移动最小二乘代理模型支持域半径的优化方法

移动最小二乘代理模型描述局部波动的能力优于一般的代理模型,但其精度受支持域半径的影响。在经验公式的基础上提出了一种针对移动最小二乘代理模型支持域半径的优化方法。对支持域内抽样点数寻优获取最佳半径值,提高近似精度进而达到减少抽样点的目的。数值实验结果表明,对于不同基函数阶次和权函数的情况,提出的方法大大提高了移动最小二乘代理模型的近似精度,与基于经验公式的移动最小二乘代理模型相比,其仅需较少的抽样点即可达到相同的近似精度。     

基于移动最小二乘法的微型光谱仪标定方法

针对现有微型光谱仪缺少一种统一、可靠的标定方法,提出了一种基于移动最小二乘法（Moving Least Squares, MLS）的微型光谱仪标定方法。首先,微型光谱仪分别获取汞氩灯和氖灯的标准光谱图;然后对含有高频噪声的原始光谱图进行小波去噪,之后通过峰值定位算法找到特征峰并筛选出需要参与拟合的特征峰所对应的像元序号,最后筛选出一定数量的标定点使用MLS进行拟合。选取一定数量的未参与标定的特征峰代入到拟合函数中进行精度验证。实验表明：基于MLS拟合标定后,标定集的误差标准差为0.136 nm,测试集的误差标准差为0.192 nm,高于传统的最小二乘法曲线拟合,该方法实现了快速、准确地对微型光谱仪进行标定,在实际工程应用中具有重要的指导意义。     

面向应用的RGB-D机器人道路坡度融合估计方法

为提高机器人在移动路径中对道路坡度的估计精度,提出一种面向应用的RGB-D（red green blue-depth）机器人融合型道路坡度估计方法。首先,引入随机采样一致性算法完成点云处理;其次,采用改进型平面拟合方法完成法向量估计;最后,采用余弦聚类及累加平均方法实现高精度道路坡度估计。实验结果表明,该算法在数据集下相较最小二乘法与稀疏子空间法,估计误差分别降低1.21%、2.13%,在实际环境下较最小二乘法平均误差降低1.43°,这证明了所提方法的可行性和准确性。     

基于多重特征匹配的点云配准算法

针对最近点迭代（ICP）算法搜索匹配点对规则单一、准确度低的问题,提出一种基于多重特征匹配的点云配准算法。首先采用改进自适应八叉树算法分割点云,通过移动最小二乘法（MLS）对其叶节点进行局部拟合后,计算点的多重特征;然后提出了基于多重特征的点对相似度,选取满足相似度约束的点对作为匹配点对,进而求取旋转矩阵和平移矩阵实现点云配准。实验表明,该算法能在保持点云配准速度较高的基础上,有效提升配准的准确度,且准确度的提升幅度随着点集数量的增大呈升高趋势。     

带互异权值的B样条曲线的最小二乘渐进迭代逼近

为使B样条拟合目标曲线的迭代过程中单独控制部分数据点,调整局部曲线形状,减小局部曲线迭代误差,提出带互异权值的最小二乘渐进迭代逼近法.首先赋统一初始权值于每个数据点,用最小二乘渐进迭代逼近法生成B样条拟合曲线;其次调整部分数据点对应的权值,运用带互异权值的最小二乘渐进迭代逼近法生成B样条拟合曲线;最后比较调整前后拟合误差.实例结果表明,本文所提出方法可调整局部拟合曲线形状,减小拟合误差.     

LSSVM改进测地距离的核函数算法研究

针对满足一定形状的非线性不均匀分布样本点的分类与拟合问题,提出一种改进的测地距离算法.该算法综合利用传统的k近邻法和ε半径近邻法来确定样本点的近邻关系点,提高了计算样本点测地距离的精确性.将算法应用于最小二乘支持向量机的核函数,通过数据分类仿真测试以及在结构健康检测中丢失数据重构的回归应用,提高了分类与拟合的精度.最后...     

基于正交投影约束的点模型去噪

传统点云消噪算法会削弱曲面特征.为此,提出一种基于正交投影约束的点模型去噪算法.利用移动最小二乘曲面投影的思想,根据采样点与其在MLS曲面上正交投影点之间的关系构建移动距离权重函数,为防止模型收缩,给出曲率权重函数,通过双边滤波器确定滤波方向,结合移动距离权因子与曲率权因子确定采样点滤波距离.实验结果表明,该算法在消除点云噪声的同时,能保持点云高频结构特征,避免模型的收缩和顶点漂移.     

