Estimating probability curves of rock variables using orthogonal polynomials and sample moments

A new algorithm using orthogonal polynomials and sample moments was presented for estimating probability curves directly from experimental or field data of rock variables. The moments estimated directly from a sample of observed values of a random variable could be conventional moments (moments about the origin or central moments) and probability-weighted moments (PWMs). Probability curves derived from orthogonal polynomials and conventional moments are probability density functions (PDF), and probability curves derived from orthogonal polynomials and PWMs are inverse cumulative density functions (CDF) of random variables. The proposed approach is verified by two most commonly-used theoretical standard distributions: normal and exponential distribution. Examples from observed data of uniaxial compressive strength of a rock and concrete strength data are presented for illustrative purposes. The results show that probability curves of rock variable can be accurately derived from orthogonal polynomials and sample moments. Orthogonal polynomials and PWMs enable more secure inferences to be made from relatively small samples about an underlying probability curve.

ORTHOGONAL MATRIX POLYNOMIALS WITH RESPECT TO LINEAR MATRIX MOMENT FUNCTION ALS:THEORY AND APPLICATIONS

In this paper orthogonal matrix polynomials with respect to a right matrix moment functional an introduced. Basic results, important examples and applications to the approximation of matrix integrals are studied. Error bounds for the proposed matrix quadrature rules are given.

ORTHOGONAL MATRIX POLYNOMIALS WITH RESPECT TO A CONJUGATE BILINEAR MATRIX MOMENT FUNCTIONAL: BASIC THEORY

In this paper basic results for a theory of orthogonal matrix polynomials with respect to a conjugate bilinear matrix moment functional are proposed. Properties of orthogonal matrix polynomial sequences including a three term matrix relationship are given. Positive definite conjugate bilinear matrix moment functionals are introduced and a characterization of positive definiteness in terms of a block Haenkel moment matrix is established. For each positive definite conjugate bilinear matrix moment functional an associated matrix inner product is defined.

Color Image Reconstruction by Discrete Orthogonal Moment

Image reconstruction can help to determine how well an image may be characterized by a small finite set of its moments. Also, we can identify the number of descriptors needed to describe an image. In this work, we present a comparative analysis using different set of discrete orthogonal moments in terms of normalized image reconstruction error (NIRE). Color image reconstruction is performed with different color channels and various orders of different discrete orthogonal moments. Finally the results obtained by the reconstruction of three color images with different families of orthogonal moments and an error analysis to compare their capacity of description are presented, also the conclusions obtained from this work are presented.

A Simple Computational Approach for the Texture Analysis of CT Scan Images Using Orthogonal Moments

This paper is a study on texture analysis of Computer Tomography (CT) liver images using orthogonal moment features. Orthogonal moments are used as image feature representation in many applications like invariant pattern recognition of images. Orthogonal moments are proposed here for the diagnosis of any abnormalities on the CT images. The objective of the proposed work is to carry out the comparative study of the performance of orthogonal moments like Zernike, Racah and Legendre moments for the detection of abnormal tissue on CT liver images. The Region of Interest (ROI) based segmentation and watershed segmentation are applied to the input image and the features are extracted with the orthogonal moments and analyses are made with the combination of orthogonal moment with segmentation that provides better accuracy while detecting the tumor. This computational model is tested with many inputs and the performance of the orthogonal moments with segmentation for the texture analysis of CT scan images is computed and compared.

Probabilistic density function estimation of geotechnical shear strength parameters using the second Chebyshev orthogonal polynomial

A method to estimate the probabilistic density function （PDF） of shear strength parameters was proposed. The second Chebyshev orthogonal polynomial（SCOP） combined with sample moments （the origin moments） was used to approximate the PDF of parameters. X^2 test was adopted to verify the availability of the method. It is distribution-free because no classical theoretical distributions were assumed in advance and the inference result provides a universal form of probability density curves. Six most commonly-used theoretical distributions named normal, lognormal, extreme value Ⅰ , gama, beta and Weibull distributions were used to verify SCOP method. An example from the observed data of cohesion c of a kind of silt clay was presented for illustrative purpose. The results show that the acceptance levels in SCOP are all smaller than those in the classical finite comparative method and the SCOP function is more accurate and effective in the reliability analysis of geotechnical engineering.

Proportional integral derivative controller design using Legendre orthogonal functions

The Legendre orthogonal functions are employed to design the family of PID controllers for a variety of plants. In the proposed method, the PID controller and the plant model are represented with their corresponding Legendre series. Matching the first three terms of the Legendre series of the loop gain with the desired one gives the PID controller parameters. The closed loop system stability conditions in terms of the Legendre basis function pole(λ) for a wide range of systems including the first order, second order, double integrator, first order plus dead time, and first order unstable plants are obtained. For first order and double integrator plants, the closed loop system stability is preserved for all values of λ and for the other plants, an appropriate range in terms of λ is obtained. The optimum value of λ to attain a minimum integral square error performance index in the presence of the control signal constraints is achieved. The numerical simulations demonstrate the benefits of the Legendre based PID controller.

