Probability distribution of eigenspectra and eigendirections of a twodimensional,symmetric rank two random tensor

Let there be given a twodimensional symmetric rank two tensor of random type (examples:strain, stress) which is either directly observed or indirectly estimated from observations by an adjustment procedure. Under the assumption of normalityof tensor components we compute the joint probability density functionas well as the marginal probability density functionsof its eigenspectra (eigenvalues) and eigendirections (orientation parameters). Due to the nonlinearity of the relation between eigenspectra-eigendirections and the random tensor components, via the inverse nonlinear error propagationbiases and aliases of their first and centralized second moments (mean value, variance-covariance) are expressed in terms of Jacobianand Hessianmatrices. The joint probability density function and the first and second moments thus form the fundamental of hypothesis testing and qualify control of eigenspectra (eigenvalues, principal components) and eigendirections (orientation parameters, eigenvectors, principial direction) of a twodimensional, symmetric rank two random tensor.     

A PROJECTION METHOD OF MAPPING FROM AIR PHOTOGRAPHS

Abstract

An instrument was previously described in the Transactions of the Royal Society of S. Africa for the setting of pairs of photographs, taken from air stations, in correspondence; that is, in the same relative positions that the camera occupied in space at the moments of exposure. The principle of the instrument may be recalled.     

地球主惯性矩

地球主惯性矩属于大地测量学和天文学的基本地球参数.研究地球主惯性矩及有关问题.第一节研究主惯性矩和地球扁率的计算公式;第二节研究主惯性轴坐标系中2阶位系数的计算;第三节研究地球主惯性轴方向的确定方法,第四节给出地球主惯性矩、主惯性轴方向和地球扁率的数值结果.     

The temporal variation of the spherical and Cartesian multipoles of the gravity field: the generalized MacCullagh representation

 The Cartesian moments of the mass density of a gravitating body and the spherical harmonic coefficients of its gravitational field are related in a peculiar way. In particular, the products of inertia can be expressed by the spherical harmonic coefficients of the gravitational potential as was derived by MacCullagh for a rigid body. Here the MacCullagh formulae are extended to a deformable body which is restricted to radial symmetry in order to apply the Love–Shida hypothesis. The mass conservation law allows a representation of the incremental mass density by the respective excitation function. A representation of an arbitrary Cartesian monome is always possible by sums of solid spherical harmonics multiplied by powers of the radius. Introducing these representations into the definition of the Cartesian moments, an extension of the MacCullagh formulae is obtained. In particular, for excitation functions with a vanishing harmonic coefficient of degree zero, the (diagonal) incremental moments of inertia also can be represented by the excitation coefficients. Four types of excitation functions are considered, namely: (1) tidal excitation; (2) loading potential; (3) centrifugal potential; and (4) transverse surface stress. One application of the results could be model computation of the length-of-day variations and polar motion, which depend on the moments of inertia. Received: 27 July 1999 / Accepted: 24 May 2000     

加入不变矩的高分辨率遥感图像分类

不变矩是表达图像几何形状信息的参数,具有几何变换的稳定性,在图像识别领域已经得到广泛应用。本文将3种常用的不变矩,即胡氏矩、Zern ike矩和小波矩,运用到高分辨率遥感图像分类中,并与只利用光谱信息的图像分类结果进行对比。结果表明,在高分辨率图像分类中加入不变矩图像可以显著提高分类精度,尤其是对那些具有相似光谱特征但同时具有不同形状和结构特征的地物分类更加有效。     

Earth＇s Temporal Principal Moments of Inertia and Variable Rotation

Based on the gravity field models EGM96 and EIGEN-GL04C, the Earth＇s time-dependent principal moments of inertia A, B, C are obtained, and the variable rotation of the Earth is determined. Numerical results show that A, B, and C have increasing tendencies; the tilt of the rotation axis increases 2.1×10^ 8 mas/yr; the third component of the rotational angular velocity, ω3 , has a decrease of 1.0×10^ 22 rad/s^2, which is around 23% of the present observed value. Studies show in detail that both 0 and ω3 experience complex fluctuations at various time scales due to the variations of A, B and C.     

