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Journal articles on the topic 'Gaussian Method'

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Published: 4 June 2021

Last updated: 21 June 2025

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Zickert, Gustav, and Can Evren Yarman. "Gaussian mixture model decomposition of multivariate signals." Signal, Image and Video Processing 16, no. 2 (2021): 429–36. http://dx.doi.org/10.1007/s11760-021-01961-y.

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AbstractWe propose a greedy variational method for decomposing a non-negative multivariate signal as a weighted sum of Gaussians, which, borrowing the terminology from statistics, we refer to as a Gaussian mixture model. Notably, our method has the following features: (1) It accepts multivariate signals, i.e., sampled multivariate functions, histograms, time series, images, etc., as input. (2) The method can handle general (i.e., ellipsoidal) Gaussians. (3) No prior assumption on the number of mixture components is needed. To the best of our knowledge, no previous method for Gaussian mixture model decomposition simultaneously enjoys all these features. We also prove an upper bound, which cannot be improved by a global constant, for the distance from any mode of a Gaussian mixture model to the set of corresponding means. For mixtures of spherical Gaussians with common variance $$\sigma ^2$$ σ 2 , the bound takes the simple form $$\sqrt{n}\sigma $$ n σ . We evaluate our method on one- and two-dimensional signals. Finally, we discuss the relation between clustering and signal decomposition, and compare our method to the baseline expectation maximization algorithm.

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Hu, Jintong, Bin Xia, Bin Chen, Wenming Yang, and Lei Zhang. "GaussianSR: High Fidelity 2D Gaussian Splatting for Arbitrary-Scale Image Super-Resolution." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 4 (2025): 3554–62. https://doi.org/10.1609/aaai.v39i4.32369.

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Implicit neural representations (INRs) have revolutionized arbitrary-scale super-resolution (ASSR) by modeling images as continuous functions. Most existing INR-based ASSR networks first extract features from the given low-resolution image using an encoder, and then render the super-resolved result via a multi-layer perceptron decoder. Although these approaches have shown promising results, their performance is constrained by the limited representation ability of discrete latent codes in the encoded features. In this paper, we propose a novel ASSR method named GaussianSR that overcomes this limitation through 2D Gaussian Splatting (2DGS). Unlike traditional methods that treat pixels as discrete points, GaussianSR represents each pixel as a continuous Gaussian field. The encoded features are simultaneously refined and upsampled by rendering the mutually stacked Gaussian fields. As a result, long-range dependencies are established to enhance representation ability. In addition, a classifier is developed to dynamically assign Gaussian kernels to all pixels to further improve flexibility. All components of GaussianSR (i.e. encoder, classifier, Gaussian kernels, and decoder) are jointly learned end-to-end. Experiments demonstrate that GaussianSR achieves superior ASSR performance with fewer parameters than existing methods while enjoying interpretable and content-aware feature aggregations.

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Gao, Lin, Jie Yang, Bo-Tao Zhang, et al. "Real-time Large-scale Deformation of Gaussian Splatting." ACM Transactions on Graphics 43, no. 6 (2024): 1–17. http://dx.doi.org/10.1145/3687756.

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Neural implicit representations, including Neural Distance Fields and Neural Radiance Fields, have demonstrated significant capabilities for reconstructing surfaces with complicated geometry and topology, and generating novel views of a scene. Nevertheless, it is challenging for users to directly deform or manipulate these implicit representations with large deformations in a real-time fashion. Gaussian Splatting (GS) has recently become a promising method with explicit geometry for representing static scenes and facilitating high-quality and real-time synthesis of novel views. However, it cannot be easily deformed due to the use of discrete Gaussians and the lack of explicit topology. To address this, we develop a novel GS-based method (GaussianMesh) that enables interactive deformation. Our key idea is to design an innovative mesh-based GS representation, which is integrated into Gaussian learning and manipulation. 3D Gaussians are defined over an explicit mesh, and they are bound with each other: the rendering of 3D Gaussians guides the mesh face split for adaptive refinement, and the mesh face split directs the splitting of 3D Gaussians. Moreover, the explicit mesh constraints help regularize the Gaussian distribution, suppressing poor-quality Gaussians ( e.g. , misaligned Gaussians, long-narrow shaped Gaussians), thus enhancing visual quality and reducing artifacts during deformation. Based on this representation, we further introduce a large-scale Gaussian deformation technique to enable deformable GS, which alters the parameters of 3D Gaussians according to the manipulation of the associated mesh. Our method benefits from existing mesh deformation datasets for more realistic data-driven Gaussian deformation. Extensive experiments show that our approach achieves high-quality reconstruction and effective deformation, while maintaining the promising rendering results at a high frame rate (65 FPS on average on a single commodity GPU).

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Muhammad Ali, Muhammad. "Parallel Gaussian Elimination Method." AL-Rafidain Journal of Computer Sciences and Mathematics 5, no. 2 (2008): 59–77. http://dx.doi.org/10.33899/csmj.2008.163986.

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Babich, V. M., and M. M. Popov. "Gaussian summation method (review)." Radiophysics and Quantum Electronics 32, no. 12 (1989): 1063–81. http://dx.doi.org/10.1007/bf01038632.

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Yu, Zehao, Torsten Sattler, and Andreas Geiger. "Gaussian Opacity Fields: Efficient Adaptive Surface Reconstruction in Unbounded Scenes." ACM Transactions on Graphics 43, no. 6 (2024): 1–13. http://dx.doi.org/10.1145/3687937.

