基于弦中点Hough变换的同心圆检测方法

给出了一种基于Hough变换的同心圆检测方法,其核心思想是降低经典Hough变换圆检测中的Hough累积维数,将经典Hough变换圆检测时的三维参量统计,转变成基于弦中点的圆心和半径的参量统计。根据圆上所有点的内切圆必经过圆中心的事实,提取黑白边缘图像来建立二维数组累加器,依照像素点分布扫描边缘图像,累加器计数,计算出圆心位置,对每个圆心进行半径累积,确定同心圆半径集。与经典的Hough变换检测方法相比,该方法降低了计算复杂度。     

一维概率Hough变换的实时鲁棒多圆检测方法

针对现有圆检测算法以像素为投票主体在二维或三维空间进行参数累积,运算复杂度高,难以达到复杂自然场景中的实时检测要求的问题,提出一种以线段为投票主体并基于一维概率Hough变换的实时圆检测算法.首先基于梯度方向对Canny边缘像素实施逐段分割,从中选取满足一定曲率条件的线段作为种子,对每个种子沿半径进行一维概率Hough累积;然后根据峰值大小和位置提取有效圆及其初始半径;最后利用圆的直接最小二乘拟合进一步定位圆半径和圆心.对复杂的自然场景图像进行实验的结果表明,通过选取合适的分割阈值,该算法在确保圆检测可靠性的前提下在速度上显著优于现有算法.     

基于Zernike矩的字符特征归一化方法

提取Zernike矩的幅值作为字符的模式特征具有旋转不变性,但单位圆半径的选择对特征计算影响较大。本文提出一种根据字符外部边框信息计算最佳单位圆半径的归一化方法。经实验证明该方法能保证单位圆合适地把整个字符包含在内,同时由于单位圆半径不变使数字图像离散化对Zernike矩旋转不变性的影响降到最低。     

基于类圆目标归一化的木材切面轮廓检测方法

在材积检测系统中,对木材切面轮廓精确检测是一大难点,该文采用首先局部二值化图像,并且寻找切面最大内接圆初步确定切面中心以及类圆半径,然后将类圆切面归一化为矩形,在矩形上根据灰度信息寻找切面轮廓边缘点,通过归一化后的边缘计算原图木材切面边缘。实验结果表明,该方法能够精确检测木材切面任意轮廓,在实时性要求不高的情况下相比用圆或椭圆检测的传统算法在精度上有显著提高。     

圆及椭圆链码的识别

提出一个识别圆链码的算法。首先根据链码计算假设圆的半径及起点。然后从起点开始逐点检测由链码指示的每一点到圆心的距离是否等于半径，以决定是否是圆链码。该算法稍加改动之后又可用于椭圆链码的识别。     

一种新的压裂支撑剂圆度球度测定方法

圆度和球度是压裂支撑剂的两个重要质量指标,直接影响着压裂支撑剂能否实际应用.为了提高支撑剂的圆度和球度测定效率,提出了基于分形理论和形状上下文方法的压裂支撑剂圆度球度测定算法.第一,在显微镜成像方法得到的压裂支撑剂图像基础上进行预处理;第二,利用边缘检测技术检测出图像中所有的支撑剂颗粒边缘;第三,利用形状上下文方法对所有检测到的支撑剂颗粒边缘进行处理,得到每个支撑剂颗粒的半径—角度分布曲线,根据曲线的变化确定每个颗粒的球度;第四,利用分形理论确定每个支撑剂颗粒边缘的分形维度,根据分形维度确定每个颗粒的圆度.通过实际的压裂支撑剂颗粒测定实验发现,提出的算法求得的颗粒圆度和球度值与依据模板对比得到的圆度和球度值基本吻合,为实现压裂支撑剂质量评定的自动化奠定了基础.     

改进的随机圆检测算法

介绍了一种基于随机圆检测的改进算法。解决了随机圆检测算法随机采样阶段引入的大量无效累积和验证阶段假设圆之外的边缘点所进行的无效计算的问题,首先对边缘图像进行8邻接连通,3个随机采样点在同一个连通曲线内选择,然后利用圆的性质求得圆的参数,再应用证据收集过程来进一步验证圆的真实性,该验证过程中只考虑假设圆的外切正方形和内接正方形之间的边缘点。实验结果表明,该算法计算量小,对比改进前,检测性能有所提高,且鲁棒性也相应提高,同时能够检测圆弧和有相互重叠的多个圆。     

改进的Hough变换检测圆方法

计算机视觉目前已经得到广泛的应用, 通过图像检测圆在工程应用中具有重要的意义. 为了在实时系统中自动检测图像中的圆并且精确得到圆心和半径, 提出了一种改进的Hough变换检测圆的方法. 先对图像边界进行过滤, 得到连续边界, 然后对每条连续边界进行排序并等分, 选择三点进行圆心和半径计算, 将传统Hough变换检测圆的三维参数降到一维参数来统计, 在降低了计算时间和内存资源占用的同时, 提高了检测圆的准确性. 实验表明, 该方法能够满足实际检测的需要. 同时, 在检测时间上, 可以满足实时性的要求.     

