基于相机标定的双目三维景物重建方法

介绍了一种基于相机标定的双目静止镜头下的三维景物重建方法.方法假设已经通过相机标定的方法得到两个相机的内外投影矩阵参数,通过投影矩阵和几何的方法,配合图像配准技术,恢复感兴趣场景的深度信息,达到三维景物重建的目的.本方法主要是基于几何变换的方法,巧妙避开了三维投影矩阵的计算,直接从真实图像映射为虚拟极平面图像,可以达到比较好的效果.     

双机拍摄全景视频拼接算法研究

全景视频是一种新型的视频,近年成为研究热点.已有的研究和产品中,全景视频需六个或以上的相机拍摄,设备成本大,拼接时间长.提出一种双机拍摄拼接的算法.通过分析鱼眼图像的坐标系变换,得出了全景视频图像变换矩阵的求解方法,再采用变换矩阵对鱼眼视频图像进行转换,得到全景视频.实验表明文章的全景视频拼接算法拼接效果好,拼接速度快...     

基于平稳Contourlet变换的图像去噪方法

多尺度几何分析中的Contourlet变换可以实现灵活的多分辨、多方向图像表示,但是由于不具有平移不变性,在图像去噪中容易产生伪吉布斯现象,本文应用具有平移不变性且能有效表示图像纹理信息的平稳Contourlet变换,提出了软硬阈值结合的去噪法.试验结果表明该方法有效提高去噪声后图像的PSNR,有效保存图像纹理信息以及更好的视觉效果.     

射影平面的模型和莫比乌斯带

射影几何研究图形在射影变换下的不变性,射影变换可以直观地看成是由连续施行若干次中心投影所得到的变换,为了使中心投影成为两平面的点之间的一一对应,我们必须把通常的欧氏平面加以拓广,添加无穷远点和无穷远直线,即对平面上的一族平行线添加一个无穷远点,且规定平面上所有无穷远点的集合为一条无穷远直线,这和经过拓广以后的平面,若对     

二阶曲线射影仿射分类的合同变换法

二阶曲线的射影(仿射)分类是指:凡在射影(仿射)变换下互为对应的二阶曲线归为一类,分类常用方法是在射影(仿影)平面上选取适当的坐标系化简方程,其中涉及到高等几何的概念较多,分析与解题的过程也较为繁杂。本文避开对坐标三点形的选择,对二阶曲线的系数矩阵施以合同变换,达到分类的目的。     

Beltrami定理的推广

本文研究了Berwald流形之间的射影对应.利用Berwald流形上Weyl射影曲率张量的射影不变性,证明了当n>2时,与射影平坦的Berwald流形射影对应的黎曼流形M~n是常曲率流形,从而推广了Beltrami定理.     

空间有理三次Bezier曲线的射影变换和权系数的几何性质

本文讨论了空间有理三次Ｂｅｚｉｅｒ曲线的射影变换和权系数的一系列几何性质。其权系数组成构成了控制四顶点基下的权心的齐次坐标;权心是六个特殊平面的公共交点。含权心和曲线“肩点”的某四个共线点之比恒为常数３;权心可作为有理曲线所在射影坐标系的单位点;此有理曲线是对应整有理曲线在射影变换下的象,此变换把控制四面体的形心映为权心;权系数是此射影变换的特征值（差－常数因子）;权系数是变换前后两曲线上对应点关     

基于Fourier-Mellin变换的全景图像拼接与曲线匹配

基于Fourier-Mellin变换的图像配准方法,对于图像拼接与曲线匹配进行新探讨.该方法在不需要准确控制相机运动,不需要知道相机的焦距等内部参数及检测图像特征,在配准精度要求不高的情况下,直接生成的全景图像可以满足很多实际需求;先将图像曲线转化为二值图像,然后应用。Fourier-Mellin变换对这些二值图像进行配准,从而达到两条曲线的匹配.     

数码相机系统标定的数学模型

利用RAC两步法和最小二乘法,给出了世界坐标系到相机坐标系的旋转变换矩阵R和平移向量T及径向畸变系数k的算法,通过Matalb编程,提取图像的边缘数字信息,计算了靶标上圆心的像坐标,并讨论了算法的稳定性.     

二次曲线上射影变换是对合的充要条件及对合的变换式

本文研究了二次曲线上射影变换是对合的充要条件 ,同时给出对合的变换式 ,填补了《射影几何》教材中的空白 .本文的主要结论是定理 3、定理 4 .     

利用三角形及其九点圆的摄像机标定

提出基于三角形及其九点圆的摄像机标定方法.利用了三角形九点圆中其九个点的特殊性,并且利用透视投影变换保二次曲线不变性,得到其像点在像平面共椭圆,从而可以通过九点的映射关系将透视投影变换的非线性问题线性化.图像分割和角点提取的误差会直接影响标定的精度,在此三角形及其九点圆中的点特别是算法中的关键点三角形顶点和垂心都是三条直线的交点,减小图像分割与提取时造成的误差.DLT方法的不精确就源于图像分割和角点提取的误差,方法克服了DLT方法的不足.张的方法无法保证单应性矩阵的正交性,因此为了保证正交性和提高精度需要优化.与传统方法相比操作简单,应用九点圆定理,仿射变换的引入将透视投影非线性问题线性化,避免了参数之间的非线性方程求解,降低了参数求解的复杂性,因此其定标过程快捷,准确.模板的构造,减少了图像分割和交点提取误差,算法实现保证旋转矩阵的正交性.综合上述分析,理论上表明方法的有效性.同时实验表明,标定方法操作简单,不需要计算机视觉的专业知识,快速,精度高,鲁棒性好.     