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Recently, 3D Gaussian Splatting (3DGS) has demonstrated impressive novel view synthesis results, while allowing the rendering of high-resolution images in real-time. However, leveraging 3D Gaussians for surface reconstruction poses significant challenges due to the explicit and disconnected nature of 3D Gaussians. In this work, we present Gaussian Opacity Fields (GOF), a novel approach for efficient, high-quality, and adaptive surface reconstruction in unbounded scenes. Our GOF is derived from ray-tracing-based volume rendering of 3D Gaussians, enabling direct geometry extraction from 3D Gaussians by identifying its levelset, without resorting to Poisson reconstruction or TSDF fusion as in previous work. We approximate the surface normal of Gaussians as the normal of the ray-Gaussian intersection plane, enabling the application of regularization that significantly enhances geometry. Furthermore, we develop an efficient geometry extraction method utilizing Marching Tetrahedra, where the tetrahedral grids are induced from 3D Gaussians and thus adapt to the scene's complexity. Our evaluations reveal that GOF surpasses existing 3DGS-based methods in surface reconstruction and novel view synthesis. Further, it compares favorably to or even outperforms, neural implicit methods in both quality and speed.

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Koga, Toshikatsu, and Ajit J. Thakkar. "Improvement of the long-range behavior of Gaussian basis sets using asymptotic constraints." Canadian Journal of Chemistry 70, no. 2 (1992): 362–65. http://dx.doi.org/10.1139/v92-051.

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It is suggested that atomic orbitals with improved long-range behavior can be obtained by using energy-optimized Gaussian basis sets to which Gaussians have been added to satisfy a subset of some recently derived constraints that must be satisfied by the exact Hartree–Fock orbitals. This procedure is demonstrated by illustrative calculations for helium. This method is found to be superior to the adhoc method of adding diffuse Gaussians in an even-tempered fashion. Keywords: Gaussian basis sets, long-range behavior, asymptotic constraints.

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Zhou, Jingqiu, Lue Fan, Xuesong Chen, Linjiang Huang, Si Liu, and Hongsheng Li. "GaussianPainter: Painting Point Cloud into 3D Gaussians with Normal Guidance." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 10 (2025): 10788–96. https://doi.org/10.1609/aaai.v39i10.33172.

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In this paper, we present GaussianPainter, the first method to paint a point cloud into 3D Gaussians given a reference image. GaussianPainter introduces an innovative feed-forward approach to overcome the limitations of time-consuming test-time optimization in 3D Gaussian splatting. Our method addresses a critical challenge in the field: the non-uniqueness problem inherent in the large parameter space of 3D Gaussian splatting. This space, encompassing rotation, anisotropic scales, and spherical harmonic coefficients, introduces the challenge of rendering similar images from substantially different Gaussian fields. As a result, feed-forward networks face instability when attempting to directly predict high-quality Gaussian fields, struggling to converge on consistent parameters for a given output. To address this issue, we propose to estimate a surface normal for each point to determine its Gaussian rotation. This strategy enables the network to effectively predict the remaining Gaussian parameters in the constrained space. We further enhance our approach with an appearance injection module, incorporating reference image appearance into Gaussian fields via a multiscale triplane representation. Our method successfully balances efficiency and fidelity in 3D Gaussian generation, achieving high-quality, diverse, and robust 3D content creation from point clouds in a single forward pass. A video is provided in our supplementary material for a more detailed explanation of our method.

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Li, Xiaoqing, and Xiaoling Ji. "Complex Gaussian functions expansion method applied to truncated Gaussian beams." Journal of Modern Optics 58, no. 12 (2011): 1060–64. http://dx.doi.org/10.1080/09500340.2011.595835.

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Cagniot, Emmanuel, Michael Fromager, and Kamel Ait-Ameur. "Adaptive Laguerre-Gaussian variant of the Gaussian beam expansion method." Journal of the Optical Society of America A 26, no. 11 (2009): 2373. http://dx.doi.org/10.1364/josaa.26.002373.

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KHOMCHENKO, А. N., Yu M. BARDACHOV, O. I. LYTVYNENKO, and I. O. ASTIONENKO. "INTERPRETATIONS METHOD AND GAUSSIAN QUADRATURES." Applied Questions of Mathematical Modeling 3 (2019): 143–50. http://dx.doi.org/10.32782/2618-0340-2019-3-13.

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Tsuchida, Takahiro, and Koji Kimura. "ICONE23-1591 EQUIVALENT NON-GAUSSIAN EXCITATION METHOD FOR RESPONSE MOMENT CALCULATION OF SYSTEMS UNDER NON-GAUSSIAN RANDOM EXCITATION." Proceedings of the International Conference on Nuclear Engineering (ICONE) 2015.23 (2015): _ICONE23–1—_ICONE23–1. http://dx.doi.org/10.1299/jsmeicone.2015.23._icone23-1_280.

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Witkovský, Viktor. "Characteristic Function of the Tsallis q-Gaussian and Its Applications in Measurement and Metrology." Metrology 3, no. 2 (2023): 222–36. http://dx.doi.org/10.3390/metrology3020012.

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The Tsallis q-Gaussian distribution is a powerful generalization of the standard Gaussian distribution and is commonly used in various fields, including non-extensive statistical mechanics, financial markets and image processing. It belongs to the q-distribution family, which is characterized by a non-additive entropy. Due to their versatility and practicality, q-Gaussians are a natural choice for modeling input quantities in measurement models. This paper presents the characteristic function of a linear combination of independent q-Gaussian random variables and proposes a numerical method for its inversion. The proposed technique makes it possible to determine the exact probability distribution of the output quantity in linear measurement models, with the input quantities modeled as independent q-Gaussian random variables. It provides an alternative computational procedure to the Monte Carlo method for uncertainty analysis through the propagation of distributions.

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Preuss, Roland, and Udo von Toussaint. "Outlier-Robust Surrogate Modeling of Ion–Solid Interaction Simulations." Entropy 25, no. 4 (2023): 685. http://dx.doi.org/10.3390/e25040685.

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Data for complex plasma–wall interactions require long-running and expensive computer simulations. Furthermore, the number of input parameters is large, which results in low coverage of the (physical) parameter space. Unpredictable occasions of outliers create a need to conduct the exploration of this multi-dimensional space using robust analysis tools. We restate the Gaussian process (GP) method as a Bayesian adaptive exploration method for establishing surrogate surfaces in the variables of interest. On this basis, we expand the analysis by the Student-t process (TP) method in order to improve the robustness of the result with respect to outliers. The most obvious difference between both methods shows up in the marginal likelihood for the hyperparameters of the covariance function, where the TP method features a broader marginal probability distribution in the presence of outliers. Eventually, we provide first investigations, with a mixture likelihood of two Gaussians within a Gaussian process ansatz for describing either outlier or non-outlier behavior. The parameters of the two Gaussians are set such that the mixture likelihood resembles the shape of a Student-t likelihood.

