## What is/are Isotropic Gaussian?

Isotropic Gaussian - Using the estimators derived from a simple isotropic Gaussian model of turbulent wind fluctuations, we proposed modified models for estimating the turbulence intensity of wind components.^{[1]}Drawing on preliminary works, we introduce here a Bayesian anisotropic Gaussian source model in which the phase is no longer uniform.

^{[2]}In the reported literature, the measurement error of the image points is usually assumed to obey isotropic Gaussian distribution.

^{[3]}We present a new technique to extract the intensity variations from input images using anisotropic Gaussian directional derivative filters with multiple scales.

^{[4]}Specifically, consider a sequence of labeled examples (a1,b1), (a2,b2)…, with ai drawn independently from a d-dimensional isotropic Gaussian, and where bi = ⟨ ai, x⟩ + ηi, for a fixed x ∈ ℝd with ||x||2 = 1 and with independent noise ηi drawn uniformly from the interval [−2−d/5,2−d/5].

^{[5]}The standard concept of isotropic Gaussian microturbulence was assumed in this study.

^{[6]}In this paper, we present such a method based on the first derivative of anisotropic Gaussian kernels.

^{[7]}In this study, the conventional coplanar relative reachable domain with initial state uncertainty in isotropic Gaussian distribution is extended to the three-dimensional case with uncertainty in arbitrary Gaussian distribution.

^{[8]}Stable evaluation algorithms for isotropic Gaussians (Gaussian radial basis functions) have been proposed based on a Chebyshev expansion of the Gaussians by Fornberg, Larsson & Flyer and based on a Mercer expansion with Hermite polynomials by Fasshauer & McCourt.

^{[9]}Simply stated, the problem that we address is the following: estimate the angle of rotation of a pattern with steerable filters centered at the same location, where the image is corrupted by colored isotropic Gaussian noise.

^{[10]}Although in the general case the calculation of optical quantities requires evaluation of double integrals, it is shown that for the PSDF given by the isotropic Gaussian function some integrals can be calculated analytically and only single integrals have to be evaluated numerically.

^{[11]}This paper derives central and noncentral limit results for the first Minkowski functional subordinated to homogeneous and isotropic Gaussian and chi-squared random fields, restricted to the sphere in R3.

^{[12]}The anisotropic edge strength is obtained through the first derivative of anisotropic Gaussian kernels which incorporates an adaptive anisotropy factor.

^{[13]}Notice that their result was generalized by Wu and Xiao [Continuity in the Hurst index of the local times of anisotropic gaussian random fields, Stoch.

^{[14]}We show that k-means (Lloyd’s algorithm) is obtained as a special case when truncated variational EM approximations are applied to Gaussian mixture models (GMM) with isotropic Gaussians.

^{[15]}The numerical results are compared with those from Euler–Lagrange simulations and two other quadrature-based moment methods, namely, anisotropic Gaussian (AG) and 8-node tensor-product (TP) quadrature.

^{[16]}Numerical calculations are carried out for new spectral function of electron density fluctuations containing both anisotropic Gaussian and power-law spectral functions using the experimental data.

^{[17]}In this paper, we consider the behavior of the maximum likelihood estimators of parameters of the homogeneous isotropic Gaussian random field with squared exponential covariance function.

^{[18]}In the present work, two new kinetic models are introduced and compared: an approach based on the Shakhov kinetic model and an approach involving an anisotropic Gaussian equilibrium function.

^{[19]}To better detect edges with heterogeneous widths, in this paper, we propose a multiscale edge detection method based on first-order derivative of anisotropic Gaussian kernels.

^{[20]}Diffusion-attenuated MR signal for heterogeneous media has been represented as a sum of signals from anisotropic Gaussian sub-domains to the extent that this approximation is permissible.

^{[21]}The moment system resulting from the two BE kinetic equations is closed at second order by invoking the anisotropic Gaussian closure.

^{[22]}The proposed approach follows a backward variable elimination procedure based on gradient descent optimisation, iteratively adjusting the widths of an anisotropic Gaussian kernel.

^{[23]}The main constituents of our approach include approximating a complex, isotropic Gaussian probability distribution by a finite-size Gauss-Hermite constellation, applying entropic continuity bounds, and leveraging previous security proofs for Gaussian-modulation protocols.

^{[24]}The most frequently used filtering technique to suppress high-frequency noise in GRACE data is the isotropic Gaussian averaging filter.

^{[25]}The published results for this landmark data under isotropic Gaussian models and procrustes theory are also discussed.

^{[26]}The present work aims at investigating the ability of a Kinetic-Based Moment Method (KBMM) to reproduce the statistics of turbulent particle-laden flows using the Anisotropic Gaussian (AG) closure.

