Image analysis by Tchebichef moments

This paper introduces a new set of orthogonal moment functions based on the discrete Tchebichef polynomials. The Tchebichef moments can be effectively used as pattern features in the analysis of two-dimensional images. The implementation of the moments proposed in this paper does not involve any numerical approximation, since the basis set is orthogonal in the discrete domain of the image coordinate space. This property makes Tchebichef moments superior to the conventional orthogonal moments such as Legendre moments and Zernike moments, in terms of preserving the analytical properties needed to ensure information redundancy in a moment set. The paper also details the various computational aspects of Tchebichef moments and demonstrates their feature representation capability using the method of image reconstruction.     

Image analysis by Gaussian-Hermite moments

Orthogonal moments are powerful tools in pattern recognition and image processing applications. In this paper, the Gaussian-Hermite moments based on a set of orthonormal weighted Hermite polynomials are extensively studied. The rotation and translation invariants of Gaussian-Hermite moments are derived algebraically. It is proved that the construction forms of geometric moment invariants are valid for building the Gaussian-Hermite moment invariants. The paper also discusses the computational aspects of Gaussian-Hermite moment, including the recurrence relation and symmetrical property. Just as the other orthogonal moments, an image can be easily reconstructed from its Gaussian-Hermite moments thanks to the orthogonality of the basis functions. Some reconstruction tests with binary and gray-level images (without and with noise) were performed and the obtained results show that the reconstruction quality from Gaussian-Hermite moments is better than that from known Legendre, discrete Tchebichef and Krawtchouk moments. This means Gaussian-Hermite moment has higher image representation ability. The peculiarity of image reconstruction algorithm from Gaussian-Hermite moments is also discussed in the paper. The paper offers an example of classification using Gaussian-Hermite moment invariants as pattern feature and the result demonstrates that Gaussian-Hermite moment invariants perform significantly better than Hu's moment invariants under both noise-free and noisy conditions.     

基于Krawtchouk不变矩的仿射攻击不变性局部水印算法

本文提出了一种基于原始图像Krawtchouk不变矩实现的仿射攻击不变性局部水印算法.具体介绍了Krawtchouk不变矩的构造方法,水印是事先产生的且与原始图像无关,通过将水印嵌入到图像的Krawtchouk不变矩中实现仿射攻击不变性.这种基于Krawtchouk矩的水印算法是局部水印技术,即水印的嵌入只是影响到部分原始图像,因此该算法对剪切攻击具有很好的鲁棒性.检测过程中采用独立分量分析技术实现真正意义上的盲检测.文中具体分析了所提出算法的计算复杂度,实验数据说明这种水印算法对通用水印测试软件Stirmark具有很好的鲁棒性.     

基于Krawtchouk矩不变量和核模糊聚类的快速分形编码

针对基于分类的快速分形编码方法存在着编码速度与解码质量间的矛盾,鉴于Krawtchouk矩不变量具有在仿射变换下保持不变的特性和核模糊聚类在处理非线性问题上的突出优势,本文首次将这两者引入到分形编码中,提出了基于Krawtchouk矩不变量和核模糊聚类的自适应分类快速分形编码方法。首先根据Domain块的方差将其粗分类,再根据Domain块的Krawtchouk矩不变量利用核模糊聚类对Domain块细分类。实验结果表明,与其他基于分类的快速分形编码方法相比,在解码图像质量提高的同时,大大加快了分形编码的速度。     

基于指数矩的图像描述

论证一种基于T指数构建的圆谐?傅里叶矩——指数矩（ EFMs）,分析其定义原理及其与基于三角函数构建的圆谐?傅里叶矩的关系,验证指数矩作为一种正交不变矩所具有的多畸变不变性质。通过在Matlab软件平台上进行的仿真实验,证明了指数矩的旋转、缩放不变性,得出了指数矩作为一种高度浓缩的图像特征,无信息冗余,抽样性能好,抗噪声能力强,与其他矩相比更适用于多畸变不变图像描述和识别的结论。     

Image focus measure based on Chebyshev moments

A new measure of image focus based on the discrete orthogonal Chebyshev moments is introduced. The low- and high-spatial-frequency components of an image can be represented as the low- and high-order Chebyshev moments, respectively. The focus measure is defined as the ratio of the norm of the high-order moments to that of low-order moments. It is shown that the focus measure is monotonic and unimodal with respect to image blurring. Additionally, it is invariant to contrast changes due to the differences in the intensities of illumination. The focus measure is tested for its discriminating power of images blurred to various degrees. Noise studies show that the focus measure is robust under Gaussian and salt-and-pepper noise. The performance of the proposed focus measure is compared with the existing focus measures.     