不同小波函数对粗差识别效果的比较

采用含孤立态、离散态与区域态三种类型粗差的含强噪声的动态变形信号,研究粗差识别中小波基函数的选择依据。分别从分解层数、支撑区间、正则性以及消失距四个角度,选用不同的小波基函数进行试验,结果表明：对于该含不同类型粗差的变形信号,在所考察的小波基函数范围内,对于区域态粗差几种小波的识别能力相当;同等条件下,对于孤立态粗差,...     

3D Zernike矩在三维地形匹配中应用

本文介绍了三维地形匹配工作原理,提出3DZernike矩在三维地形匹配中应用算法。该方法利用三维地形曲面与其3DZernike矩具有一一对应关系,计算实时恢复得到的三维地形与基准图中参考三维地形的3DZernike矩,比较这两个3DZernike矩之间欧式距离,并以欧式距离最小为最佳匹配原则实现三维地形的精确匹配。该方法充分利用3DZernike矩的性质,将三维地形匹配转换成3DZernike矩匹配。该算法对匹配地形无特殊要求,抗噪声能力强,能实现三维地形的精确匹配。     

Estimation of the third and fourth order central moments of measurement errors from sums of powers of least squares adjustment residuals

Summary In the paper a method of determination of estimators of the central moments of the third and fourth order on the basis of the least squares adjustment is presented. These estimators concern the moments of the observation results as well as to readjustment (better) of observation sets with application of methods that take into consideration moments of higher order (not only the variance-covariance matrix).The obtained estimators are not biased, but their effectiveness was not studied. That is why the presented theory is not completed (in the sense of the estimators properties).     

Evolution of the Earth's principal axes and moments of inertia: the canonical form of solution

 Harmonic coefficients of the 2nd degree are separated into the invariant quantitative (the 2nd-degree variance) and the qualitative (the standardized harmonic coefficients) characteristics of the behavior of the potential V ₂(t). On this basis the evolution of the Earth's dynamical figure is described as a solution of the time-dependent eigenvalues–eigenvectors problem in the canonical form. Such a canonical quadratic form is defined only by temporal variations of the harmonic coefficients and always remains finite, even within an infinite time interval. An additional condition for the correction or the determination of temporal variations of the 2nd degree is obtained. Temporal variations of the fully normalized sectorial harmonic coefficients are estimated in addition to ˙Cˉ ₂₀, ˙Cˉ ₂₁, and ˙Sˉ ₂₁ of the EGM96 gravity model. In addition, a non-linear hyperbolic model for Cˉ _2m (t), Sˉ _2m (t) is constructed. The trigonometric form of the hyperbolic model leads to the consideration of the potential V ₂(ψ) instead of V ₂(t) within the closed interval −π/2≤ψ≤+π/2. Thus, it is possible to evaluate the global trend of V ₂(t), the Earth's principal axes and the differences of the moments of inertia within the whole infinite time interval. Received: 25 September 1998 / Accepted: 28 June 2000     

重叠矩形图像表示及其上的精确Legendre矩计算(英文)

Linear quadtree is a popular image representation method due to its convenient imaging procedure. However, the excessive emphasis on the symmetry of segmentation, i.e. dividing repeatedly a square into four equal sub-squares, makes linear quadtree not an optimal representation. In this paper, a no-loss image representation, referred to as Overlapped Rectangle Image Representation （ORIR）, is presented to support fast image operations such as Legendre moments computation. The ORIR doesn＇t importune the symmetry of segmentation, and it is capable of representing, by using an identical rectangle, the information of the pixels which are not even adjacent to each other in the sense of 4-neighbor and 8-neighbor. Hence, compared with the linear quadtree, the ORIR significantly reduces the number of rectangles required to represent an image. Based on the ORIR, an algorithm for exact Legendre moments computation is presented. The theoretical analysis and the experimental results show that the ORIR-based algorithm for exact Legendre moments computation is faster than the conventional exact algorithms.     

