-CC method and existing methods are carried out with different factors by using UMDAA-02 Face Dataset. The results confirm that the proposed GWCK-CC method enhances authentication accuracy, by 9%, reduces the authentication time, and error rate by 44%, and 43% as compared to the existing methods.

Quantum Dark Solitons in the 1D Bose Gas: From Single to Double Dark-Solitons

We study quantum double dark-solitons, which give pairs of notches in the density profiles, by constructing corresponding quantum states in the Lieb–Liniger model for the one-dimensional Bose gas. Here, we expect that the Gross–Pitaevskii (GP) equation should play a central role in the long distance mean-field behavior of the 1D Bose gas. We first introduce novel quantum states of a single dark soliton with a nonzero winding number. We show them by exactly evaluating not only the density profile but also the profiles of the square amplitude and phase of the matrix element of the field operator between the N-particle and (N−1)-particle states. For elliptic double dark-solitons, the density and phase profiles of the corresponding states almost perfectly agree with those of the classical solutions, respectively, in the weak coupling regime. We then show that the scheme of the mean-field product state is quite effective for the quantum states of double dark solitons. Assigning the ideal Gaussian weights to a sum of the excited states with two particle-hole excitations, we obtain double dark-solitons of distinct narrow notches with different depths. We suggest that the mean-field product state should be well approximated by the ideal Gaussian weighted sum of the low excited states with a pair of particle-hole excitations. The results of double dark-solitons should be fundamental and useful for constructing quantum multiple dark-solitons.

A Comparative Study of Nonparametric Kernel estimators with Gaussian Weight Function

Nowadays, Parametric methods become unfavorable by researchers because of the restrictions on using them and losing the flexibility in estimating and analysis the data. Therefore, the researchers preferred the nonparametric method which proved their efficiency and capable to analysis the data without of predetermined assumptions. Consequently, the data and their included information are becoming who determine the functional shape for the studied population and there are no parameters instead of the observations. The objective of estimating the nonparametric regression function is to approximate the regression function to the real regression function. On the other hand, COVID-19 pandemic nowadays speared in all the countries one of them is Iraq. The function of infection speared have been studied in different countries but not in Iraq. Therefore, the aim of our research is to apply three nonparametric Kernel estimators with Gaussian weighted function to model and forecast the number of infections of COVID-19 in Iraq. R software and the data represent the daily number of COVID-19 infections for the period 23/2/2020 to 21/6/2020 are used to apply many models and choose the appropriate one. The results of applying three nonparametric Kernel model that the Priestley-Chao model is the appropriate one in all the sample sizes and other conditions

NIR-II/NIR-I Fluorescence Molecular Tomography of Heterogeneous Mice Based on Gaussian Weighted Neighborhood Fused Lasso Method.

Fluorescence molecular tomography (FMT), which can visualize the distribution of fluorescence biomarkers, has become a novel three-dimensional noninvasive imaging technique for in vivo studies such as tumor detection and lymph node location. However, it remains a challenging problem to achieve satisfactory reconstruction performance of conventional FMT in the first near-infrared window (NIR-I, 700-900nm) because of the severe scattering of NIR-I light. In this study, a promising FMT method for heterogeneous mice was proposed to improve the reconstruction accuracy using the second near-infrared window (NIR-II, 1000-1700nm), where the light scattering significantly reduced compared with NIR-I. The optical properties of NIR-II were analyzed to construct the forward model for NIR-II FMT. Furthermore, to raise the accuracy of solution of the inverse problem, we proposed a novel Gaussian weighted neighborhood fused Lasso (GWNFL) method. Numerical simulation was performed to demonstrate the outperformance of GWNFL compared with other algorithms. Besides, a novel NIR-II/NIR-I dual-modality FMT system was developed to contrast the in vivo reconstruction performance between NIR-II FMT and NIR-I FMT. To compare the reconstruction performance of NIR-II FMT with traditional NIR-I FMT, numerical simulations and in vivo experiments were conducted. Both the simulation and in vivo results showed that NIR-II FMT outperformed NIR-I FMT in terms of location accuracy and spatial overlap index. It is believed that this study could promote the development and biomedical application of NIR-II FMT in the future.