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Dattoli, Giuseppe, Emanuele Di Palma, and Silvia Licciardi. "On an Umbral Point of View of the Gaussian and Gaussian-like Functions." Symmetry 15, no. 12 (2023): 2157. http://dx.doi.org/10.3390/sym15122157.

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The theory of Gaussian functions is reformulated using an umbral point of view. The symbolic method we adopt here allows an interpretation of the Gaussian in terms of a Lorentzian image function. The formalism also suggests the introduction of a new point of view of trigonometry, opening a new interpretation of the associated special functions. The Erfi(x), is, for example, interpreted as the “sine” of the Gaussian trigonometry. The possibilities offered by the Umbral restyling proposed here are noticeable and offered by the formalism itself. We mention the link between higher-order Gaussian trigonometric functions, Hermite polynomials, and the possibility of introducing new forms of distributions with longer tails than the ordinary Gaussians. The possibility of framing the theoretical content of the present article within a redefinition of the hypergeometric function is eventually discussed.

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Li, Junqiang, John D. Valentine, and Asad E. Rana. "The modified three point Gaussian method for determining Gaussian peak parameters." Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 422, no. 1-3 (1999): 438–43. http://dx.doi.org/10.1016/s0168-9002(98)01113-9.

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Chen, Xiangbing, Chen Chen, and Xiaowen Lu. "Algebraic method for multisensor data fusion." PLOS ONE 19, no. 9 (2024): e0307587. http://dx.doi.org/10.1371/journal.pone.0307587.

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In this contribution, we use Gaussian posterior probability densities to characterize local estimates from distributed sensors, and assume that they all belong to the Riemannian manifold of Gaussian distributions. Our starting point is to introduce a proper Lie algebraic structure for the Gaussian submanifold with a fixed mean vector, and then the average dissimilarity between the fused density and local posterior densities can be measured by the norm of a Lie algebraic vector. Under Gaussian assumptions, a geodesic projection based algebraic fusion method is proposed to achieve the fused density by taking the norm as the loss. It provides a robust fixed point iterative algorithm for the mean fusion with theoretical convergence, and gives an analytical form for the fused covariance matrix. The effectiveness of the proposed fusion method is illustrated by numerical examples.

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Wang, Yuechang, Abdullah Azam, Mark CT Wilson, Anne Neville, and Ardian Morina. "Generating fractal rough surfaces with the spectral representation method." Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 235, no. 12 (2021): 2640–53. http://dx.doi.org/10.1177/13506501211049624.

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The application of the spectral representation method in generating Gaussian and non-Gaussian fractal rough surfaces is studied in this work. The characteristics of fractal rough surfaces simulated by the spectral representation method and the conventional Fast Fourier transform filtering method are compared. Furthermore, the fractal rough surfaces simulated by these two methods are compared in the simulation of contact and lubrication problems. Next, the influence of low and high cutoff frequencies on the normality of the simulated Gaussian fractal rough surfaces is investigated with roll-off power spectral density and single power-law power spectral density. Finally, a simple approximation method to generate non-Gaussian fractal rough surfaces is proposed by combining the spectral representation method and the Johnson translator system. Based on the simulation results, the current work gives recommendations on using the spectral representation method and the Fast Fourier transform filtering method to generate fractal surfaces and suggestions on selecting the low cutoff frequency of the power-law power spectral density. Furthermore, the results show that the proposed approximation method can be a choice to generate non-Gaussian fractal surfaces when the accuracy requirements are not high. The MATLAB codes for generating Gaussian and non-Gaussian fractal rough surfaces are provided.

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Qiu, Shiyu, Chunlei Wu, Zhenghao Wan, and Siyuan Tong. "High-Fold 3D Gaussian Splatting Model Pruning Method Assisted by Opacity." Applied Sciences 15, no. 3 (2025): 1535. https://doi.org/10.3390/app15031535.

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Recent advancements in 3D scene representation have underscored the potential of Neural Radiance Fields (NeRFs) for producing high-fidelity renderings of complex scenes. However, NeRFs are hindered by the significant computational burden of volumetric rendering. To address this, 3D Gaussian Splatting (3DGS) has emerged as an efficient alternative, utilizing Gaussian-based representations and rasterization techniques to achieve faster rendering speeds without sacrificing image quality. Despite these advantages, the large number of Gaussian points and associated internal parameters result in high storage demands. To address this challenge, we propose a pruning strategy applied during the Gaussian densification and pruning phases. Our approach integrates learnable Gaussian masks with a contribution-based pruning mechanism, further enhanced by an opacity update strategy to facilitate the pruning process. This method effectively eliminates redundant Gaussian points and those with minimal contributions to scene construction. Additionally, during the Gaussian parameter compression phase, we employ a combination of teacher–student models and vector quantization to compress the spherical harmonic coefficients. Extensive experimental results demonstrate that our approach reduces the storage requirements of original 3D Gaussian models by over 30 times, with only a minor degradation in rendering quality.

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Xie, Hongling. "An efficient and spectral accurate numerical method for computing SDE driven by multivariate Gaussian variables." AIP Advances 12, no. 7 (2022): 075306. http://dx.doi.org/10.1063/5.0096285.