Image fusion based on discrete Chebyshev moments

Though deep learning-based methods have demonstrated strong capabilities on image fusion, they usually improve the fusion performance by increasing the width and depth of the network, increasing the computational effort and being unsuitable for industrial applications. In this paper, an end-to-end network based on fixed convolution module of discrete Chebyshev moments is proposed, which does not need any pre- or post-processing. The proposed network is roughly composed of three parts: feature extraction module, fusion module and feature reconstruction module. In the feature extraction module, a novel fixed convolution module based on discrete Chebyshev moments is proposed to obtain different frequency components in a short time. To improve the image sharpness and fuse more details, a spatial attention mechanism based on average gradient is proposed in fusion module. Extensive results demonstrate that the proposed network can achieve remarkable fusion performance, high time efficiency and strong generalization ability.     

Direct analysis of folded dipole by method of moments

The integral equation for the current on a folded dipole is reduced to a matrix equation by the Galerkin method. The resulting current distribution allows the input impedance `step-up? to be deduced, and also the variation in input admittance with frequency to be examined.     

Printed antennas analysis by a Gabor frame-based method of moments

Gabor frame-based discretization is proposed for the first time as a fully rigorous and flexible tool in the context of antenna analysis. A rigorous discretization procedure based on frame theory is presented and applied to integral equations solution through a method of moments (MoM). In this approach, the unknown field or current is expanded in a set of spatially and spectrally translated elementary functions. The use of a Gaussian window function as basis element allows for the representation of radiated fields as a superposition of shifted and rotated Gaussian beams. By exploiting the well understood propagation and transformation features of Gaussian beams, the fields can be evaluated by summations of analytic terms, at any observation point. This method seems well suited to model antennas embedded in complex systems including arbitrary interfaces. Numerical results are presented for slot antennas at the interface between two dielectric half spaces and compared to a standard MoM to validate the approach and illustrate its attractive characteristics.     

Higher moments in cost-benefit analysis

This paper deals with the cost-benefit analysis of one-server two-unit hot standby system with imperfect switch where the repair densities depend upon the type of items (unit/standby/switch) waiting for repair. Initially one unit is put to operation (switch is working at t = 0) and the other unit is kept as a hot standby. The revenue as well as the cost of repair are arbitrary functions of time. Explicit expressions are obtained for expected net gain in [0,t] from which other characteristics like expected busy period due to repair of unit/standby/switch, expected up-time, expected number of repairs completed of unit/standby/switch etc. can be obtained.     

基于Contourlet 变换和Hu 不变矩的图像检索算法

文章提出一种基于Contourlet 变换和Hu 不变矩的图像检索算法。首先,对每幅图像进行Contourlet 变换,得到低频子带与高频方向子带,把计算得到的低频子带的Hu 不变矩和各个高频方向子带的均值与标准差作为图像的特征向量,利用Manhattan距离进行相似度度量,完成基于内容的图像检索。为对该文提出的算法的检索效果进行检验,分别与基于Contourlet 变换特征的检索算法和基于Hu不变矩特征的检索算法等方法进行了对比实验研究。结果表明,该算法有效地融合了图像的纹理特征与低频子带的形状特征,较好地实现了基于内容的图像检索,平均查准率达到73.94%。     

Method of moments analysis of offset-reflector antennas

The authors apply the method of moments to analyse the surface currents and radiation patterns of offset-reflector antennas. For a small disk, the convergence of the techniques is compared with an exact solution. The results presented for an offset reflector are compared with the physical theory of diffraction, and the discrepancies explained     