Non-Rigid Registration for Infrared and Visible Images via Gaussian Weighted Shape Context and Enhanced Affine Transformation

Image registration is a prerequisite for image fusion from multiple modalities, such as infrared (IR) and visible (VIS) images. Although there have been many various methods of image registration, non-rigid registration for IR and VIS images is still challenging due to large differences between IR and VIS images. In this work, a point feature-based method is proposed to improve the performance on non-rigid IR and VIS image registration. Firstly, a feature descriptor - Gaussian weighted shape context (GWSC) - is improved from shape context (SC) to fast extract matching point pairs from edge maps in IR and VIS images. With the set of matching point pairs, a Gaussian-field-based objective function is established to measure the distance between IR and VIS images. Then, the enhanced affine transformation (EAT) model is proposed to generalize affine model from linear to non-linear case and describe the regularity of global deformation between IR and VIS images. At last, the derivative of the distance measure is expressed with respect to the EAT model and thus, the optimal parameters are estimated by using the quasi-Newton method. The qualitative and quantitative comparisons demonstrate that the proposed method (GWSC-EAT) can be successfully applied to non-rigid registration of IR and VIS images and moreover, it is superior to the state-of-the-art methods on the accuracy and speed of non-rigid registration.

Corrections for "Bioluminescence Tomography Based on Gaussian Weighted Laplace Prior Regularization for Morphological Imaging of Glioma".

In [1], the affiliation for Y. Gao, K. Wang and J. Tian should have appeared as follows:.

Corrections to "Bioluminescence Tomography Based on Gaussian Weighted Laplace Prior Regularization for Morphological Imaging of Glioma".

The correct affiliation for Yuan Gao, Kun Wang, and Jie Tian is as follows.

Bioluminescence Tomography Based on Gaussian Weighted Laplace Prior Regularization for In Vivo Morphological Imaging of Glioma.

Bioluminescence tomography (BLT) is a powerful non-invasive molecular imaging tool for in vivo studies of glioma in mice. However, because of the light scattering and resulted ill-posed problems, it is challenging to develop a sufficient reconstruction method, which can accurately locate the tumor and define the tumor morphology in three-dimension. In this paper, we proposed a novel Gaussian weighted Laplace prior (GWLP) regularization method. It considered the variance of the bioluminescence energy between any two voxels inside an organ had a non-linear inverse relationship with their Gaussian distance to solve the over-smoothed tumor morphology in BLT reconstruction. We compared the GWLP with conventional Tikhonov and Laplace regularization methods through various numerical simulations and in vivo orthotopic glioma mouse model experiments. The in vivo magnetic resonance imaging and ex vivo green fluorescent protein images and hematoxylin-eosin stained images of whole head cryoslicing specimens were utilized as gold standards. The results demonstrated that GWLP achieved the highest accuracy in tumor localization and tumor morphology preservation. To the best of our knowledge, this is the first study that achieved such accurate BLT morphological reconstruction of orthotopic glioma without using any segmented tumor structure from any other structural imaging modalities as the prior for reconstruction guidance. This enabled BLT more suitable and practical for in vivo imaging of orthotopic glioma mouse models.

The H-scan analysis and results in tissues

The H-scan is based on a simplified framework for characterizing scattering behavior, and visualizing the results as color coding of the B-scan image. The methodology begins with a standard convolution model of pulse-echo formation from typical situations, and then matches those results to the mathematics of Gaussian Weighted Hermite Functions. The nth successive differentiation of the Gaussian pulse G = exp(-t 2) generates the nth order Hermite polynomial (Poularikas 2010). The function H 4(t)G resembles a broadband pulse. Assuming a pulse-echo system has a round trip impulse response of A 0 H 4(t)G, then we expect that a reflection from a step function of acoustic impedance will produce a corresponding received echo proportional to GH4(t). However, a thin layer of higher impedance, or a small scatterer or incoherent cloud of small scatterers would produce higher order Hermite functions as echoes. In this framework, the identification task is simply to classify echoes by similarity to either GH 4(t), or GH 5(t), or GH 6(t). The resulting B-scan image is examined and echoes can be classified and colored according to their class. Results from tissue scans also demonstrate groups of echoes separated by Hermite order Hn. A theoretical framework is introduced where reflections are characterized by their similarity to nth order Hermite polynomials.

The H-Scan Format for Classification of Ultrasound Scattering

The H-scan is based on a simplified framework for characterizing scattering behavior, and visualizing the results as color-coding of the B-scan image. The methodology begins with a standard convolution model of pulse-echo formation from typical situations, and then matches those results to the mathematics of Gaussian Weighted Hermite Functions. In this framework, echoes can be classified as returning from specific categories of scatterers, and these can be conveniently displayed as colors. Thus, some information not evident in conventional grayscale pulse-echo images can be visualized in the H-scan format.