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There are many previous studies on designing efficient and high-order numerical methods for stochastic differential equations (SDEs) driven by Gaussian random variables. They mostly focus on proposing numerical methods for SDEs with independent Gaussian random variables and rarely solving SDEs driven by dependent Gaussian random variables. In this paper, we propose a Galerkin spectral method for solving SDEs with dependent Gaussian random variables. Our main techniques are as follows: (1) We design a mapping transformation between multivariate Gaussian random variables and independent Gaussian random variables based on the covariance matrix of multivariate Gaussian random variables. (2) First, we assume the unknown function in the SDE has the generalized polynomial chaos expansion and convert it to be driven by independent Gaussian random variables by the mapping transformation; second, we implement the stochastic Galerkin spectral method for the SDE in the Gaussian measure space; and third, we obtain deterministic differential equations for the coefficients of the expansion. (3) We employ a spectral method solving the deterministic differential equations numerically. We apply the newly proposed numerical method to solve the one-dimensional and two-dimensional stochastic Poisson equations and one-dimensional and two-dimensional stochastic heat equations, respectively. All the presented stochastic equations are driven by two Gaussian random variables, and they are dependent and have multivariate normal distribution of their joint probability density.

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Pan, Xiaogang, Long Gao, Yuanyuan Jiao, and Zhiwen Chen. "A Dynamic GLR-Based Fault Detection Method for Non-Gaussain Dynamic Processes." Symmetry 14, no. 7 (2022): 1332. http://dx.doi.org/10.3390/sym14071332.

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Non-Gaussian dynamic processes are ubiquitous due to the presence of non-Gaussian distributed variables. Therefore, fault detection of non-Gaussian dynamic processes plays a vital role to maintain the safe operation of systems and symmetry of data distribution. In this paper, a dynamic generalized likelihood ratio (DGLR)-based fault detection method is proposed for non-Gaussian dynamic processes. Different from the conventional principal component analysis (PCA)-based, dynamic PCA-based, and PCA-based GLR fault detection methods, the novelty of the proposed method is that the GLR is extended to non-Gaussian dynamic processes, and the randomized algorithm is integrated for threshold setting to attenuate the influence of non-Gaussian. The application scope of these methods is also discussed. The proposed method is compared with four existing fault detection methods on a numerical simulation and the continuous stirred-tank reactor (CSTR) process. The achieved results show that the proposed method is able to significantly improve the detection performance in terms of fault detection rate and prompt response to faults.

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ANDRIJASEVIC, Andrea. "Gaussian distribution-based randomised image method." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 270, no. 3 (2024): 8478–88. http://dx.doi.org/10.3397/in_2024_4101.

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Sweeping echo is an acoustical phenomenon present in perfectly rectangular rooms that is characterised by a continuous increase in pitch arising from the concurrent arrival of multiple higher-order reflections. Even though the room acoustic simulation software predicts their presence, in most rectangular rooms sweeping echoes can hardly be perceived due to the existence of small irregularities in the room geometry. In this paper, the image sources' position randomisation model developed within the randomised image method framework with which the incongruence between the original image method results and in situ measurements can successfully be reduced is replaced with a Gaussian distribution model. The results indicate that with the proposed model an improvement in the stability of the room transfer function across realisations can be achieved.

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Ricciardi, Giuseppe. "A non-Gaussian stochastic linearization method." Probabilistic Engineering Mechanics 22, no. 1 (2007): 1–11. http://dx.doi.org/10.1016/j.probengmech.2006.04.001.

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Nakada, H., K. Mizuyama, M. Yamagami, and M. Matsuo. "RPA calculations with Gaussian expansion method." Nuclear Physics A 828, no. 3-4 (2009): 283–305. http://dx.doi.org/10.1016/j.nuclphysa.2009.07.010.

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Zhao, Mengyuan, Yazheng Tao, Kevin Weber, et al. "Method Comparison for Simulating Non-Gaussian Beams and Diffraction for Precision Interferometry." Sensors 23, no. 22 (2023): 9024. http://dx.doi.org/10.3390/s23229024.

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In the context of simulating precision laser interferometers, we use several examples to compare two wavefront decomposition methods—the Mode Expansion Method (MEM) and the Gaussian Beam Decomposition (GBD) method—for their precision and applicability. To assess the performance of these methods, we define different types of errors and study their properties. We specify how the two methods can be fairly compared and based on that, compare the quality of the MEM and GBD through several examples. Here, we test cases for which analytic results are available, i.e., non-clipped circular and general astigmatic Gaussian beams, as well as clipped circular Gaussian beams, in the near, far, and extremely far fields of millions of kilometers occurring in space-gravitational wave detectors. Additionally, we compare the methods for aberrated wavefronts and their interaction with optical components by testing reflections from differently curved mirrors. We find that both methods can generally be used for decomposing non-Gaussian beams. However, which method is more accurate depends on the optical system and simulation settings. In the given examples, the MEM more accurately describes non-clipped Gaussian beams, whereas for clipped Gaussian beams and the interaction with surfaces, the GBD is more precise.

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Hill, N. Ross. "Gaussian beam migration." GEOPHYSICS 55, no. 11 (1990): 1416–28. http://dx.doi.org/10.1190/1.1442788.

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Just as synthetic seismic data can be created by expressing the wave field radiating from a seismic source as a set of Gaussian beams, recorded data can be downward continued by expressing the recorded wave field as a set of Gaussian beams emerging at the earth’s surface. In both cases, the Gaussian beam description of the seismic‐wave propagation can be advantageous when there are lateral variations in the seismic velocities. Gaussian‐beam downward continuation enables wave‐equation calculation of seismic propagation, while it retains the interpretive raypath description of this propagation. This paper describes a zero‐offset depth migration method that employs Gaussian beam downward continuation of the recorded wave field. The Gaussian‐beam migration method has advantages for imaging complex structures. Like finite‐difference migration, it is especially compatible with lateral variations in velocity, but Gaussian beam migration can image steeply dipping reflectors and will not produce unwanted reflections from structure in the velocity model. Unlike other raypath methods, Gaussian beam migration has guaranteed regular behavior at caustics and shadows. In addition, the method determines the beam spacing that ensures efficient, accurate calculations. The images produced by Gaussian beam migration are usually stable with respect to changes in beam parameters.

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Wu, Xing Hui, and Yu Ping Zhou. "Regression and Classification Method Based on Gaussian Processes." Advanced Materials Research 971-973 (June 2014): 1949–52. http://dx.doi.org/10.4028/www.scientific.net/amr.971-973.1949.