On the Distribution of the Estimated Coherence

The recent paper by Abdelfattah and Nicolas proposed a novel coherence magnitude estimator and studied its properties. Here, we derive simpler and more explicit expressions for four of the properties that were studied: 1) the probability density function; 2) moments; 3) Mellin transform; and 4) second-kind moments. We establish numerical efficiency of these expressions and provide simple Maple programs for inversion. We expect that the results presented here could enhance applicability of the new estimator.     

PSO-Based Optimal Selection of Zernike Moments for Target Discrimination in High-Resolution SAR Imagery

Target discrimination is the key step of automatic target detection in synthetic aperture radar (SAR) images. In this paper, a new algorithm, effective and robust feature sets for target discrimination in high resolution SAR images has been proposed. Two main steps in target discrimination of SAR images have been developed, the feature extraction based on Zernike moments (ZMs) having linear transformation invariance properties and the PSO based feature selection to select the optimal feature subset of Zernike moments for decreasing computational complexity of feature extraction step. The input regions of interest (ROIs) have been segmented and passed to a number of preprocessing stages such as histogram equalization, position and size normalization. Two groups of Zernike moments (shape and margin (intensity) characteristic) have been extracted from the preprocessed images and they have been applied to the feature selection step. Each group includes 34 moments with different orders and iterations. The selected moments have been applied to a SVM classifier. The proposed scheme has been tested on the MSTAR database. The Receiver Operational Characteristics (ROC) curve and the performance of proposed method using some measured data have been analyzed. Experimental results demonstrate the efficiency of the proposed approach in target discrimination of SAR imagery.     

内核晃动对地球主惯性矩的时变性影响

高密度内核相对于地幔的晃动将改变地球内部物质的密度分布并导致地球主惯性矩随时间变化。本文在重力场球谐分析理论的基础上,给出了时变的地球主惯性矩A、B、C及主惯性轴,并研究了内核晃动对A、B、C的时变性影响。计算结果表明,A、B、C平均每年增大约4.5×1027kg m2,而内核晃动使A、B、C均表现出振幅为1022~1024kg m2的似正弦式变化,不足以维持其长期增大趋势,这进一步支持了"地球在膨胀"的结论。     

用不变矩从机载激光扫描测高点云数据中重建规则房屋

介绍了不变矩的概念，结合实例，基于机载激光扫描测高的三雏点云数据，用不变矩实现了规则房屋的模型重建。对不变矩重建房屋模型的精度进行了讨论和分析．得出了一些有益的结论。     

Approximate representation of thep-norm distribution

［1］Liu D J,Shi W Z,Tong X H,et al.Precision analysis and quality cont rol of GIS spatial data.Shanghai:Shanghai Publishing House of Scientific Documen ts,1999 ［2］Chen X R,Fang Z B,Li G Y,et al.Non_parameter statistics.S hanghai:Shanghai Publishing House of Science and Technology,1989 ［3］Li Q H,Tao B Z.Application of probability statistical theory in survey ing.Beijing:Beijing Publishing House of Surveying and Mapping,1982 ［4］Sun H Y.p_norm distribution theory and its application in surveyin g data processing:[Ph.D Thesis].Wuhan:Wuhan Technical University of Surveying and Mapping,1995     

Overlapped rectangle image representation and its application to exact legendre moments computation

Linear quadtree is a popular image representation method due to its convenient imaging procedure. However, the excessive emphasis on the symmetry of segmentation, i.e. dividing repeatedly a square into four equal sub-squares, makes linear quadtree not an optimal representation. In this paper, a no-loss image representation, referred to as Overlapped Rectangle Image Representation (ORIR), is presented to support fast image operations such as Legendre moments computation. The ORIR doesn’t importune the symmetry of segmentation, and it is capable of representing, by using an identical rectangle, the information of the pixels which are not even adjacent to each other in the sense of 4-neighbor and 8-neighbor. Hence, compared with the linear quadtree, the ORIR significantly reduces the number of rectangles required to represent an image. Based on the ORIR, an algorithm for exact Legendre moments computation is presented. The theoretical analysis and the experimental results show that the ORIR-based algorithm for exact Legendre moments computation is faster than the conventional exact algorithms.