空间矩和Zernike矩亚像素边缘算子分析

讨论了空间矩、Zernike矩两个亚像素边缘算子的运行时间和定位精度。分析结果表明,Zernike具有更快的运行速度,当计算3个用于边缘定位的参数时,其运行时间较空间矩算子节约了50%。理论分析了空间矩和Zernike矩算子的关系,并推导出了两个算子边缘距离为l的差值公式。测试结果表明,当两个算子的l都限制在中心像素内时,空间矩算子的边缘厚度多达3个像素,而Zernike矩算子的边缘厚度小于1个像素,可见Zernike矩算子的定位精度为真正的亚像素级。经比较,Zernike矩算子的运行时间和定位精度均好于空间矩算子。     

用雅可比-傅里叶矩进行图像描述

提出了雅可比—傅里叶矩,它是用雅可比多项式作为径向函数,用傅里叶因子作为角向函数构造而成的,是广义正交傅里叶—梅林矩。经过归一化处理后的雅克比—傅立叶矩具有平移、尺度、旋转、灰度多畸不变性。从归一化图像重建误差、噪声灵敏度等方面对雅可比—傅里叶矩的图像描述能力进行了研究,结果显示雅可比—傅里叶矩在各种参量选择的情况下,具有良好的图像描述和抗噪声能力,是一个优良的图像特征。以前的研究多为单纯构建某一个函数,而现在将其扩展为构建一个函数族,开阔了矩描述量的研究视野。     

Moments of the Wigner distribution of rotationally symmetric partially coherent light

The Wigner distribution of rotationally symmetric partially coherent light is considered, and the constraints for its moments are derived. Although all odd-order moments vanish, these constraints lead to a drastic reduction in the number of parameters that we need to describe all even-order moments: whereas in general we have (N + 1)(N + 2)(N + 3)/6 different moments of order N, this number reduces to (1 + N/2)2 in the case of rotational symmetry. A way to measure the moments as intensity moments in the output planes of (generally anamorphic) fractional Fourier-transform systems is presented.     

Spatial moments for the nonstationary one-velocity problem of transport theory with isotropic scattering. I. Point instantaneous source

Equations for the moments of spatial particle distribution in a homogeneous medium with isotropic scattering are derived for the nonstationary one-velocity problem of transport theory. Exact analytical and numerical solutions are found for five even moments (from the second to the tenth one) by the Laplace transform method, and an algorithm for calculating the moments of arbitrary order is described. Convergence to the corresponding moments is investigated in the diffusion approximation for t→∞, and its nonuniform character is established: higher moments differ significantly from the corresponding diffusion moments at any t. The physical causes for such behavior of the moments are discussed. Ul'yanovsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 88–94, February, 2000.     

等时量子输运理论

在普遍量子情形下,建立了协变Ｗｉｇｎｅｒ函数的能量矩的等时动力论链和链的截断方案,得到了与低阶矩相关的物理密度量的输运方程和约束方程,并且证明高阶矩都能通过低阶矩表示．     

On the mechanics of rim instabilities in viscoelastic polymer thin films

We determine appropriate attractors for higher than third-order central moments for the relaxation process in three-dimensional lattice Boltzmann methods. It was previously assumed that the appropriate attractors for the relaxation of these moments were their equilibria values as derived from a Maxwell-Boltzmann distribution. However, when the attractor for fourth-order central moments is derived that way, the solution of three-dimensional lattice Boltzmann differs significantly from the analytical solution of the Navier-Stokes equation for simple test cases like Poiseuille flow. We show that the Navier-Stokes solution is recovered when we chose products of low order central moments as the attractors of the higher order central moments.     

Disorder-induced local magnetic moments in weakly correlated metallic systems

We consider the formation and the Kondo effect of local magnetic moments in the Anderson-Hubbard model with off-diagonal disorder. The existence of moments at sites weakly coupled to the environment is deduced in effective medium approximation. The distribution of moments is calculated both deep in the metallic phase and near the metal-insulator transition. We discuss the Kondo quenching of the moments and derive a distribution of local Kondo temperatures.     

伪Zernike矩在低信噪比红外目标检测中的应用

由于探测器本身固有的特性以及军事上的极限使用要求,红外图像普遍存在目标-背景间对比度较差、目标边缘模糊和噪声较大等特点,采用常规模板匹配、Hu矩方法难以取得理想的检测效果。针对低信噪比红外目标图像,分析了伪Zernike矩的基本原理、不变性和计算方法,提出了低信噪比红外目标检测的伪Zernike矩方法,并比较了模板匹配、Hu矩、伪Zernike矩方法的目标检测效果。理论分析和实验验证了该方法的有效性。     

Chemisorption of Li and Na on iridium surfaces: An investigation with nuclear spin polarized atoms

The chemisorption of Li and Na on clean and oxygen covered polycrystalline iridium was investigated using nuclear spin polarized alkali atoms. During adsorption on the surface the moments of the nuclei act as microscopic probes. The nuclear quadrupole moments of the alkali atoms are interacting with the electric field gradient. The interaction reflects the charge distribution around the nucleus. The nuclear magnetic moments are interacting with magnetic fields generated by the magnetic moments of electrons.     