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Gaussian processes is a kind of machine learning method developed in recent years and also a promising technology that has been applied both in the regression problem and the classification problem. In this paper, the general principle of regression and classification based on Gaussian process and experimental verification was described. A comparison about accuracy between this method and Support Vector Machine (SVM) is made during the experiments.Finally, it was summarized of the regression and classification of Gaussian process application and future development direction.

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Coelho, A. A., P. A. Chater, and A. Kern. "Fast synthesis and refinement of the atomic pair distribution function." Journal of Applied Crystallography 48, no. 3 (2015): 869–75. http://dx.doi.org/10.1107/s1600576715007487.

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A fast method for calculating the atomic pair distribution function is described in the context of performing refinements of structural models. Central to the speed of synthesis is the approximation of Gaussian functions of varying full widths at half-maximum using a narrower Gaussian with a fixed full width at half-maximum. The initial Gaussians are first laid down as delta functions which are then convoluted with the narrower Gaussian to form the final pattern. The net result is an algorithm, which has been included in the Rietveld refinement computer programTOPAS, that synthesizes and refines structural parameters a factor of 300–1000 times faster than alternative algorithms/programs, with speed advantages increasing as the number of atomic pairs increases.

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Sun, Xu Feng. "A Study on the Non-Gaussian Property by the Method of Limiting Streamline." Advanced Materials Research 919-921 (April 2014): 1390–95. http://dx.doi.org/10.4028/www.scientific.net/amr.919-921.1390.

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Under wind action, the property of non-Gaussian wind pressure distribution is very important for determination of peak factor, simulation of fluctuating wind pressure and design of cladding and components. Since the distribution of non-Gaussian zone is highly irregular based on the statistical method, any effort on giving regular non-Gaussian zone regions cant reflect the real non-Gaussian property. Considering the fact that non-Gaussian property was induced by flow separation and generally the movement of vortex showed the character of time averaged steady, taking a typical low-rise building as the example, the distribution of limiting streamlines and the theory of flow separation was applied in the research. Results show that the distribution of limiting streamlines has a close relationship with the intensity of non-Gaussian property and can be used as an intuitionistic tool in the research of identification and mechanism for non-Gaussian properties.

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Chang, R. J. "Non-Gaussian Linearization Method for Stochastic Parametrically and Externally Excited Nonlinear Systems." Journal of Dynamic Systems, Measurement, and Control 114, no. 1 (1992): 20–26. http://dx.doi.org/10.1115/1.2896503.

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A new practical non-Gaussian linearization method is developed for the problem of the dynamic response of a stable nonlinear system under both stochastic parametric and external excitations. The non-Gaussian linearization system is derived through a non-Gaussian density that is constructed as the weighted sum of undetermined Gaussian densities. The undetermined Gaussian parameters are then derived through solving a set of nonlinear algebraic moment relations. The method is illustrated by a Duffing-type stochastic system with/without parametric noise excited term. The accuracy in predicting the stationary and nonstationary variances by the present approach is compared with some exact solutions and Monte Carlo simulations.

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Fang, Jinli, Yuanqing Wang, and Jinji Zheng. "Gaussian convolution decomposition for non-Gaussian shaped pulsed LiDAR waveform." Measurement Science and Technology 34, no. 3 (2022): 035203. http://dx.doi.org/10.1088/1361-6501/aca3c6.

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Abstract The full waveform decomposition technique is significant for LiDAR ranging. It is challenging to extract the parameters from non-Gaussian shaped waveforms accurately. Many parametric models (e.g. the Gaussian distribution, the lognormal distribution, the generalized normal distribution, the Burr distribution, and the skew-normal distribution) were proposed to fit sharply-peaked, heavy-tailed, and negative-tailed waveforms. However, these models can constrain the shape of the waveform components. In this article, the Gaussian convolution model is established. Firstly, a set of Gaussian functions is calculated to characterize the system waveform so that asymmetric and non-Gaussian system waveforms can be included. The convolution result of the system waveform and the target response is used as the model for fitting the overlapped echo. Then a combination method of the Richardson–Lucy deconvolution, layered iterative, and Gaussian convolution is introduced to estimate the initial parameters. The Levenberg–Marquardt algorithm is used for the optimization fitting. Through experiments on synthetic data and practical recorded coding LiDAR data, we compare the proposed method with two decomposition approaches (Gaussian decomposition and skew-normal decomposition). The experiment results revealed that the proposed method could precisely decompose the overlapped non-Gaussian heavy-tailed waveforms and provide the best ranging accuracy, component fitting accuracy, and anti-noise performance. However, the traditional Gaussian and skew-normal decomposition methods can not fit the components well, resulting in inaccurate range estimates.

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Sajib, Anamul Haque. "Efficient Generation of Gaussian Varaiates Via Acceptance-Rejection Framework." Dhaka University Journal of Science 67, no. 2 (2019): 123–30. http://dx.doi.org/10.3329/dujs.v67i2.54584.

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The Gaussian distribution is often considered to be the underlying distribution of many observed samples for modelling purposes, and hence simulation from the Gaussian density is required to verify the fitted model. Several methods, most importantly, Box-Muller method, inverse transformation method and acceptance-rejection method devised by Box and Muller1, Rao et al.7 and Sigman8 respectively, are available in the literature to generate samples from the Gaussian distribution. Among these methods, Box-Muller method is the most popular and widely used because of its easy implementation and high efficiency,which produces exact samples2. However, generalizing this method for generating non-standard multivariate Gaussian variates is not discovered yet. On the other hand, inverse transformation method uses numerical approximation to the CDF of Gaussian density which may not be desirable in some situations while performance of acceptance-rejection method depends on choosing efficient proposal density. In this paper, we introduce a more general technique by exploiting the idea invented by Wakefield9 under acceptance rejection framework to generate one dimensional Gaussian variates, in which we don’t require to choose any proposal density and it can be extended easily for non-standard multivariate Gaussian density. The proposed method is compared to the existing acceptance-rejection method (Sigman8 method), and we have shown both mathematically and empirically that the proposed method performs better than Sigman8 method as it has a higher acceptance rate (79.53 %) compared to Sigman (76.04 %) method. Dhaka Univ. J. Sci. 67(2): 123-130, 2019 (July)

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Sun, Yuma. "Research on a Human Moving Object Detection Method Based on Gaussian Model and Deep Learning." Scalable Computing: Practice and Experience 25, no. 4 (2024): 2250–59. http://dx.doi.org/10.12694/scpe.v25i4.2958.

