超Grassmannian流形上的超Plücker映射

■表示■-维向量空间中的■-维子空间构成的超Grassmannian流形。本文研究超Grassmannian流形上的超Plücker映射,刻画了■和■上的超Plücker映射的齐次坐标矩阵。

基于Plücker直线的LiDAR点云配准法

高精度的LiDAR点云配准是实现点云数据整体性和保证空间目标三维表面拓扑重建的关键,本文提出了基于Plücker直线的LiDAR点云配准模型,利用Plücker直线表示LiDAR待配准点云与基准点云间的同名直线,根据同名Plücker直线重合的几何拓扑关系,建立Plücker直线共线条件方程,再用最小二乘法确定待配准LiDAR点云与基准点云间的相对位姿参数。结果表明,Plücker直线共线条件配准模型几何约束性较强,配准精度较高。

基于Plücker直线的机载LiDAR点云与航空影像的配准

机载LiDAR点云与航空影像的配准是地物提取的关键。本文提出了基于Plücker直线的机载LiDAR点云与航空影像的配准模型。基于三维线空间线变换Plücker直线方程,确定点云和影像中的同名直线间的相对位姿关系,建立Plücker直线共面条件方程,通过影像上的Plücker直线在三维线空间中的螺旋运动,实现像点到其对应LiDAR点的坐标变换。结果表明,Plücker直线共面条件配准模型简洁,将旋转和平移统一处理,避免了两者间的耦合误差,提高了配准精度,为获取高质量的地球三维空间信息提供了技术支持。

利用Plücker直线的点云与立体影像配准

现有的基于直线特征的点云与立体影像配准未充分利用直线的几何拓扑关系,针对几何约束强度弱的问题,提出一种基于Plücker直线的配准方法.将点云与立体影像的同名直线用Plücker坐标表示,分别以立体影像的Plücker直线与摄影中心组成的平面作为基本单元,通过同名平面的连续螺旋运动,使同名平面相交于控制直线,构建Plücker直线共面条件方程.实验结果表明,该方法简洁明了,几何约束性强,配准精度高.

基于Plücker坐标的秘密共享方案(英文)

基于 Plücker坐标这一数学中的重要概念,提出一个构造门限秘密共享方案的新方法.该方案不仅是安全的,并且几个著名的线性秘密共享方案都能够由Plücker坐标表示.

Calibration method for multi-line structured light vision sensor based on Plücker line

For the rapid calibration of multi-line structured light system,a method based on Plücker line was proposed.Most of the conventional line-structured light calibration methods extract the feature points and transform the coordinates of points to obtain the plane equation.However,a large number of points lead to complicated operation which is not suitable for the application scenarios of multi-line structured light.To solve this issue,a new calibration method was proposed that applied the form of Plücker matrix throughout the whole calibration process,instead of using the point characteristics directly.The advantage of this method is that the light plane equation can be obtained quickly and accurately in the camera coordinate frame.Correspondingly a planar target particularly for calibrating multi-line structured light was also designed.The regular lines were transformed into Plücker lines by extending the two-dimensional image plane and defining a new image space.To transform the coordinate frame of Plücker lines,the perspective projection mathematical model was re-expressed based on the Plücker matrix.According to the properties of the line and plane in the Plücker space,a linear matrix equation was efficiently constructed by combining the Plücker matrices of several coplanar lines so that the line-structured light plane equation could be furtherly solved.The experiments performed validate the proposed method and demonstrate the significant improvement in the calibration accuracy,when the test distance is 1.8 m,the root mean square(RMS)error of the three-dimensional point is within 0.08 mm.

Plücker Coordinate System of Screws and the Study of Generating Gears

After an introductiou of the Plucker coordinate geometry, a discussion is made of the expression of screws in Plucker coordiuates and the addition of screws’ As a result, the geometry or geuerating gears is re-studied and a formula is derived for calculating the axode leugth or hypoid gears’