Fractional calculus approach to the statistical characterization of random variables and vectors

Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has inverse power-law tails and, consequently, it lacks integer order moments. In this paper, starting from the Mellin transform of the characteristic function and by fractional calculus method we present a new perspective on the statistics of random variables. Introducing the class of complex moments, that include both integer and fractional moments, we show that every random variable can be represented within this approach, even if its integer moments diverge. Applications to the statistical characterization of raw data and in the representation of both random variables and vectors are provided, showing that the good numerical convergence makes the proposed approach a good and reliable tool also for practical data analysis.     

The sixth frequency moments for an anisotropic paramagnet with exchange-bond dilution

The sixth frequency moments of the spin correlation function for a bond-diluted anisotropic Heisenberg paramagnet in the high temperature limit are evaluated for arbitrary spin values. Results for both the transverse and longitudinal moments are presented for a model in which the transverse and longitudinal exchange bonds can fluctuate independently. The results are presented in a form which allows the moments for the undiluted, site diluted, and single-bond diluted moments to be also written down.     

Studies of nuclear second moments for pre-equilibrium nuclear reaction theories

The nuclear second moments, important inputs to pre-equilibrium reaction theories, are evaluated by assuming a simple model. The positive definite nature of the second moments is examined, and the nuclear level densities are calculated using positive definite second moments.     

一种新型不变矩在图像识别中的应用

给出了仿射变换的定义,并在此基础上建立了一种新的仿射变换途径——多尺度自卷积变换。构造了一组新的仿射不变矩(MSA矩),分析了其性质,给出了它的明确表达式及其具体实现方法。分别应用最小距离法、k-近邻法和相似性测度三种识别方法进行了仿真实验。结果表明,MSA矩对平移、比例、旋转、拉伸和扭曲等仿射变换均具有很好的不变性,与典型的Flusser矩相比,稳健性好、识别率高、抗噪声干扰能力强,具有一定的应用价值。     

Electric Quadrupole and Magnetic Dipole Moments of Mirror Nuclei and Self-Conjugate Nuclei

A transformation, which brings about the unification of the nuclear collective and single particle models, yields sumrules for the magnetic dipole moments and for the electric quadrupole moments of mirror nuclei. These sumrules are applied to cases, for which the numerical values of these moments are known.     

Kinetic equations with soluble moment equations

If the moments of the kernel in a kinetic equation are polynomials, then the moment equations have a symmetry property, which permits the general solution in the form of a Laguerre series, and its coefficients (Laguerre moments) satisfy the same equations as the ordinary moments.     

Hadronic quark distribution amplitudes from QCD sum-rule moments

We discuss the reliability of hadronic wave functions (quark distribution amplitudes) determined by a finite number of QCD sum-rule moments. Although the expansion coefficients for polynomial models of the wave function are uniquely determined by the moments, the inherent uncertainty in such moments leads to a considerable indeterminacy in the wave functions because minimal changes of the moments can lead to large oscillations of the model function. In particular, the freedom in the moments left by QCD sum rules leads to a nonconverging polynomial expansion. This remains true even if additional constraints on the wave functions are used. As a consequence of this, the widely used procedure of constructing polynomial models of hadronic wave function from QCD sum rule moments does not guarantee even a reasonable approximation to the true wave function. The differences among the model wave functions persist also in the calculations of physical observables like hadronic form factors. This implies that physical observables calculated by means of such model wave functions are in general very unreliable. As specific examples, we examine the pion and nucleon wave functions and show that Gegenbauer as well as Appell polynomial expansions constructed from QCD sum rule moments are ruled out. The implications for the wave functions which are generally used in the literature are discussed.     

Recoil corrections to magnetic moments of charmed baryons in themit bag model

Recoil corrections to magnetic moments of charmed baryons are studied in themit bag model. It is noticed that such corrections which improve the octet baryon magnetic moments have considerably significant contributions to charmed baryon’s moments also.     

A generalized moments expansion

A new generalized moments expansion (GMX), which is based on the t-expansion, is derived. The well-known connected moments expansion (CMX) and alternate moments expansion (AMX) are shown to be special cases of the GMX.     

Relativistic expressions for current electric moments of nuclei

Relativistic expressions for the operators of current electric moments caused by electromagnetic spin-orbit interaction are obtained. Formulas for the matrix elements of the current electric moments of nuclei are derived. The contributions of the current electric moments to the quadrupole moment of the deuteron and to its root-mean-square radius are calculated with allowance for relativistic effects.