High-precision automatic measurement of two-dimensional geometric features based on machine vision

To realize high-precision automatic measurement of two-dimensional geometric features on parts, a cooperative measurement system based on machine vision is constructed. Its hardware structure, functional composition and working principle are introduced. The mapping relationship between the feature image coordinates and the measuring space coordinates is established. The method of measuring path planning of small field of view （FOV） images is proposed. With the cooperation of the panoramic image of the object to be measured, the small FOV images with high object plane resolution are acquired automatically. Then, the auxiliary measuring characteristics are constructed and the parameters of the features to be measured are automatically extracted. Experimental results show that the absolute value of relative error is less than 0. 03% when applying the cooperative measurement system to gauge the hole distance of 100 mm nominal size. When the object plane resolving power of the small FOV images is 16 times that of the large FOV image, the measurement accuracy of small FOV images is improved by 14 times compared with the large FOV image. It is suitable for high-precision automatic measurement of two-dimensional complex geometric features distributed on large scale parts.

SOLVING THE PROPAGATION OF ELECTROMAGNETIC WAVE IN A SIMPLE TWO-DIMENSIONALINHOMOGENEOUS MEDIUM BASED ON SYMPLECTIC GEOMETRICAL THEORY

A new symplectic geometrical high-frequency approximation method for solving the propagation of electromagnetic wave in the two-dimensional inhomogeneous medium is used in this paper. The propagating caustic problem of electromagnetic wave is translated into non-caustic problem by the coordinate transform on the symplectic space. The high-frequency approximation solution that includes the caustic region is obtained with the method combining with the geometrical optics. The drawback that the solution in the caustic region can not be obtained with geometrical optics is overcome by this method. The results coincide well with that of finite element method.

A General Representation of Geometrical Solution Model for Predicting Ternary Thermodynamic Properties

The existing geometrical solution models for predicting ternary thermodynamic properties from relevant binary ones have been analysed,and a general representation was proposed in an integral form on the bases of these models.

Numerical Convergence of the Sinc Discrete Variable Representation for Solving Molecular Vibrational States with a Conical Intersection in Adiabatic Representation

Within the Born-Oppenheimer(BO)approximation,nuclear motions of a molecule are often envisioned to occur on an adiabatic potential energy surface(PES).However,this single PES picture should be reconsidered if a conical intersection(CI)is present,although the energy is well below the CI.The presence of the CI results in two additional terms in the nuclear Hamiltonian in the adiabatic presentation,i.e.,the diagonal BO correction(DBOC)and the geometric phase(GP),which are divergent at the CI.At the same time,there are cusps in the adiabatic PESs.Thus usually it is regarded that there is numerical difficulty in a quantum dynamics calculation for treating CI in the adiabatic representation.A popular numerical method in nuclear quantum dynamics calculations is the Sinc discrete variable representation(DVR)method.We examine the numerical accuracy of the Sinc DVR method for solving the Schrodinger equation of a two dimensional model of two electronic states with a CI in both the adiabatic and diabatic representation.The results suggest that the Sinc DVR method is capable of giving reliable results in the adiabatic representation with usual density of the grid points,without special treatment of the divergence of the DBOC and the GP.The numerical uncertainty is not worse than that after the introduction of an arbitrary vector potential for accounting the GP,whose accurate form usually is not easy to obtain.

Atomic coherent states as energy eigenstates of a Hamiltonian describing a two-dimensional anisotropic harmonic potential in a uniform magnetic field

In this paper we find that a set of energy eigenstates of a two-dimensional anisotropic harmonic potential in a uniform magnetic field is classified as the atomic coherent states ｜τ） in terms of the spin values of j in the Schwinger bosonic realization. The correctness of the above conclusions can be verified by virtue of the entangled state 〈η｜ representation of the state ｜τ）.

A Geometric Approach to Conditioning and the Search for Minimum Variance Unbiased Estimators

Our purpose is twofold: to present a prototypical example of the conditioning technique to obtain the best estimator of a parameter and to show that this technique resides in the structure of an inner product space. The technique uses conditioning of an unbiased estimator on a sufficient statistic. This procedure is founded upon the conditional variance formula, which leads to an inner product space and a geometric interpretation. The example clearly illustrates the dependence on the sampling methodology. These advantages show the power and centrality of this process.

Unsupervised Feature Selection Using Structured Self-Representation

Unsupervised feature selection has become an important and challenging problem faced with vast amounts of unlabeled and high-dimension data in machine learning. We propose a novel unsupervised feature selection method using Structured Self-Representation( SSR) by simultaneously taking into account the selfrepresentation property and local geometrical structure of features. Concretely,according to the inherent selfrepresentation property of features,the most representative features can be selected. Mean while,to obtain more accurate results,we explore local geometrical structure to constrain the representation coefficients to be close to each other if the features are close to each other. Furthermore,an efficient algorithm is presented for optimizing the objective function. Finally,experiments on the synthetic dataset and six benchmark real-world datasets,including biomedical data,letter recognition digit data and face image data,demonstrate the encouraging performance of the proposed algorithm compared with state-of-the-art algorithms.