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In order to understand human motion object detection methods, the author proposes a research on human motion object detection method based on Gaussian model. Firstly, traditional Gaussian models are unable to detect complex scenes or slow moving targets. Therefore, an improved Gaussian model based moving object detection algorithm is proposed. Secondly, multiple Gaussian models are used to represent the features of each pixel in the moving target image, and based on the matching of each pixel in the image with the Gaussian model, it is considered as a background point. Conversely, it is based on the principle of the foreground, and the Gaussian model is updated. Finally, by updating the foreground model and calculating short-term stability indicators, the detection effect of moving targets is improved. By determining the Gaussian distribution and pixel relationship, new parameters are set to construct the background model and eliminate the impact caused by sudden changes in lighting. The experimental analysis results show that this method can effectively detect and track moving targets, with good noise resistance, high clarity, and an accuracy rate of up to 99%. Compared with traditional Gaussian model methods, the improved method can more effectively detect moving targets and has better robustness.

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Huang, Dongmei, Zhaokun Zhu, and Hongling Xie. "Peak Factor Deviation Ratio Method for Division of Gaussian and Non-Gaussian Wind Pressures on High-Rise Buildings." Mathematical Problems in Engineering 2022 (September 28, 2022): 1–18. http://dx.doi.org/10.1155/2022/9712998.

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The reasonable division of Gaussian and non-Gaussian wind pressures of building structure is beneficial to study the mechanism of wind load and adopt a reasonable peak factor estimation method. In this study, a pressure measurement wind tunnel test of a square high-rise building was conducted to study the division method for Gaussian and non-Gaussian wind pressures. Firstly, the skewness and kurtosis of wind pressures were analyzed, and then a normalized kurtosis-skewness linear distance difference ( δ ) was proposed. Moreover, the Gaussian and non-Gaussian criticality of wind pressure was discussed in combination with the wind pressure guarantee rate, and a peak factor deviation ratio (that is the deviation ratio between the complete probability peak factor with 99.95% guarantee rate and the Davenport peak factor) was proposed as the basis for Gaussian and non-Gaussian division. Subsequently, the functional relationships between the deviation ratio and the skewness and kurtosis as well as the δ were proposed, and then two classification criteria for Gaussian, weak non-Gaussian, and strong non-Gaussian regions were provided. Finally, the building surface wind pressures were divided into regions according to the classification criteria. The results show that the two Gaussian and non-Gaussian region division methods are reliable.

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Wen, Wu, Tao Jiang, and Yu Fang Gou. "Moving Object Detection Based on Improved Background Updating Method for Gaussian Mixture Model." Advanced Materials Research 1049-1050 (October 2014): 1561–65. http://dx.doi.org/10.4028/www.scientific.net/amr.1049-1050.1561.

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An effective improvement method was put forward caused by the traditional Gaussian mixture model has poor adaptability to illumination mutation. When illumination mutation is detected, improved Frame difference could detect the foreground region and background region, and then adopts a new replacing update methods to the Gaussian distribution with the least weights of Gaussian mixture background models in different regions. The experimental results show that improved method makes Gaussian mixture model can quickly adaptive to the light mutation, and exactly detect the moving object.

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Isonuma, Masaru, Junichiro Mori, Danushka Bollegala, and Ichiro Sakata. "Unsupervised Abstractive Opinion Summarization by Generating Sentences with Tree-Structured Topic Guidance." Transactions of the Association for Computational Linguistics 9 (2021): 945–61. http://dx.doi.org/10.1162/tacl_a_00406.

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Abstract This paper presents a novel unsupervised abstractive summarization method for opinionated texts. While the basic variational autoencoder-based models assume a unimodal Gaussian prior for the latent code of sentences, we alternate it with a recursive Gaussian mixture, where each mixture component corresponds to the latent code of a topic sentence and is mixed by a tree-structured topic distribution. By decoding each Gaussian component, we generate sentences with tree-structured topic guidance, where the root sentence conveys generic content, and the leaf sentences describe specific topics. Experimental results demonstrate that the generated topic sentences are appropriate as a summary of opinionated texts, which are more informative and cover more input contents than those generated by the recent unsupervised summarization model (Bražinskas et al., 2020). Furthermore, we demonstrate that the variance of latent Gaussians represents the granularity of sentences, analogous to Gaussian word embedding (Vilnis and McCallum, 2015).

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Wei, San Xi, and Zong Hai Sun. "A Multi-Classification Method Based on Gaussian Processes." Applied Mechanics and Materials 198-199 (September 2012): 1333–37. http://dx.doi.org/10.4028/www.scientific.net/amm.198-199.1333.

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Gaussian processes (GPs) is a very promising technology that has been applied both in the regression problem and the classification problem. In recent years, models based on Gaussian process priors have attracted much attention in the machine learning. Binary (or two-class, C=2) classification using Gaussian process is a very well-developed method. In this paper, a Multi-classification (C>2) method is illustrated, which is based on Binary GPs classification. A good accuracy can be obtained through this method. Meanwhile, a comparison about decision time and accuracy between this method and Support Vector Machine (SVM) is made during the experiments.

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Konzou, Essomanda. "Stein's method in two limit theorems involving the generalized inverse Gaussian distribution." Afrika Statistika 16, no. 1 (2021): 2561–86. http://dx.doi.org/10.16929/as/2021.2561.174.

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The generalized hyperbolic (GH) distribution converges in law to the generalized inverse Gaussian (GIG) distribution under certain conditions on the parameters. When the edges of an infinite rooted tree are equipped with independent resistances that are inverse Gaussian or reciprocal inverse Gaussian distributions, the total resistance converges almost surely to some random variable which follows the reciprocal inverse Gaussian (RIG) distribution. In this paper we provide explicit upper bounds for the distributional distance between GH (resp. infinite tree) distribution and their limiting GIG (resp. RIG) distribution applying Stein's method.