Non-local Three-dimensional Otsu Image Thresholding Segmentation Based on Anisotropic Adaptive Gaussian Weighted Window

针对传统3维Otsu(3D-Otsu)门限分割方法中的滤噪性能和小目标保持性能的不足，该文提出一种基于各向异性自适应高斯加权方向窗的3D-Otsu门限分割的新方法。新方法改进了3D-Otsu的邻域窗口设置方法，采用中心点的局部特征来自适应地确定邻域各向异性高斯加权方向窗口的尺寸、尺度和滤波方向。然后，提出非局部多方向相似度测量来更有效地捕捉图像中的模式冗余。最终，结合像素点灰度值、加权均值、加权中值构建3维直方图，并基于最大类间方差计算门限矢量进行分割。实验结果表明：与目前广泛使用的2维Otsu, 2维最大熵以及传统3维Otsu方法相比，新方法有着更好的门限分割效果，并具有更好的滤噪性能和小目标保持性能。

Radial basis function interpolation of unstructured, three-dimensional, volumetric particle tracking velocimetry data

Unstructured three-dimensional fluid velocity data were interpolated using Gaussian radial basis function (RBF) interpolation. Data were generated to imitate the spatial resolution and experimental uncertainty of a typical implementation of defocusing digital particle image velocimetry. The velocity field associated with a steadily rotating infinite plate was simulated to provide a bounded, fully three-dimensional analytical solution of the Navier–Stokes equations, allowing for robust analysis of the interpolation accuracy. The spatial resolution of the data (i.e. particle density) and the number of RBFs were varied in order to assess the requirements for accurate interpolation. Interpolation constraints, including boundary conditions and continuity, were included in the error metric used for the least-squares minimization that determines the interpolation parameters to explore methods for improving RBF interpolation results. Even spacing and logarithmic spacing of RBF locations were also investigated. Interpolation accuracy was assessed using the velocity field, divergence of the velocity field, and viscous torque on the rotating boundary. The results suggest that for the present implementation, RBF spacing of 0.28 times the boundary layer thickness is sufficient for accurate interpolation, though theoretical error analysis suggests that improved RBF positioning may yield more accurate results. All RBF interpolation results were compared to standard Gaussian weighting and Taylor expansion interpolation methods. Results showed that RBF interpolation improves interpolation results compared to the Taylor expansion method by 60% to 90% based on the average squared velocity error and provides comparable velocity results to Gaussian weighted interpolation in terms of velocity error. RMS accuracy of the flow field divergence was one to two orders of magnitude better for the RBF interpolation compared to the other two methods. RBF interpolation that was applied to vortex identification in experimental data showed reduced noise and reliable calculation of vortex ring geometry.

WE-E-213CD-02: Gaussian Weighted Multi-Atlas Based Segmentation for Head and Neck Radiotherapy Planning.

To develop a multi-atlas segmentation strategy for IMRT head and neck therapy planning. The method was tested on thirty-one head and neck simulation CTs, without demographic or pathology pre-clustering. We compare Fixed Number (FN) and Thresholding (TH) selection (based on normalized mutual information ranking) of the atlases to be included for current patient segmentation. Next step is a pairwise demons Deformable Registration (DR) onto current patient CT. DR was extended to automatically compensate for patient different field of view. Propagated labels are combined according to a Gaussian Weighted (GW) fusion rule, adapted to poor soft tissues contrast. Agreement with manual segmentation was quantified in terms of Dice Similarity Coefficient (DSC). Selection methods, number of atlases used, as well as GW, average and majority voting fusion were discriminated by means of Friedman Test (a=5%). Experimental tuning of the algorithm parameters was performed on five patients, deriving an optimal configuration for each structure. DSC reduction was not significant when ten or more atlases are selected, whereas DSC for single most similar atlas selection is 10% lower in median. DSC of FN selection rule were significantly higher for most structures. Tubular structures may benefit from computing average contour rather than looking at the singular voxel contribution, whereas the best performing strategy for all other structures was GW. When half database is selected, final median DSC were 0.86, 0.80, 0.51, 0.81, 0.69 and 0.79 for mandible, spine, optical nerves, eyes, parotids and brainstem respectively. We developed an efficient algorithm for multiatlas based segmentation of planning CT volumes, based on DR and GW. FN selection of database atlases is foreseen to increase computational efficiency. The absence of clinical pre-clustering and specific imaging protocol on database subjects makes the results closer to real clinical application. "Progetto Roberto Rocca" funded by the Fondazione Fratelli Agostino and Enrico Rocca, Italy.