EVALUATION OF SINGULAR AND NEARLY SINGULAR INTEGRALS IN THE BEM WITH EXACT GEOMETRICAL REPRESENTATION＊

The geometries of many problems of practical interest are created from circular or ellip- tic arcs. Arc boundary elements can represent these boundaries exactly, and consequently, errors caused by representing such geometries using polynomial shape functions can be removed. To fully utilize the geometry of circular boundary, the non-singular boundary integral equations （BIEs） and a general nonlinear transformation technique available for arc elements are introduced to remove or damp out the singular or nearly singular proper- ties of the integral kernels. Several benchmark 2D elastostatic problems demonstrate that the present algorithm can effectively handle singular and nearly singular integrals occur- ring in the boundary element method （BEM） for boundary layer effect and thin-walled structural problems. Owing to the employment of exact geometrical representation, only a small number of elements need to be divided along the boundary and high accuracy can be achieved without increasing other more computational efforts.

A general framework for progressive point-sampled geometry

Recently unstructured dense point sets have become a new representation of geometric shapes. In this paper we introduce a novel framework within which several usable error metrics are analyzed and the most basic properties of the pro- gressive point-sampled geometry are characterized. Another distinct feature of the proposed framework is its compatibility with most previously proposed surface inference engines. Given the proposed framework, the performances of four representative well-reputed engines are studied and compared.

Majorana's stellar representation for the quantum geometric tensor of symmetric states

Majorana's stellar representation provides an intuitive picture in which quantum states in highdimensional Hilbert space can be observed using the trajectory of Majorana stars.We consider the Majorana's stellar representation of the quantum geometric tensor for a spin state up to spin-3/2.The real and imaginary parts of the quantum geometric tensor,corresponding to the quantum metric tensor and Berry curvature,are therefore obtained in terms of the Majorana stars.Moreover,we work out the expressions of quantum geometric tensor for arbitrary spin in some important cases.Our results will benefit the comprehension of the quantum geometric tensor and provide interesting relations between the quantum geometric tensor and Majorana's stars.

An Integral Representation for the Weighted Geometric Mean and Its Applications

By virtue of Cauchy’s integral formula in the theory of complex functions,the authors establish an integral representation for the weighted geometric mean,apply this newly established integral representation to show that the weighted geometric mean is a complete Bernstein function,and find a new proof of the well-known weighted arithmetic-geometric mean inequality.

Multifunctional application of nonlinear metamaterial with two-dimensional bandgap

Mechanical metamaterials with low-frequency and broadband bandgaps have great potential for elastic wave control.Inspired by the ancient window mullions,a novel plate-type metamaterial with a two-dimensional bandgap is designed.Based on the local resonance mechanism,the broadband low-frequency in-plane and out-of-plane bandgaps on the designed structure are realized.The bandgaps can be adjusted by the mass re-distribution of the main-slave resonators,the stiffness design of the support beam,and the adjustment of the excitation amplitude.A semi-analytical method is proposed to calculate the in-plane and out-of-plane bandgaps and the corresponding wave attenuation characteristics of the infinite periodic metamaterial.We explored how mass re-distribution,stiffness changes,and geometric nonlinearity influence the bandgap.Then,to verify the conclusions,we fabricated a finite periodic structure and obtained its wave transmission characteristics both numerically and experimentally.Finally,the designed metamaterial is applied to the waveguide control,elastic wave imaging,and vibration isolation.This study may provide new ideas for structural design and engineering applications of mechanical metamaterials.

On Geometric Realization of the General Manakov System

It is well-known that the general Manakov system is a 2-components nonlinear Schrodinger equation with 4 nonzero real parameters.The analytic property of the general Manakov system has been well-understood though it looks complicated.This paper devotes to exploring geometric properties of this system via the prescribed curvature representation in the category of Yang-Mills’theory.Three models of moving curves evolving in the symmetric Lie algebras u(2,1)=k_(α)⊕m_(α)(α=1,2)and u(3)=k_(3)⊕m_(3)are shown to be simultaneously the geometric realization of the general Manakov system.This reflects a new phenomenon in geometric realization of a partial differential equation/system.

Neural 3D reconstruction from sparse views using geometric priors

Sparse view 3D reconstruction has attracted increasing attention with the development of neural implicit 3D representation.Existing methods usually only make use of 2D views,requiring a dense set of input views for accurate 3D reconstruction.In this paper,we show that accurate 3D reconstruction can be achieved by incorporating geometric priors into neural implicit 3D reconstruction.Our method adopts the signed distance function as the 3D representation,and learns a generalizable 3D surface reconstruction model from sparse views.Specifically,we build a more effective and sparse feature volume from the input views by using corresponding depth maps,which can be provided by depth sensors or directly predicted from the input views.We recover better geometric details by imposing both depth and surface normal constraints in addition to the color loss when training the neural implicit 3D representation.Experiments demonstrate that our method both outperforms state-of-the-art approaches,and achieves good generalizability.