A NOTE ON SOBOLEV ORTHOGONALITY FOR LAGUERRE MATRIX POLYNOMIALS

Abstract. Let {L（Ln^（A,λ）（x）}n≥0 be the sequence of monic Laguerre matrix polynomials defined on [0,∞） byLn^（A,λ）（x）=n!/（-λ）^n ∑nk-0（-λ）^k/k!（n-k）!（A＋I）n[（A＋I）k]^-1x^k,where A ∈ C^r×r. It is known that {Ln^（A,λ）（x）}n≥0 is orthogonal with respect to a matrix moment functional when A satisfies the spectral condition that Re（z） 〉 -1 for every z E or（a）. In this note we show that forA such that σ（A） does not contain negative integers, the Laguerre matrix polynomials Ln^（A,λ）（x） are orthogonal with respect to a non-diagonal SobolevLaguerre matrix moment functional, which extends two cases： the above matrix case and the known scalar case.

Performance Analysis for Orthogonal Time Frequency Space Modulation Systems with Generalized Waveform

Orthogonal time-frequency space(OTFS),which exhibits beneficial advantages in high-mobility scenarios,has been considered as a promising technology in future wireless communication systems.In this paper,a universal model for OTFS systems with generalized waveform has been developed.Furthermore,the average bit error probability(ABEP)upper bounds of the optimal maximum likelihood(ML)detector are first derived for OTFS systems with generalized waveforms.Specifically,for OTFS systems with the ideal waveform,we elicit the ABEP bound by recombining the transmitted signal and the received signal.For OTFS systems with practical waveforms,a universal ABEP upper bound expression is derived using moment-generating function(MGF),which is further extended to MIMO-OTFS systems.Numerical results validate that our theoretical ABEP upper bounds are concur with the simulation performance achieved by ML detectors.

正交Gaussian-Krawtchouk不变矩的构建及在图像匹配中的应用研究

针对基于几何矩及不变矩的图像特征描述存在信息冗余,计算复杂,图像表征能力不强等问题,本文深入研究了正交的Gaussian-Krawtchouk矩及其不变矩的表达形式。依据不同的尺度因子特点,提出了基于多尺度Gaussian-Krawtchouk不变矩的图像局部特征描述方法,并用于五种不同类型图像的特征匹配。实验结果表明,这种不变矩较其他传统的特征描述方法具有更好的图像表征能力,更强的数字稳健性。该不变矩用于图像匹配是有效可行的,具有良好的实用价值。

Image Analysis by Two Types of Franklin-Fourier Moments

In this paper,we first derive two types of transformed Franklin polynomial:substituted and weighted radial Franklin polynomials.Two radial orthogonal moments are proposed based on these two types of polynomials,namely substituted Franklin-Fourier moments and weighted Franklin-Fourier moments(SFFMs and WFFMs),which are orthogonal in polar coordinates.The radial kernel functions of SFFMs and WFFMs are transformed Franklin functions and Franklin functions are composed of a class of complete orthogonal splines function system of degree one.Therefore,it provides the possibility of avoiding calculating high order polynomials,and thus the accurate values of SFFMs and WFFMs can be obtained directly with little computational cost.Theoretical and experimental results show that Franklin functions are not well suited for constructing higher-order moments of SFFMs and WFFMs,but compared with traditional orthogonal moments(e.g.,BFMs,OFMs and ZMs)in polar coordinates,the proposed two types of Franklin-Fourier Moments have better performance respectively in lower-order moments.

Offline Handwritten Characters Recognition Using Moments Features and Neural Networks

In this paper we revise the moment theory for pattern recognition designed, to extract patterns from the noisy character datas, and develop unconstrained handwritten. Amazigh character recognition method based upon orthogonal moments and neural networks classifier. We argue that, given the natural flexibility of neural network models and the extent of parallel processing that they allow, our algorithm is a step forward in character recognition. More importantly, following the approach proposed, we apply our system to two different databases, to examine the ability to recognize patterns under noise. We discover overwhelming support for different style of writing. Moreover, this basic conclusion appears to remain valid across different levels of smoothing and insensitive to the nuances of character patterns. Experiments tested the effect of set size on recognition accuracy which can reach 97.46%. The novelty of the proposed method is independence of size, slant, orientation, and translation. The performance of the proposed method is experimentally evaluated and the promising results and findings are presented. Our method is compared to K-NN （k-nearest neighbors） classifier algorithm; results show performances of our method.

