A Geometrical Transformations Resistant Digital Watermarking Based on Quantization

A geometrical transformations resistant digital image watermarking based on quantization is described. Taking advantage of the rotation, scale and translation invariants of discrete Fourier transform (DFT), each watermark bit is embedded into each homocentric circles around the zero frequency term in DFT domain by quantizing the magnitude vector of Fourier spectrum. The embedded sequence can be extracted by “majority principles” without restoring to the original unmarked image. The experimental results show that the watermark is invisible and robust to any combination of geometrical transformations or common image processing techniques.

GEOMETRICALLY INVARIANT WATERMARKING BASED ON RADON TRANSFORMATION

The weakness of classical watermarking methods is the vulnerability to geometrical distortions that widely occur during normal use of the media. In this letter, a new image- watermarking method is presented to resist Rotation, Scale and Translation (RST) attacks. The watermark is embedded into a domain obtained by taking Radon transform of a circular area selected from the original image, and then extracting Two-Dimensional (2-D) Fourier magnitude of the Radon transformed image. Furthermore, to prevent the watermarked image from degrading due to inverse Radon transform, watermark signal is inversely Radon transformed individually. Experimental results demonstrate that the proposed scheme is able to withstand a variety of attacks including common geometric attacks.

Derived Categories in Langlands Geometrical Ramifications: Approaching by Penrose Transforms

Some derived categories and their deformed versions are used to develop a theory of the ramifications of field studied in the geometrical Langlands program to obtain the correspondences between moduli stacks and solution classes represented cohomologically under the study of the kernels of the differential operators studied in their classification of the corresponding field equations. The corresponding D-modules in this case may be viewed as sheaves of conformal blocks (or co-invariants) (images under a version of the Penrose transform) naturally arising in the framework of conformal field theory. Inside the geometrical Langlands correspondence and in their cohomological context of strings can be established a framework of the space-time through the different versions of the Penrose transforms and their relation between them by intertwining operators (integral transforms that are isomorphisms between cohomological spaces of orbital spaces of the space-time), obtaining the functors that give equivalences of their corresponding categories.(For more information,please refer to the PDF version.)

Symmetry transformations for magnetohydrodynamics and Chew–Goldberger–Low equilibria revisited

We generalize the symmetry transformations for magnetohydrodynamic(MHD) equilibria with isotropic pressure and incompressible flow parallel to the magnetic field introduced by Bogoyavlenskij in the case of the respective Chew–Goldberger–Low(CGL) equilibria with anisotropic pressure. We find that the geometrical symmetry of the field-aligned equilibria can be broken by those transformations only when the magnetic field is purely poloidal. In this situation we derive three-dimensional CGL equilibria from given axisymmetric ones. Also, we examine the generic symmetry transformations for MHD and CGL equilibria with incompressible flow of an arbitrary direction, introduced in a number of papers, and find that they cannot break the geometrical symmetries of the original equilibria, unless the velocity and magnetic field are collinear and purely poloidal.

图Transformer支持下的河网模式识别

河网模式识别在地形地貌分析、地质矿物探测、河网数据多尺度变换等研究中发挥重要作用。为克服基于形态特征与几何特征的空间统计方法的稳健性不足问题,引进图卷积神经网络是当前的主要手段,然而图卷积方法仅关注河网形态的局部特征,仍未实现从全局视角出发的河网模式识别决策。因此,本文提出了一种图Transformer支持下的河网模式识别方法。该方法在河网几何形态知识支持下利用对偶图思想构建河网图结构,进一步通过GraphSAGE设计局部学习模块及Transformer设计全局学习模块。试验结果表明,相比已有的1^(st)-ChebNet和GraphSAGE方法,本文方法能够结合局部河段组合特征与全局河网形态特征,做出准确的河网模式识别决策,识别精度可达94%。这为实现智能化河网模式识别提供了一种技术途径。

Poisson-Geometric二维风险模型的生存概率

研究一种索赔到达服从复合Poisson-Geometric过程的二维风险模型,得到了该模型的生存概率Laplace变换后所满足的积分微分方程。

Digital watermarking algorithm based on scale-invariant feature regions in non-subsampled contourlet transform domain

Contraposing the need of the robust digital watermark for the copyright protection field, a new digital watermarking algorithm in the non-subsampled contourlet transform （NSCT） domain is proposed. The largest energy sub-band after NSCT is selected to embed watermark. The watermark is embedded into scaleinvariant feature transform （SIFT） regions. During embedding, the initial region is divided into some cirque sub-regions with the same area, and each watermark bit is embedded into one sub-region. Extensive simulation results and comparisons show that the algorithm gets a good trade-off of invisibility, robustness and capacity, thus obtaining good quality of the image while being able to effectively resist common image processing, and geometric and combo attacks, and normalized similarity is almost all reached.