体积保持的多分辨率多边形网格的光顺造型

给出了一个高效的多边形网格的多分辨率光顺造型算法 .该算法首先通过引入体积保持约束 ,快速地实现稠密多边形网格的多分辨率表示 .然后结合一个有效的无收缩光顺算法 ,对网格执行高效的多分辨率光顺编辑 .与传统编辑方法不同 ,该方法利用体积保持约束及优化技术 ,来自动恢复编辑区域中相应的细节 ,而无需引入非常损耗资源的局部标架 .实验结果表明 ,该算法计算稳定、高效 ,能产生复杂的模型 .

3D多尺度几何分析研究进展

3D多尺度几何分析是图像、视频和几何模型等数字可视媒体处理的技术基础,其目的在于高效地表示这些媒体中存在的点、线、面奇异.为此,依据不同变换捕获奇异的能力演进及其非线性逼近效率的提高,从2D图像多尺度几何分析的研究进展切入,着重阐述视频3D多尺度几何分析的发展,并将其归纳为3类:由2D基函数直接扩展的3D多尺度几何分析、基于3D基函数的3D多尺度几何分析和基于时空非局部相关性的3D多尺度几何分析,深入探讨了各种典型变换方法的主要思想、非线性逼近效率、计算复杂度、优势和不足.同时,概要介绍了数字几何模型的3D多尺度几何分析研究进展.在此基础上,对3D多尺度几何分析的未来发展趋势进行了展望.

Ground-roll separation of seismic data based on morphological component analysis in twodimensional domain

Ground roll is an interference wave that severely degrades the signal-to-noise ratio of seismic data and affects its subsequent processing and interpretation.In this study,according to differences in morphological characteristics between ground roll and reflected waves,we use morphological component analysis based on two-dimensional dictionaries to separate ground roll and reflected waves.Because ground roll is characterized by lowfrequency,low-velocity,and dispersion,we select two-dimensional undecimated discrete wavelet transform as a sparse representation dictionary of ground roll.Because of a strong local correlation of the reflected wave,we select two-dimensional local discrete cosine transform as the sparse representation dictionary of reflected waves.A sparse representation model of seismic data is constructed based on a two-dimensional joint dictionary then a block coordinate relaxation algorithm is used to solve the model and decompose seismic record into reflected wave part and ground roll part.The good effects for the synthetic seismic data and application of real seismic data indicate that when using the model,strong-energy ground roll is considerably suppressed and the waveform of the reflected wave is effectively protected.

基于Gabor感知多成份字典的图像稀疏表示算法研究

如何设计合适的能够匹配各层面几何结构的图像稀疏表示过完备字典,进而形成对图像的稀疏分解是当前研究者关注的热点问题.根据图像的几何结构特性,从人类视觉系统特性出发,建立了匹配各层面图像结构的Gabor感知多成份字典,进而提出一种高效的基于匹配追踪的图像稀疏分解算法.实验结果表明:Gabor感知多成份字典具有对图像中平滑、边缘与纹理结构的自适应性,与Anisotropic refinement-Gaussian(AR-Gauss)混合字典相比以较少的原子实现了对图像更为高效的稀疏分解.

基于几何公差描述逻辑的公差类型的自动生成

为了使公差信息更好地被计算机理解,将描述逻辑引入到对公差设计的研究中。从几何要素之间的基本空间关系出发,提出几何公差描述逻辑GTDL(Df),并给出该逻辑的Tableau判定算法。应用GTDL(Df)的刻画能力,构建几何公差的GTDL(Df)表示模型;在此基础上,借助GTDL(Df)的Tableau判定算法,设计公差类型的自动生成算法。通过工程实例验证了生成算法的有效性。

基于最优匹配的三维CAD模型相似性评价算法

提出一种基于最优匹配的三维计算机辅助设计模型相似性评价算法。根据三维计算机辅助设计模型的边界表示,将相比较的两个计算机辅助设计模型拆分成面,并分别对面进行分类。将两模型中同种类型的面两两匹配,运用相应的准则计算出每对面的相似性系数iδj,从而使同种类型的面形成了一个二分图。利用图论中二分图的最优匹配算法,计算出两个模型同类型面中各面的最优匹配方案,并计算出加权最优匹配值,最后将各种类型面的最优匹配值相加得到模型的相似系数,以此作为评价模型相似性的依据。为恰当地评价两个类型相同面的相似性,给出了能够综合反映面几何特征和拓扑特征的评价准则。试验表明本方法能够客观地反映两计算机辅助设计模型的相似程度,并较好地反映人视觉上的相似经验。