指数矩耦合局部敏感哈希的图像伪造检测算法

为了解决图像伪造检测算法在定位篡改内容时忽略了不同颜色分量之间的关系,使其对图像特征描述不足,导致其识别结果中存在误检与漏检等情况,本文提出了基于多元指数矩与欧式局部敏感哈希的图像伪造检测算法。引入高斯低通滤波,消除可疑图像中的噪声;随后,将滤波图像分割为一系列的重叠圆形子块,改善其对旋转等内容操作的鲁棒性;基于四元指数矩(QEM),计算每个圆形子块的QEM,以提取相应的鲁棒特征,将其组合成特征矢量;采用欧式局部敏感哈希机制,生成每个子块对应的哈希序列;计算任意两个相邻哈希元素之间的空间距离,通过与预设阈值比较,完成所有子块的匹配;最后,借助随机样本一致性方法来剔除错误匹配,通过形态学处理,定位出篡改内容。实验数据显示：较已有的伪造检测方法而言,在各种几何内容修改下,所提算法具有更高的伪造检测准确性。     

用不变矩实现花粉粒显微图像的归一化

显微图像易受光照、视角、方位、噪声等的影响.在这些因素的作用下,同一类显微图像的不同变形体差距有时大于另一类图像,因此进行显微图像识别以前需要进行图像的归一化.本文推导了基于变形雅可比(p=4,q=3)-傅立叶矩的草药花粉粒显微图像的归一化标准,并对8种中蒙花药显微特征图像进行归一化实验,发现同一种花粉粒图像不同变形体归一化后的矩值方差明显小于归一化前.另外,用加权最小平均距离分类器对320个花粉粒归一化显微图像进行初步识别实验,平均识别率达97.4%.     

Image analysis

Image analysis systems perform measurements or quantification of features in an image. One of the most recently developed areas for the use of image analysis is industrial machine vision, in which the image analyser contributes to the automation of an industrial processing system. One such application is in guiding robots, the image analyser locates the part, checks its conformity to the required model and directs the robot to grasp the part or perform some operation on it     

Hybrid nonlinear moments in array processing and spectrum analysis

The aim of this paper is to provide a theoretical basis for the use of hybrid nonlinear (HNL) moments in array processing and spectrum analysis. These moments are defined as the expected value of the product of one random variable times a nonlinear function of another random variable. They generalize a class of twofold higher order moments, and their additional flexibility can be exploited for optimization purposes or for computational convenience. A number of properties beyond the classical Bussgang's (1952) and Price's (1958) theorems are found for HNL moments and matrices, making these statistics suitable for harmonic analysis and bearing estimation. Covariance based and higher order moments based methods are extended to the HNL moments domain, and a new class of Gaussian noise rejecting statistics is added to cumulants. The properties of some classes of matrices of HNL moments of practical interest are analyzed in detail     

基于Krawtchouk矩的自适应门限四叉树分形编码

编码时间过长是分形图像压缩存在的主要问题,同时固定匹配门限影响着编码效率.本文首次将Krawtchouk矩引入到自适应分形编码中,提出了基于Krawtchouk矩的自适应门限四叉树分形编码方法.该方法计算图像块的12个Krawtchouk矩不变量,将这些矩不变量构成特征向量,并用这样的特征向量取代Range块和Domain块的灰度值矩阵进行匹配计算.文中给出了实验结果,并与基于四叉树的自适应门限分形图像IFS压缩方法进行了比较.结果表明,本文方法不仅大幅度减少了编码时间,而且同时也能提高图像恢复质量.     

一种广义正交不变图像矩:雅可比-傅立叶矩

提出一种多畸变不变的正交图像矩:雅可比-傅立叶矩.其核函数由径向雅可比多项式和角向傅立叶复指数因子组成.雅可比多项式中的两个参数p和q的变化能够形成各种正交多项式,因而形成各种正交图像矩:勒让德-傅立叶矩(p＝1,q＝1)、切比雪夫-傅立叶矩(p＝2,q＝3/2)、正交傅立叶-梅林矩(p＝2,q＝2)和Zernike矩以及变形Zemike矩,等等.因此雅可比-傅立叶矩是核函数由径向多项式和角向傅立叶复指数因子组成的正交图像矩的一般形式,为这种正交图像矩的数学分析和优化提供了理论基础.