直线特征约束下利用Plücker坐标描述的LiDAR点云无初值配准方法

经典的基于点状特征匹配的地面激光雷达（light detection and ranging,LiDAR）点云配准算法实现过程中,点状特征的提取精度对算法运行结果的影响通常较大;基于迭代运算的LiDAR点云配准算法计算量大,对未知参数的初值依赖程度较高,在求解大转角刚体变换参数时算法不稳定。对此,提出了一种线状特征约束下基于Plücker直线坐标描述的LiDAR点云配准算法。立足于经典的向量代数与对偶四元数的相关理论与方法,分析并确定了Plücker直线坐标与对偶四元数之间的相互转换关系以及模型描述方法;以LiDAR点云配准前后同名线状特征的Plücker直线坐标相等为约束条件,构建了线状特征约束下基于Plücker直线坐标描述的刚体变换模型;立足于最小二乘基本准则,通过目标函数的极值化分析实现了线状特征约束下地面LiDAR点云配准参数的直接求解。实验结果表明,所构建的基于Plücker直线坐标描述的地面LiDAR点云配准模型,无需事先确定变换参数的初值,避免了多元函数的线性化过程,解除了参数结果对于迭代初值的依赖,理论上克服了迭代法在求解大转角相似变换参数时的算法不稳定问题。此外,较之单纯基于点状特征匹配的LiDAR点云配准算法,该算法可以有效地增强LiDAR点云配准过程的约束,达到提高配准质量的目的。

A Line Complex-Based Evolutionary Algorithm for Many-Objective Optimization

In solving many-objective optimization problems(MaO Ps),existing nondominated sorting-based multi-objective evolutionary algorithms suffer from the fast loss of selection pressure.Most candidate solutions become nondominated during the evolutionary process,thus leading to the failure of producing offspring toward Pareto-optimal front with diversity.Can we find a more effective way to select nondominated solutions and resolve this issue?To answer this critical question,this work proposes to evolve solutions through line complex rather than solution points in Euclidean space.First,Plücker coordinates are used to project solution points to line complex composed of position vectors and momentum ones.Besides position vectors of the solution points,momentum vectors are used to extend the comparability of nondominated solutions and enhance selection pressure.Then,a new distance function designed for high-dimensional space is proposed to replace Euclidean distance as a more effective distancebased estimator.Based on them,a novel many-objective evolutionary algorithm(MaOEA)is proposed by integrating a line complex-based environmental selection strategy into the NSGAⅢframework.The proposed algorithm is compared with the state of the art on widely used benchmark problems with up to 15 objectives.Experimental results demonstrate its superior competitiveness in solving MaOPs.

一个新的基于Plcker坐标的门限方案(英文)

给出了构造秘密共享方案的一般框架 ,同时给出了一个结构简单。

Closed form of the inverse Plücker correspondence in line geometry

By mapping the homogeneous coordinates of two points in space to the Plücker coordinates of the line they determine, any transformation of type SL(4) upon points in space is mapped to a transformation of type SO0(3, 3), the latter being the connected component containing the identity of the special orthogonal transformation group of the linear space spanned by Plücker coordinates. This is the classical Plücker correspondence, two-to-one and onto. It has important applications in line geometry and projective transformations.While the explicit form of Plücker correspondence is trivial to present, its inverse in explicit form, which is also important in application, is not found in the literature. In this paper, we present a simple and unified formula for the inverse of the Plücker correspondence.

Crum定理的一个新证明(英文)

导出了新的Plücker关系式,利用Wronskian技巧和Plücker关系式证明著名的Crum定理.给出了Crum定理一个新的简洁证明.在附录中证明了三个plücker关系式.

考虑重投影尺度因子的特征直线三维重建

文章首先用Plücker坐标表示3D直线;然后用重投影几何误差作为线特征三角法的目标函数,实现算法的最大似然估计;最后用线性和非线性两种方法分别实现空间直线的重建。在重投影时,考虑了每条直线投影时的尺度因子λ,提高了重建精度。真实图像和仿真数据的实验结果表明,该方法能够准确有效地实现直线三维重建。

基于图优化的单目线特征SLAM算法

提出了基于图优化的单目线特征同时定位和地图构建(SLAM)的方法.首先,针对主流视觉SLAM算法因采用点作为特征而导致构建的点云地图稀疏、难以准确表达环境结构信息等缺点,采用直线作为特征来构建地图.然后,根据现有线特征的SLAM算法都是基于滤波器的SLAM框架、存在线性化及更新效率的问题,采用基于图优化的SLAM解决方案以提高定位精度及地图构建的一致性和准确性.将线特征的Plücker坐标和Cayley参数化方式相结合,一方面采用Plücker坐标便于线性投影计算,另一方面采用Cayley参数化方式有利于线特征参数的非线性优化.仿真实验结果显示:所提出算法的位姿估计误差平方和与均方根误差分别是里程计位姿估计的2.5%和10.5%,是基于EKF线特征SLAM算法估计位姿误差的22.4%和33%,重投影误差仅为45.5像素;实际图像实验中的位姿估计误差平方和为958 cm^2,均方根误差为3.9413 cm,从而证明了所提出算法的有效性和准确性.