Normalization of the Gaussian binning trajectory method for indirect reactions

The method of Gaussian weighted trajectories combines the classical description of gas-phase chemical reactions and Bohr quantization of final fragment vibrations. In practice, trajectories are assigned Gaussian statistical weights such that the closer the final vibrational actions to integer values, the larger the weights. This approach, called classical trajectory method with Gaussian binning (CT-GB) in the following, is a practical implementation of classical S matrix theory (CSMT) in the random phase approximation. However, CSMT is non unitary and consequently, the most utilized version of CT-GB is not strictly normalized to unity. In other words, the sum of product and re-formed reagent state populations is not exactly equal to one. The purpose of this work is to show that normalizing these populations to unity should significantly improve the quality of the predictions for indirect reactions. This finding is illustrated from calculations on the D++H2 reaction.

Classical treatment of molecular collisions: striking improvement of the description of recoil energy distributions using Gaussian weighted trajectories

The Gaussian weighting (GW) procedure, recently used in the classical treatment of molecular collisions, is a practical way of taking into account quantization of product vibrational actions. The goal of this brief communication is to show that the GW procedure may drastically improve the predictions of the recoil energy distribution between final fragments, an observable frequently measured in molecular beam experiments.

Applying instance-based techniques to prediction of final outcome in acute stroke

Acute cerebral stroke is a frequent cause of death and the major cause of adult neurological disability in the western world. Thrombolysis is the only established treatment of ischemic stroke; however, its use carries a substantial risk of symptomatic intracerebral hemorrhage. A clinical tool to guide the use of thrombolysis would be very valuable. One of the major goals of such a tool would be the identification of potentially salvageable tissue. This requires an accurate prediction of the extent of infarction if untreated. In this study, we investigate the applicability of highly flexible instance-based (IB) methods for such predictions. Based on information obtained from magnetic resonance imaging of 14 patients with acute stroke, we explored three different implementations of the IB method: k-NN, Gaussian weighted, and constant radius search classification. Receiver operating characteristics analysis, in particular area under the curve (AUC), was used as performance measure. We found no significant difference (P = 0.48) in performance for the optimal k-NN (k = 164, AUC = 0.814 +/- 0.001) and Gaussian weight (sigma = 0.17, AUC = 0.813 +/- 0.001) implementations, while they were both significantly better (P < 1 x 10(-6) for both) than the constant radius implementation (R = 0.28, AUC = 0.809 +/- 0.001). Qualitative analyses of the distribution of instances in the feature space indicated that non-infarcted instances tends to cluster together while infarcted instances are more dispersed, and that there may not exist a stringent boundary separating infarcted from non-infarcted instances. This study shows that IB methods can be used, and may be advantageous, for predicting final infarct in patients with acute stroke, but further work must be done to make them clinically applicable.

Higher-Dimensional Integration with Gaussian Weight for Applications in Probabilistic Design

Higher-dimensional Gaussian weighted integration is of interest in probabilistic simulations. Motivated by the need for variance calculations with functions being at least quadratic, the family of degree 5 formulae is considered. Using an existing formula for the integration over the surface of an n-sphere, an efficient, new formula for Gaussian weighted integration is obtained. Several other formulae that have appeared in the numerical integration literature are also given. The number of function evaluations required by the formulae is compared to a minimal bound result. The degree 5 formulae are applied to simple test problems and the relative errors are compared.

Spatial integration of signal information in Gabor stimuli.

We studied spatial integration of Gaussian weighted cosine gratings (Gabor gratings) in contrast detection by using a two-alternative forced-choice method. The Gabor gratings, which were either complete or sharply truncated to a square shape, were presented either in the presence or absence of static noise. Contrast thresholds were determined for different truncation areas and different widths of the two-dimensional Gaussian weighting function. Contrast detection performance was found to depend only on the effective spatial spread of the stimuli. The spatial spread is a physical description of signal area, which takes into account the spatial inhomogeneity of the signal. The highest detection efficiencies were obtained when the spatial spread was small independently of whether the stimuli were sharply truncated or complete smooth Gabor gratings. The results show that the contrast detection mechanism takes into account the shape of the signal window and does not collect information outside the area of the signal.