Zernike矩的快速算法

给出了Zernike矩求解的一种快速算法 .利用Zernike多项式迭代性质 ,找出了Zernike正交矩之间的内在关系 ,这样 ,高阶的Zernike矩可由低价的Zernike矩求出 ,再在Chan等人提出的关于一维几何矩有效算法的基础上 ,得出了一种快速算法 .与已有方法相比 ,该算法大大减少了求解过程中的乘法次数 ,降低了计算复杂度 ,从而提高了运算速度和效率 ;并可以有效用于模式识别。

基于非极大值抑制的圆目标亚像素中心定位

圆形目标在基于图像的测量系统中应用广泛,针对圆目标中心的高定位精度和快速提取的要求,提出了一种基于非极大值抑制的亚像素中心定位方法。该方法利用Sobel算子进行边缘检测,通过改进非极大值抑制方法获取连续细化的边缘,实现了像素级边缘定位,采用Zernike正交矩对边缘点进行亚像素级定位,并用最小二乘法进行二次拟合来获取精确的标志点的中心坐标。仿真图像和实测图像的实验结果验证了该方法的有效性和准确性,其定位精度可以达到0.02像素,通过测试算法的运行时间,证明该算法具有很好的实时性。

不同对比度下自适应的自动调焦新算法

针对大多数自动调焦函数不能克服对比度变化引起的调焦曲线失去理想特性、陷入局部极小值甚至失去单峰性等问题,介绍了Zernike正交矩,分析了各阶Zernike矩的调焦函数曲线并且提出了一种新的基于Zernike正交矩的自动调焦算法,定义了此算法的公式.与几种常用自动调焦函数在不同对比度条件下进行了调焦效果的比较分析,验证了通过调整各阶Zernike矩的权重系数、可以灵活变换调焦公式,能够适应不同对比度下的调焦过程.实验比较了基于Zernike正交矩的自动调焦算法应用于完全对称型物体和非对称型物体时焦效果的差别,证明了该算法应用于圆形或球状等完全对称型的物体时调焦效果较好.

不同小波基下滤波性能之比较

不同的小波基有各自的特点和优点。对三种典型的具有紧支撑的小波 ,即Haar小波、正交小波[1] 、双正交小波[2 ] 在滤波中的应用进行了研究 ,对其滤波效果进行了对比并分析了其原因。指出了Haar小波具有最高的时间分辨率 ,能够对信号的瞬态特征进行很好的识别 ;而正交和双正交小波具有二阶的消失矩 ,对信号的逼近精度高。但正交小波缺乏对称 (反对称 )性 ,有可能造成较多的失真。若能做到对信号的不同特征自适应地采用不同的小波基进行分析 ,则可使滤波效果达到最佳。

一种改进的Zernike正交矩亚像素边缘检测算法

在分析Ghosal提出的基于Zernike正交矩亚像素边缘检测算法的基础上,对Ghosal算法进行了改进。指出了Ghosal算法的两点不足,即没有考虑模板效应和没有考虑边缘梯度方向上的一阶导数模型。针对这种不足提出了改进方法。改进后的算法在计算边缘亚像素坐标时更准确,同时还具有细化边缘的能力,使边缘定位更精确。

北极涛动对我国冬季同期极端气温的影响研究

使用1955～2004年1月500 hPa高度场和同期我国107个测站最高和最低气温的逐月资料,计算极端气温与北极涛动指数的相关矩场,并对此相关矩场进行经验正交函数分析来研究我国最高和最低气温对北极涛动响应的年际变化。北极涛动指数定义为1月500 hPa标准化高度场经验正交函数分解所得到的第1时间函数。研究过程中对北极涛动一般年份和异常年份两种情况进行比较分析。研究发现北极涛动指数的正负极端异常年份,对我国冬季同期最高和最低气温有十分明显的影响。我国冬季最高气温响应主要表现地域是长江中下游、华北和河套地区,最低气温的响应主要表现地域是东部沿海和长江黄河上游地区。同时分析了不同年份冬季极端气温对于北极涛动响应的不同形势。

基于Legendre正交矩的配准方法及其在二值图像配准中的应用

Legendre矩在模式识别、图像分析等领域有广泛的应用 ,具有正交、无冗余性等优点 .本文提出了一种基于Legendre正交矩的配准方法 ,它在医学图像多模态数据的配准、融合中具有重要的实用价值 .

三维U系统矩与三维模型检索

提出3D U系统矩的定义,并将其应用于3D模型检索.作为一种可选定次数的完备正交多项式系统,U系统所定义的矩具有标准正交性、收敛性等优良性质.根据U系统理论实现了U1系统矩的高阶的快速计算,可以定义任意维数的特征空间.实验结果表明,3D U1系统矩优于几何矩和Zernike矩,具有更高的检索效率.