基于导数法的变电站接地网方向检测

为了测量接地网的拓扑结构，必须对接地网方向进行准确的检测。为此提出了一种用于高压变电站接地网方向检测的导数方法。当电流通过垂直导线注入电网时，磁通密度的分布垂直于地球表面。通过对垂直导线定心圆进行三阶求导，增加曲线的切线斜率来减小峰宽，克服了峰宽较大造成的假峰现象，精确地得到了与接地导线方向相吻合的主峰，从而运用接地支路方向相对应的峰值完成方向检测。利用Comsol Multiphysics 5.0进行仿真，结果表明，该方法计算接地网方向精度高，并且峰宽与圆半径成反比关系，增大圆半径可以进一步精确接地网方向的检测。     

基于改进Hough变换的电梯轿厢内人数统计算法

考虑电梯轿厢内人数的电梯群控调度算法,可以在有限的时间内,找到更优解,对电梯的调度具有重要意义。针对目前基于视觉的人数统计算法正确率不够稳定,速度较慢的问题,提出了一种基于改进Hough变换检测人头轮廓的电梯轿厢内人数统计算法。该算法将标准Hough变换检测圆时的三维空间转换为一维空间,利用圆的几何特性遍历图像数据,通过一维Hough变换进行半径累积,并和阈值进行比较来确定人头轮廓的半径和圆心。结果表明,和用Hough变换检测人头轮廓的传统方法相比,该算法具有速度快,正确率高,抗噪性能好等优点。     

椭圆抛物面/球面求交算法

基于广义特征多项式给出了判断椭圆抛物面与球面是否有交的方法,在有交的条件下,得到了交线为圆的条件以及圆心、半径和法向量等重要几何参数,确保了交线的准确绘制。以平行圆族为基础进行坐标变换,在新坐标系下将椭圆抛物面的一个参数方程代入球面的方程中,得到一个一元四次方程,由方程根的分布情况确定交线的拓扑结构,在每一个有交子区间上,给出所有交曲线段的参数方程。给出了几个具体的实例进行说明。     

Modelling and animation of generalized cylinders with variable radius offset space curves

A method is presented for the modelling and animation of generalized cylinders with variable radius offset space curves. The boundary surface of a generalized cylinder is constructed: either as a translational sweep of cross-sectional curves along the skeleton curve, or as a rotational sweep of profile curves around the skeleton curve. The cross-sectional curves are computed as the variable radius offset curves of a circle in the normal plane, and the profile curves are computed as the variable radius offset space curves of the skeleton curve. The offset curves are approximated by spline curves, and the boundary surface of a generalized cylinder is approximated by the tensor product surface patches of the offset spline curves.     

Computing the minimum distance between a point and a NURBS curve

A new method is presented for computing the minimum distance between a point and a NURBS curve. It utilizes a circular clipping technique to eliminate the curve parts outside a circle with the test point as its center point. The radius of the elimination circle becomes smaller and smaller during the subdivision process. A simple condition for terminating the subdivision process is provided, which leads to very few subdivision steps in the new method. Examples are shown to illustrate the efficiency and robustness of the new method.     

基于圆盘近似的动态场景柔和阴影实时绘制

采用圆盘对物体表面进行近似,对每个圆盘形成的遮挡使用椭圆遮挡域表示,预计算过程中根据每个椭圆遮挡域参数进行采样并用球面调和系数表示,同时将其转换为对数,对采样数据采用主元分析方法进行压缩;在绘制的过程中,根据圆盘的法线、半径以及和阴影接收点之间的相对位置确定其椭圆遮挡域的值,然后采用球面调和指数算法进行累积.该方法将圆盘近似算法和球面调和指数算法相结合,能够灵活地描述柔性物体以及较薄的物体形成的柔和阴影.     

求一个包含点集所有点的最小圆的算法

提出一种算法,以解决求一个最小圆包含给定点集所有点的问题.证明了这种算法的时间复杂性为O(|lg(d/R)|*n),其中R是所求的最小圆的半径,d为点集中不在圆周上但距圆周最近的点到圆周的距离.     