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Byrne, Peter C. "Novel Method for The Generation of the Gaussian Density and Distribution Functions." International Journal of Electrical Engineering & Education 31, no. 2 (1994): 148–51. http://dx.doi.org/10.1177/002072099403100207.

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Novel method for the generation of the Gaussian density and distribution functions A method is presented for generating the Gaussian density and distribution functions. These functions are generated in a novel way, using a simple structure to first generate the Gaussian density and then integrating this function to generate the distribution function.

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Smallwood, David. "Vibration with Non-Gaussian Noise." Journal of the IEST 52, no. 2 (2009): 13–30. http://dx.doi.org/10.17764/jiet.52.2.gh0444564n8765k1.

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Three methods are introduced for generating realizations of time histories with a specified auto-spectral density while controlling the kurtosis. One of the methods also allows the skewness to be specified. A second method allows large excursions (that produce large kurtosis) to be randomly distributed or almost periodic. In addition, the second method allows the average number of large excursions per unit of time to be specified. All the methods are variations of the inverse Welch method. The shape of the discrete Fourier magnitude is specified for a frame of data, thus controlling the shape of the auto-spectral density. The phase of the frame of data or the magnitude of the amplitude spectrum is modified to control the kurtosis or the skewness. The frames of data are multiplied by a window and overlapped and added to produce the realization.

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Lakshmanan, Valliappa, and John S. Kain. "A Gaussian Mixture Model Approach to Forecast Verification." Weather and Forecasting 25, no. 3 (2010): 908–20. http://dx.doi.org/10.1175/2010waf2222355.1.

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Abstract Verification methods for high-resolution forecasts have been based either on filtering or on objects created by thresholding the images. The filtering methods do not easily permit the use of deformation while identifying objects based on thresholds can be problematic. In this paper, a new approach is introduced in which the observed and forecast fields are broken down into a mixture of Gaussians, and the parameters of the Gaussian mixture model fit are examined to identify translation, rotation, and scaling errors. The advantages of this method are discussed in terms of the traditional filtering or object-based methods and the resulting scores are interpreted on a standard verification dataset.

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Domadiya, Prashant, Pratik Shah, and Suman K. Mitra. "Shadow-Free, Expeditious and Precise, Moving Object Separation from Video." International Journal of Image and Graphics 18, no. 01 (2018): 1850005. http://dx.doi.org/10.1142/s0219467818500055.

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The foreground–background separation is an essential part of any video-based surveillance system. Gaussian Mixture Models (GMM) based object segmentation method accurately segments the foreground, but it is computationally expensive. In contrast, single Gaussian-based segmentation is computationally inexpensive but inaccurate because it can not handle the variations in the background. There is a trade-off between computation efficiency and precision in the segmentation approach. From the experimental observations, the variations such as lighting variations, shadows, background motion, etc., affect only a few pixels in the frames in temporal direction. So, unaffected pixel can be modeled by single Gaussian in temporal direction while the affected pixels may need GMM to handle the variations in the background. We propose an adaptive algorithm which models pixel dynamically in terms of number of Gaussians in temporal direction. The proposed method is computationally inexpensive and precise. The flexibility in terms of number of Gaussians used to model each pixel, along with adaptive learning approach, reduces the time complexity of the algorithm significantly. To resolve spacial occlusion problem, a spatial smoothing is carried out by weighted [Formula: see text] nearest neighbors which improves the overall accuracy of proposed algorithm. To avoid false detection due to illumination variations and shadows in a particular image, illumination invariant representation is used.

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Yu, Bin, Yongzheng Zhang, Wenshu Xie, Wenjia Zuo, Yiming Zhao, and Yuliang Wei. "A Network Traffic Anomaly Detection Method Based on Gaussian Mixture Model." Electronics 12, no. 6 (2023): 1397. http://dx.doi.org/10.3390/electronics12061397.

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How can we learn the normal behavior of some communication processes and predict whether a single communication is under attack, with massive network traffic data representing the time costs of each stage in a single communication process? This paper introduces a statistical method for detecting network traffic anomalies using the Gaussian mixture model. There are two aspects to our contributions. First, we show how to learn the normal behavior of a communication process under the assumption that its time costs are generated from the Gaussian mixture model. Secondly, we show that with the learned Gaussian mixture model, we can predict whether a data point is under attack by computing the likelihood that the data point is drawn from the learned Gaussian distribution. The experimental results show that our method reached high accuracy in some cases, while in some other cases that are more complicated, the data point may have more factors and cannot be represented simply by only one Gaussian mixture model.

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Mao, Ke Ming, Zhi Liang Zhu, Hui Yan Jiang, and Zhuo Fu Deng. "A Novel Skin Image Detection Method Based on GMM and GAs." Applied Mechanics and Materials 128-129 (October 2011): 482–86. http://dx.doi.org/10.4028/www.scientific.net/amm.128-129.482.

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This paper proposes a new skin image detection method. First, skin pixel histogram in RGB color space is analyzed. Then Gaussian Mixture Model is used to constructed distribution of skin pixels. Second, a Gaussian parameter combination and selection procedure is implemented with Genetic Algorithms, and the optimal Gaussian Mixture Model can be obtained. Experimental results on public database show that our proposed method outperforms the traditional method with ROC test.

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Xu, Zhen, Yinghao Xu, Zhiyuan Yu, et al. "Representing Long Volumetric Video with Temporal Gaussian Hierarchy." ACM Transactions on Graphics 43, no. 6 (2024): 1–18. http://dx.doi.org/10.1145/3687919.