螺旋定理在曲柄摇杆机构中的应用研究

理清现有机构的演化脉络是归纳机构创新方法的重要途径之一,但机构演化的脉络在目前主要还是停留在图、文等定性描述的层面上,因此,为提升到精确、定量的层面上,可以把最原始、最典型的曲柄摇杆机构到曲柄滑块机构的演化过程作为研究对象。依据螺旋定理,得出四杆机构转动副与移动副的Plücker坐标表达式,并在此基础上基于对偶矩阵,以矩阵的形式定量地阐述曲柄摇杆机构向曲柄滑块机构的演化过程。这既有助于对机构演化脉络的认识从定性层面提升到定量层面,又为机构的演化脉络、创新方法的研究提供了一种新的路径,同时,也为计算机提供了分析并演绎机构演化过程的新手段。

MOTOR METHOD OF ROBOT END EFFECTOR PATH GENERATION

According to the theory that rotation transformation from the basecoordinate to an arbitrary one can be described by a single equivalent rotation about agiven rotational axis,it is proposed that the orientation of robot can be described by usingthe vector of equivalent angular displacement.And the concept of pose motor and itsPlücker linear coordinate are established and used to describe the position and orientationof robot.Based on the fact that there is a one-to-one correspondence between the ori-ented straight lines in three-dimensional dual space,the interpolation plannings corre-sponding to the pose motors are developed in dual space.A new algorithm of robot CPmotion trajectory planning is presented.The correctness of the theory and derivation isconformed by an example.

The Pfaffian Technique: A (2 + 1)-Dimensional Korteweg de Vries Equation

The (2 + 1)-dimensional Korteweg de Vries (KdV) equation, which was first derived by Boiti et al., has been studied by various distinct methods. It is known that this (2 + 1)-dimensional KdV equation has rich solutions, such as multi-soliton solutions and dromion solutions. In the present article, a unified representation of its N-soliton solution is given by means of pfaffian. We’ll show that this (2 + 1)-dimensional KdV equation is nothing but the Plücker identity when its &#964-function is given by pfaffian.

New Mathematical Tools for the Study of the DNA Structure

We propose a number of new mathematical tools for the study of the DNA structure. In particular, we establish a connection between the DNA molecule and the Grassmann-Plücker coordinates, which, in both in mathematics and physics, are of great importance.

基于点线结合特征的单目视觉里程计

SLAM(即时定位与地图构建)系统是近年来计算机视觉领域的一大重要课题,其中特征法的SLAM凭借稳定性好、计算效率高的优点成为SLAM算法的主流。目前特征法SLAM主要基于点特征进行。针对基于点特征的视觉里程计依赖于数据质量,相机运动过快时容易跟丢,且生成的特征地图不包含场景结构信息等缺点,提出了一种基于点线结合特征的优化算法。相较于传统基于线段端点的六参数表达方式,算法采用一种四参数的方式表示空间直线,并使用点线特征进行联合图优化估计相机位姿。使用公开数据集和自采集鱼眼影像数据分别进行实验的结果表明,与仅使用点特征的方法相比,该方法可有效改善因相机运动过快产生的跟丢问题,增加轨迹长度,提升位姿估计精度,且生成的稀疏特征地图更能反映场景结构特征。

一种高精度线结构光视觉传感器现场标定方法

针对现有线结构光视觉传感器标定方法存在的局限性,提出一种不需要求解光平面标定点的标定方法。根据光条图像求解平面靶标上光条在摄像机坐标系下的Plücker矩阵。在视觉传感器前合适位置将平面靶标摆放多次,联立所有光条空间直线的Plücker矩阵,求解光平面在摄像机坐标系的平面方程。最后通过非线性优化方法得到光平面方程在最大似然准则下的最优解。在标定过程中,所有光条点都参与光平面参数的计算过程,因此该方法标定结果精度高、稳健性强。实验证明,与现有方法相比该方法标定精度提高30%左右。