多险种多复合Poisson-Geometric过程的常利率风险模型

建立多险种多复合Poisson-Geometric过程的常利率风险模型,得到该模型的生存概率所满足的积分-微分方程.当无保费收入时,由所得到的积分-微分方程推出生存概率的Laplace变换的表达式,对于初始盈余为0时,得到生存概率的精确解.并给出具体的数值计算的实例以解释我们的结果.

Characteristic Analysis of Underwater Acoustic Scattering Echoes in the Wavelet Transform Domain

Underwater acoustic scattering echoes have time–space structures and are aliasing in time and frequency domains. Different series of echoes properties are not identified when incident angle is unknown. This article investigates variations in target echoes of monostatic sonar to address this problem. The mother wavelet with similar structures has been proposed on the basis of preprocessing signal waveform using matched filter, and the theoretical expressions between delay factor and incident angle are derived in the wavelet domain. Analysis of simulation data and experimental results in free-field pool show that this method can effectively separate geometrical scattering components of target echoes. The time delay estimation obtained from geometrical echoes at a single angle is consistent with target geometrical features, which provides a basis for object recognition without angle information. The findings provide valuable insights for analyzing elastic scattering echoes in actual ocean environment.

Fast Algorithm for Nonsubsampled Contourlet Transform

多尺度的几何分析(MGA ) 为图象处理作为有效策略被认出了。作为 MGA 的分离工具之一， nonsubsampled contourlet 变换(NSCT ) 广泛地被使用了图象降噪，图象熔化，图象改进，特征抽取等等。然而，处理表演由于它的高冗余性被限制，并且导致集中的计算效率。因此，它的快算法在实践被需要。在这份报纸，我们采用一个优化方向性的过滤器银行(DFB ) 并且把它嵌进 NSCT 当使重建的表演的损失细微时，显著地加速计算速度。试验性的结果证明重建的图象质量能满足人的视觉系统。而且，改进 NSCT 有速度关于若干次比传统的的。图象降噪上的试验性的结果也验证建议方法的可行性和效率。

Geometric Computing Based on Computerized Descriptive Geometric

Computer-aided Design （CAD）, video games and other computer graphic related technology evolves substantial processing to geometric elements. A novel geometric computing method is proposed with the integration of descriptive geometry, math and computer algorithm. Firstly, geometric elements in general position are transformed to a special position in new coordinate system. Then a 3D problem is projected to new coordinate planes. Finally, according to 2D/3D correspondence principle in descriptive geometry, the solution is constructed computerized drawing process with ruler and compasses. In order to make this method a regular operation, a two-level pattern is established. Basic Layer is a set algebraic packaged function including about ten Primary Geometric Functions （PGF） and one projection transformation. In Application Layer, a proper coordinate is established and a sequence of PGFs is sought for to get the final results. Examples illustrate the advantages of our method on dimension reduction, regulatory and visual computing and robustness.

带干扰的索赔次数为复合Poisson-Geometric过程的风险模型下的罚金函数

研究了带干扰的索赔次数为复合Poisson-Geometric过程的风险模型,针对此模型,给出了罚金函数满足的积分微分方程,利用Dickson and Hipp(2001)中引入的变换方法,得到了罚金函数的拉普拉斯变换的精确表达式.

The geometric phase of the quantum systems with slow but finite rate of the external time-dependent field

With the help of the time-dependent gauge transformation technique, we have studied the geometric phase of a spin-half particle in a rotating magnetic field. We have found that the slow but finite frequency of the rotating magnetic field will make the difference between the adiabatic geometric phase and the exact geometric phase. When the frequency is much smaller than the energy space and the adiabatic condition is perfectly guaranteed, the adiabatic approximation geometric phase is exactly consistent with the adiabatic geometric phase. A simple relation for the accuracy of the adiabatic approximation is given in terms of the changing rate of the frequency of the rotating magnetic field and the energy level space.

On Geometric Correction Method of BJ-1 Panchromatic Image Covering Kingdom of Lesotho

The purpose is to find a suitable geometric correction method of BJ-1 panchromatic image covering Kingdom of Lesotho.The methods are carrying out two geo-correction experiments based on the push-broom model and the projective transform model for BJ-1 small satellite real panchromatic covering flat and mountain area of Lesotho.Results show that the projective transform model has equal or higher accuracy compared to the push-broom model.Conclusion is the projective transform model can be used in producing land use image map.