可变半径Alpha Shapes提取机载LiDAR点云建筑物轮廓

目的 机载激光雷达（light detection and ranging,LiDAR）能够快速获取建筑物表面的3维点云,为提取建筑物轮廓提供重要的数据支撑,但由于激光脚点的随机性和点云自身的离散性,常规固定半径Alpha Shapes（A-Shapes）算法难以兼顾轮廓提取的精细度和完整度,且在点数量较大情况下计算效率较低。因此,提出一种基于网格的可变半径Alpha Shapes方法用于提取机载LiDAR点云建筑物轮廓。方法 对3维点云进行投影降维,对投影后2维离散点的范围构建规则格网,接着根据网格内点云填充情况筛选出边界网格,计算边界网格的平滑度并加权不同的滚动圆半径,再以边界网格为中心生成3×3邻域网格检测窗口,利用滚动圆原理提取窗口内点集的边界点,迭代检测直到所有边界网格遍历完成,最后获取点云的完整轮廓。结果 在精度评价实验中,与固定半径A-Shapes方法和可变半径Alpha Shapes（variable radius Alpha Shapes,VA-Shapes）方法相比,若建筑物以直线特征为主且边缘点云参差不齐,则本文方法的提取效果不理想;若建筑物含有较多拐角特征,则本文方法的提取效果较好。在效率评价实验中,与A-Shapes方法、VA-Shapse方法以及包裹圆方法相比,若点云数据量较小,则4种方法的耗时差距不大;若数据量较大,则本文方法和包裹圆方法的耗时远小于固定半径A-Shapes方法。实验结果表明,本文提出的轮廓提取方法适用于多种形状的建筑物点云。从轮廓完整性、几何精度以及计算效率等几方面综合考虑,本文方法提取建筑物点云轮廓效果较好。结论 本文提出的基于网格的可变半径Alpha Shapes建筑物点云轮廓提取方法结合了网格划分和滚动圆检测的优点,能够有效提取机载LiDAR建筑物点云顶部轮廓,具有较高的提取效率和良好的鲁棒性,提取的轮廓精度较高。     

Estimating inter-group interaction radius for point processes with nested spatial structures

A statistical procedure is proposed in order to estimate the interaction radius between points of a non-stationary point process when the process can present local aggregated and regular patterns. The model under consideration is a hierarchical process with two levels, points and clusters of points. Points will represent individuals, clusters will represent groups of individuals. Points or clusters do not interact as soon as they are located beyond a given interaction radius, and are assumed to interact if their distance is less than this interaction radius. Interaction radius estimation is performed in the following way. For a given distance, observations are split into several clusters whose in-between distances are larger than this distance. For each cluster, a neighbourhood and an area in which this cluster is randomly located is defined under the assumption that the distance between the cluster and its neighbourhood is larger than the interaction radius. The p-value of a test of this assumption is then computed for each cluster. Modelling the expectation of this p-value as a function of the distance leads to an estimate of the interaction radius by a least-square method. This approach is shown to be robust against non-stationarity. Unlike most classical approaches, this method makes no assumption on the point spatial distribution inside the clusters. Two applications are presented in animal and plant ecology.     

Buffon's Needle on Caustics and Torus Quantization

The probability of n + 1 intersections of a long needle in the Buffon problem is the eikonal of a Hankel function which is the principal term in the uniform asymptotic expansion in powers of the small distance between the parallel lines. Evaluating this probability using the torus quantization conditions shows that in the physically meaningful region, where a closed convergence of rays covers the caustic circle, the probability is greater than unity. In addition, the method of steepest descent shows that the caustic and reflection indices are more general than the ones given by torus quantization. The distance from the light source to the center of caustic circle corresponds to the length of the needle, and n times the distance between the parallel lines is the radius of the caustic. Unlike diffraction problems, the solution cannot be extended to the shadow zone since the angles become imaginary. In the continuum limit where the distance between the parallels tends to zero, the number of intersections is governed by an arc sine law in which maximum number of intersections, or the maximum chord length in a circle of a given radius, is most probable.     

Circular Arcs Fitted on a Riemann Sphere

A method for fitting a circle to a set of points in two dimensions is presented. The method applies a stereographic projection to map the 2D points onto a cricle on a 3D Riemann sphere. Then, a plane is fitted to the transformed points, and the parameters of the sought circle are determined from the identified plane parameters. The method is direct, and it is shown that the estimator is unbiased to first-order accuracy. The best performance is obtained when the circle has unit radius and is centered at the origin. The method is unbiased to second order in this case, and experiments with synthetic data show that the method is practically unbiased. In addition, the simulations show that origin centering and unit radius requirements are not critical. Circular arcs down to 45° can be estimated at realistic noise levels. Comparisons with three alternative methods are done, and the accuracy and computational simplicity of this method compares favorably with the alternatives.