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This paper aims to address the challenge of reconstructing long volumetric videos from multi-view RGB videos. Recent dynamic view synthesis methods leverage powerful 4D representations, like feature grids or point cloud sequences, to achieve high-quality rendering results. However, they are typically limited to short (1~2s) video clips and often suffer from large memory footprints when dealing with longer videos. To solve this issue, we propose a novel 4D representation, named Temporal Gaussian Hierarchy, to compactly model long volumetric videos. Our key observation is that there are generally various degrees of temporal redundancy in dynamic scenes, which consist of areas changing at different speeds. Motivated by this, our approach builds a multi-level hierarchy of 4D Gaussian primitives, where each level separately describes scene regions with different degrees of content change, and adaptively shares Gaussian primitives to represent unchanged scene content over different temporal segments, thus effectively reducing the number of Gaussian primitives. In addition, the tree-like structure of the Gaussian hierarchy allows us to efficiently represent the scene at a particular moment with a subset of Gaussian primitives, leading to nearly constant GPU memory usage during the training or rendering regardless of the video length. Moreover, we design a Compact Appearance Model that mixes diffuse and view-dependent Gaussians to further minimize the model size while maintaining the rendering quality. We also develop a rasterization pipeline of Gaussian primitives based on the hardware-accelerated technique to improve rendering speed. Extensive experimental results demonstrate the superiority of our method over alternative methods in terms of training cost, rendering speed, and storage usage. To our knowledge, this work is the first approach capable of efficiently handling hours of volumetric video data while maintaining state-of-the-art rendering quality.

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Pachalieva, Aleksandra, and Alexander J. Wagner. "Molecular dynamics lattice gas equilibrium distribution function for Lennard–Jones particles." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 379, no. 2208 (2021): 20200404. http://dx.doi.org/10.1098/rsta.2020.0404.

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The molecular dynamics lattice gas (MDLG) method maps a molecular dynamics (MD) simulation onto a lattice gas using a coarse-graining procedure. This is a novel fundamental approach to derive the lattice Boltzmann method (LBM) by taking a Boltzmann average over the MDLG. A key property of the LBM is the equilibrium distribution function, which was originally derived by assuming that the particle displacements in the MD simulation are Boltzmann distributed. However, we recently discovered that a single Gaussian distribution function is not sufficient to describe the particle displacements in a broad transition regime between free particles and particles undergoing many collisions in one time step. In a recent publication, we proposed a Poisson weighted sum of Gaussians which shows better agreement with the MD data. We derive a lattice Boltzmann equilibrium distribution function from the Poisson weighted sum of Gaussians model and compare it to a measured equilibrium distribution function from MD data and to an analytical approximation of the equilibrium distribution function from a single Gaussian probability distribution function. This article is part of the theme issue ‘Progress in mesoscale methods for fluid dynamics simulation’.

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Yu, Shou Hua, Ji Hong Chen, and Jing Ying Ou. "Study on the Detection Method of Pigs in Piglet Pigsty Based on the Characteristics of Pigs." Advanced Materials Research 403-408 (November 2011): 2271–76. http://dx.doi.org/10.4028/www.scientific.net/amr.403-408.2271.

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Pig detection plays an important role in intelligent monitoring system of pigsty. According to the features of piglets acting in a large scope with high frequency, an improved Gaussian mixture background model was proposed for detecting piglets, which improves processing speed by reducing the number of Gaussian functions. Since the sow is confined to the sow limitation crate and its activities’ state is simple within a small range, an skin color look-up table method which was based on characteristics of skin was proposed for detecting the sow. The experimental results demonstrated that the pigs detection methods including an improved mixture Gaussian background model and an skin color Look-Up table method are superior to frame subtraction method, mixture Gaussian background model method and optical flow method.

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Cen, Jiazhong, Jiemin Fang, Chen Yang, et al. "Segment Any 3D Gaussians." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 2 (2025): 1971–79. https://doi.org/10.1609/aaai.v39i2.32193.

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This paper presents SAGA (Segment Any 3D GAussians), a highly efficient 3D promptable segmentation method based on 3D Gaussian Splatting (3D-GS). Given 2D visual prompts as input, SAGA can segment the corresponding 3D target represented by 3D Gaussians within 4 ms. This is achieved by attaching a scale-gated affinity feature to each 3D Gaussian to endow it a new property towards multi-granularity segmentation. Specifically, a scale-aware contrastive training strategy is proposed for the scale-gated affinity feature learning. It 1) distills the segmentation capability of the Segment Anything Model (SAM) from 2D masks into the affinity features and 2) employs a soft scale gate mechanism to deal with multi-granularity ambiguity in 3D segmentation through adjusting the magnitude of each feature channel according to a specified 3D physical scale. Evaluations demonstrate that SAGA achieves real-time multi-granularity segmentation with quality comparable to state-of-the-art methods. As one of the first methods addressing promptable segmentation in 3D-GS, the simplicity and effectiveness of SAGA pave the way for future advancements in this field.

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Hahm, Dae-Gi, Hyun-Moo Koh, and Kwan-Soon Park. "A Failure Probability Estimation Method of Nonlinear Bridge Structures using the Non-Gaussian Closure Method." Journal of the Earthquake Engineering Society of Korea 14, no. 1 (2010): 25–34. http://dx.doi.org/10.5000/eesk.2010.14.1.025.

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Meyzia, Bunga, Saktioto Saktioto, Tengku Emrinaldi, et al. "Novel approach peak tracking method for FBG: Gaussian polynomial technique." Science, Technology and Communication Journal 4, no. 3 (2024): 61–68. http://dx.doi.org/10.59190/stc.v4i3.262.

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This paper presents a novel approach for tracking the peaks in the FBG spectrum using the Gaussian polynomial method. The proposed algorithm involves preprocessing the FBG signal, detecting the peaks, and fitting the peaks with a Gaussian function. The performance of the algorithm is evaluated using both simulated and experimental FBG spectra. This method involves fitting a Gaussian function to the peak of interest and using the fitted parameters to estimate peak height, width, and location. The method is highly accurate and precise and can provide detailed information about peak shape and position, making it effective for tracking complex or overlapping peaks. However, the method can be computationally intensive and may require careful selection of initial parameters to ensure accurate results. Despite these limitations, the Gaussian polynomial method is a powerful tool for peak tracking and analysis in various application.

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