Wavelet Transform Modulus Maxima-Based Robust Digital Image Watermarking in Wavelet Domain

A new robust watermarking approach was proposed in 2D continuous wavelet domain （CWT）. The watermark is embedded into the large coefficients in the middle band of wavelet transform modulus maxima （WTMM） of the host image. After possible attacks, the watermark is then detected and extracted by correlation analysis. Compared with other wavelet domain watermarking approaches, the WTMM approach can endow the image with beth rotation and shift invariant properties. On the other hand, scale invariance is achieved with the geometric normalization during watermark detection. Case studies involve various attacks such as shifting, lossy compression, scaling, rotation and median filtering on the watermarked image, and the result shows that the approach is robust to these attacks.

Sumudu Transformation or What Else Can Laplace Transformation Do

The transition from a known Taylor series ?of a known function f(x) to a new function ?primarily defined by the infinite power series ?with coefficients f(n)(0)?from the Taylor series of the function f(x)?can be made by an integral transformation which is a modified Laplace transformation and is called Sumudu transformation. It makes the transition from the Exponential series to the Geometric series and may help to evaluate new infinite power series from known Taylor series. The Sumudu transformation is demonstrated to be a limiting case of Fractional integration. Apart from the basic Sumudu integral transformation we discuss a modification where the coefficients ?from the Taylor series are not changed to f(n)(0)?but only to . Beside simple examples our applications are mainly concerned to calculate new Generating functions for Hermite polynomials from the basic ones.

Geometric Inversion of Two-Dimensional Stokes Flows – Application to the Flow between Parallel Planes

Geometric inversion is applied to two-dimensional Stokes flow in view to find new Stokes flow solutions. The principle of this method and the relations between the reference and inverse fluid velocity fields are presented. They are followed by applications to the flow between two parallel plates induced by a rotating or a translating cylinder. Thus hydrodynamic characteristics of flow around circular bodies obtained by inversion of the plates are thus deduced. Typically fluid flow patterns around two circular cylinders in contact placed in the centre of a rotating or a translating circular cylinder are illustrated.

舵类结构件几何量误差视觉检测方法及误差评定

针对现有接触式测量方法装夹定位后只能测量一种或两种参数、检测效率低等问题,提出一种舵类结构件几何量误差和装配误差视觉检测方法。首先,利用计算机视觉系统获取舵轴和舵面区域图像,利用图像预处理技术去除图像畸变和噪声,为了更有效地提取舵类结构件边缘,分别采用Sobel算子、Scharr算子、Laplace算子和Canny算子对图像进行边缘检测以确定轮廓,实验对比发现Scharr算子处理后的舵轴图像边缘更清晰且无间断,Canny算子处理后的摇臂图像边缘比较清晰,因此选用Scharr算子提取舵轴图像边缘、Canny算子提取摇臂图像边缘。结合被测要素特点,采用霍夫直线和霍夫圆检测方法提取舵面边缘线特征、舵轴母线特征、摇臂圆轮廓特征;确定了舵芯对称度、舵轴垂直度、摇臂夹角的基准要素,构建了几何量误差检测目标函数,运用自适应遗传算法计算最优解;结合相机标定的内外参矩阵,得到舵芯对称度、舵轴垂直度、摇臂夹角的测量值。最后,研发了舵类结构件几何量误差和装配误差视觉检测软件,搭建了视觉检测实验平台,实现了几何量误差及装配角度误差快速检测功能。经过多次重复测量实验,对称度检测精度达到0.055 mm,垂直度检测精度达到0.225 mm,装配角度检测精度达到0.772°,完成单次检测耗时7 s。该方法不仅提高了几何量误差检测精度和检测效率,同时有助于提高舵类结构件成型-制造-在机检测的自动化和智能化水平。

矩阵初等变换的几何意义

矩阵的初等变换在线性代数中应用十分广泛,以初等行变换为例,分别给出了非退化的初等变换、退化的初等变换的实例与对应的几何图形,在此基础上给出了任意角度的旋转.在教学过程中,通过挖掘初等变换的几何意义,可以使学生建立代数与几何的统一观,促进学生抽象思维与形象思维协调发展.

四轴联动机床几何误差建模分析与评估

机床几何误差是影响工件加工精度的主要因素之一,对其进行分析和评估可提高工件加工精度。以一台四轴立式加工中心为研究对象,分析机床几何误差对机床空间精度的影响,并辨识出其中的关键误差项,以提高机床精度补偿的效率。通过D-H齐次坐标变换理论建立机床的几何误差模型;利用拉丁超立方采样和Sobol全局灵敏度分析方法对机床几何误差进行评估,并辨识出关键误差项;最后,通过对比辨识得到的优化模型和原模型,验证了辨识结果的可靠性。因此,可以通过补偿关键误差项来获得较高的机床精度。