^{[27]}We test these bounds for the case of isotropic Gaussians with equal covariances and whose means are separated by a distance $\eta$, and find (1) that $\gg \log k$ separation suffices to drive the proportion of mismatches of the MLE to 0, and (2) that the expected fraction of mismatched observations goes to zero at rate $O((\log k)^{2}/\eta^{2})$.

^{[28]}Using an isotropic Gaussian kernel framework, we show that vector movement is likely to be greater when applying a temporal effect, than when estimated by traditional methods.

^{[29]}Let $$X=\{X(t)\in {{\mathbb {R}}}^d, t\in {{\mathbb {R}}}^N\}$$ be a centered space–time anisotropic Gaussian random field with stationary increments, whose components are independent but may not be identically distributed.

^{[30]}The standard concept of isotropic Gaussian microturbulence was assumed in this study.

^{[31]}Let $$X= \{X(t) \in \mathbb{R}^d, t\in \mathbb{R}^N\}$$X={X(t)∈Rd,t∈RN} be a centered space-anisotropic Gaussian random field whose components satisfy some mild conditions.

^{[32]}A spectral algorithm is proposed to simulate an isotropic Gaussian random field on a sphere equipped with a geodesic metric.

^{[33]}The second avenue corresponds to the long‐time limit, when the observed signal can be approximated as a sum of multiple nonexchanging anisotropic Gaussian components.

^{[34]}As an important case, when X is an anisotropic Gaussian random field, then we show that its expected number of critical points becomes proportional to that of an isotropic field Z , while the height distribution remains the same as that of Z.

^{[35]}In order to design a line detector that minimizes the impact of noise, regardless of the scale or direction of the lines, in this paper, we present a framework for multiscale line detection based on second-order anisotropic Gaussian kernels.

^{[36]}

## isotropic gaussian kernel

In this paper, we present such a method based on the first derivative of anisotropic Gaussian kernels.^{[1]}The anisotropic edge strength is obtained through the first derivative of anisotropic Gaussian kernels which incorporates an adaptive anisotropy factor.

^{[2]}To better detect edges with heterogeneous widths, in this paper, we propose a multiscale edge detection method based on first-order derivative of anisotropic Gaussian kernels.

^{[3]}The proposed approach follows a backward variable elimination procedure based on gradient descent optimisation, iteratively adjusting the widths of an anisotropic Gaussian kernel.

^{[4]}Using an isotropic Gaussian kernel framework, we show that vector movement is likely to be greater when applying a temporal effect, than when estimated by traditional methods.

^{[5]}In order to design a line detector that minimizes the impact of noise, regardless of the scale or direction of the lines, in this paper, we present a framework for multiscale line detection based on second-order anisotropic Gaussian kernels.

^{[6]}

## isotropic gaussian random

Notice that their result was generalized by Wu and Xiao [Continuity in the Hurst index of the local times of anisotropic gaussian random fields, Stoch.^{[1]}In this paper, we consider the behavior of the maximum likelihood estimators of parameters of the homogeneous isotropic Gaussian random field with squared exponential covariance function.

^{[2]}Let $$X=\{X(t)\in {{\mathbb {R}}}^d, t\in {{\mathbb {R}}}^N\}$$ be a centered space–time anisotropic Gaussian random field with stationary increments, whose components are independent but may not be identically distributed.

^{[3]}Let $$X= \{X(t) \in \mathbb{R}^d, t\in \mathbb{R}^N\}$$X={X(t)∈Rd,t∈RN} be a centered space-anisotropic Gaussian random field whose components satisfy some mild conditions.

^{[4]}A spectral algorithm is proposed to simulate an isotropic Gaussian random field on a sphere equipped with a geodesic metric.

^{[5]}As an important case, when X is an anisotropic Gaussian random field, then we show that its expected number of critical points becomes proportional to that of an isotropic field Z , while the height distribution remains the same as that of Z.

^{[6]}

## isotropic gaussian model

Using the estimators derived from a simple isotropic Gaussian model of turbulent wind fluctuations, we proposed modified models for estimating the turbulence intensity of wind components.^{[1]}The published results for this landmark data under isotropic Gaussian models and procrustes theory are also discussed.

^{[2]}

## isotropic gaussian distribution

In the reported literature, the measurement error of the image points is usually assumed to obey isotropic Gaussian distribution.^{[1]}In this study, the conventional coplanar relative reachable domain with initial state uncertainty in isotropic Gaussian distribution is extended to the three-dimensional case with uncertainty in arbitrary Gaussian distribution.

^{[2]}

## isotropic gaussian microturbulence

The standard concept of isotropic Gaussian microturbulence was assumed in this study.^{[1]}The standard concept of isotropic Gaussian microturbulence was assumed in this study.

^{[2]}