数码相机定位研究

讨论了数码相机的定位问题,假设针孔镜头成像,根据射影几何的理论建立数学模型．首先,对靶标的像图形进行处理,求出其中每个图形的外切点,通过交比不变性和点的共线理论对所求的外切点进行约束从而得到最优的外切点,最后求出各个圆圆心在像平面的坐标．然后,考虑图形在成像过程中发生的“畸变”,通过空间坐标变换把在像平面局部坐标的分析...     

A novel cutting force modelling method for cylindrical end mill

This paper proposes a new and simplified method for the calibration of cutting force coefficients and cutter runout parameters for cylindrical end milling using the instantaneous cutting forces measured instead of average ones. The calibration procedure is derived for a mechanistic cutting force model in which the cutting force coefficients are expressed as the power functions of instantaneous uncut chip thickness (IUCT). The derivations are firstly performed by establishing mathematical relationships between instantaneous cutting forces and IUCT. Then, nonlinear algorithms are proposed to solve the established nonlinear contradiction equations. The typical features of this new calibration method lie in twofold. On the one hand, all derivations are directly based on the tangential, radial and axial cutting force components transformed from the forces which are measured in the workpiece Cartesian coordinate system. This transformation makes the calibration procedure very simple and efficient. On the other hand, only a single cutting test is needed to be performed for calibrating the cutting force coefficients that are valid over a wide range of cutting conditions. The effectiveness of the proposed method in developing cutting force model is demonstrated experimentally with a series of verification cutting tests.     

A new method for solving the eikonal equation in the spherical computing domain

In order to overcome the problem of singularities and nonuniform grids arising when solving eikonal equation in spherical coordinate systems, a spherical Cartesian coordinate system is defined and the Hamiltonian form of the eikonal equation according to this coordinate system is given. A modified velocity function that can transform spherical coordinate system–based eikonal equation into ones based on a spherical Cartesian coordinate system is deduced by using a differential geometric method where a layered distribution of the velocity function is assumed. After comparing the results of using this approach with the traditional method of solving eikonal equation based on a spherical coordinate system, the viability of the transformation to a spherical Cartesian coordinate system based on a modified velocity function is proven. Despite the assumption of a layered distribution of the velocity function, it is also proven that the method will hold for a velocity function under any three-dimensional distribution. The new method overcomes problems present in traditional approaches and opens up a new way of solving eikonal equation in a spherical computational domain.     

Singular limit cycle bifurcations to closed orbits and invariant tori

This paper investigates singular limit cycle bifurcations for a singularly perturbed system. Based on a series of transformations (the modified curvilinear coordinate, blow-up, and near-identity transformation) and bifurcation theory of periodic orbits and invariant tori, the bifurcations of closed orbits and invariant tori near singular limit cycles are discussed.     

A general algorithm for the numerical evaluation of nearly singular integrals on 3D boundary element

A general numerical method is proposed to compute nearly singular integrals arising in the boundary integral equations (BIEs). The method provides a new implementation of the conventional distance transformation technique to make the result stable and accurate no matter where the projection point is located. The distance functions are redefined in two local coordinate systems. A new system denoted as (α,β) is introduced here firstly. Its implementation is simpler than that of the polar system and it also performs efficiently. Then a new distance transformation is developed to remove or weaken the near singularities. To perform integration on irregular elements, an adaptive integration scheme is applied. Numerical examples are presented for both planar and curved surface elements. The results demonstrate that our method can provide accurate results even when the source point is very close to the integration element, and can keep reasonable accuracy on very irregular elements. Furthermore, the accuracy of our method is much less sensitive to the position of the projection point than the conventional method.     

An energy-momentum conserving scheme for Hamiltonian wave equation based on multiquadric trigonometric quasi-interpolation

Based on multiquadric trigonometric quasi-interpolation, the paper proposes a meshless symplectic scheme for Hamiltonian wave equation with periodic boundary conditions. The scheme first discretizes the equation in space using an iterated derivative approximation method based on multiquadric trigonometric quasi-interpolation and then in time with an appropriate symplectic scheme. This in turn yields a finite-dimensional semi-discrete Hamiltonian system whose energy and momentum (approximations of the continuous ones) are invariant with respect to time. The key feature of the scheme is that it conserves both the energy and momentum of the Hamiltonian system for both uniform and scattered centers, while classical energy-momentum conserving schemes are only for uniform centers. Numerical examples provided at the end of the paper show that the scheme is efficient and easy to implement.     

Characteristics of multivariate distributions and the invariant coordinate system

We consider a semiparametric multivariate location–scatter model where the standardized random vector of the model is fixed using simultaneously two location vectors and two scatter matrices. The approach using location and scatter functionals based on the first four moments serves as our main example. The four functionals yield in a natural way the corresponding skewness, kurtosis and unmixing matrix functionals. Affine transformation based on the unmixing matrix transforms the variable to an invariant coordinate system. The limiting properties of the skewness, kurtosis, and unmixing matrix estimates are derived under general conditions. We discuss related statistical inference problems, the role of the sample statistics in testing for normality and ellipticity, and connections to invariant coordinate selection and independent component analysis.