离散数据拟合模型的研究与实现

最小二乘支持向量机引入到离散数据拟合中,代替传统的最小二乘法解决离散数据拟合问题。推导了用于函数估计的最小二乘支持向量机算法,构建了基于最小二乘支持向量机的离散数据拟合模型,并对电机数据拟合进行了研究。结果表明,最小二乘支持向量机拟合离散数据比最小二乘法精度更高、拟合效果更好。     

基于弧长密度的自动邻域半径鉴别FPFH提取算法

在快速点特征直方图(FPFH)的特征计算过程中,需要人工多次选择邻域半径,计算过程复杂且效率较低。针对该问题,提出基于弧长密度的自动邻域半径鉴别FPFH特征提取算法。给出点云弧长密度的计算方法,依据弧长密度估算多对点云的邻域半径,以提取FPFH特征并完成采样一致性初始配准,确定配准性能最优的半径与弧长密度值。在此基础上,使用最小二乘法拟合邻域半径与弧长密度之间的函数表达式,并与FPFH特征提取算法结合得到自动邻域半径鉴别FPFH特征提取算法。实验结果表明,该算法可根据点云弧长密度自动鉴别出合适的邻域半径,运算速度较快。     

基于IRANSAC-IRLS直线拟合算法及应用

针对工业视觉检测中直线边缘存在沾连、毛刺等噪声,导致拟合效率不高、精度较差的问题,提出一种基于梯度方向改进的随机采样一致性（improved random sample consensus,IRANSAC）的迭代加权最小二乘（iterative reweighted least-squares,IRLS）直线拟合算法,即IRANSAC-IRLS算法。首先,利用直线上边缘点的梯度方向相近,将梯度方向引入边缘点RANSAC拟合,来降低错误的随机抽取的次数;然后,对IRANSAC提取出来的局内点进行迭代加权最小二乘拟合,求得最终的直线参数。在噪声点比例为20%、40%、60%、80%的条件下,将IRANSAC-IRLS与基于随机采样一致性算法的最小二乘（RANSAC-LS）拟合算法的仿真实验结果进行对比,IRANSAC-IRLS比RANSAC-LS的拟合效率分别提高16.3%、41.9%、47.5%、53.2%,拟合精度分别提升14.3%、16.7%、44.0%、69.0%。     

Sharp feature preserving MLS surface reconstruction based on local feature line approximations

Sharp features in manufactured and designed objects require particular attention when reconstructing surfaces from unorganized scan point sets using moving least squares (MLS) fitting. It is an inherent property of MLS fitting that sharp features are smoothed out. Instead of searching for appropriate new fitting functions our approach computes a modified local point neighborhood so that a standard MLS fitting can be applied enhanced by sharp features reconstruction.We present a two-stage algorithm. In a pre-processing step sharp feature points are marked first. This algorithm is robust to noise since it is based on Gauss map clustering. In the main phase, the selected feature points are used to locally approximate the feature curve and to segment and enhance the local point neighborhood. The MLS projection thus leads to a piecewise smooth surface preserving all sharp features. The method is simple to implement and able to preserve line-type features as well as corner-type features during reconstruction.     

移动最小二乘法在多功能传感器数据重构中的应用

针对传统最小二乘法全局拟合的局限性, 将一种新型的数值算法---移动最小二乘法应用于非线性多功能传感器的信号重构. 通过详细研究插值函数的构造方法及性质, 合理地选取基函数和权函数, 求出试函数的系数, 进而得到信号的重构值. 详细分析了基函数维数、影响域节点数及权函数因子对计算结果的影响, 并对最小二乘法以及移动最小二乘法的重构数据进行了对比, 重构的相对误差分别小于 15.3 % 和 1.03 %, 结果表明移动最小二乘法更适合非线性曲面拟合, 且适当地增加基函数维数或影响域节点数可以进一步提高数据重构的精度.     

The discrete collocation method for Fredholm–Hammerstein integral equations based on moving least squares method

The purpose of this paper is to investigate the discrete collocation method based on moving least squares (MLS) approximation for Fredholm–Hammerstein integral equations. The scheme utilizes the shape functions of the MLS approximation constructed on scattered points as a basis in the discrete collocation method. The proposed method is meshless, since it does not require any background mesh or domain elements. Error analysis of this method is also investigated. Some numerical examples are provided to illustrate the accuracy and computational efficiency of the method.     

Moving least squares collocation method for Volterra integral equations with proportional delay

In this work, we apply the moving least squares (MLS) method for numerical solution of Volterra integral equations with proportional delay. The scheme utilizes the shape functions of the MLS approximation constructed on scattered points as a basis in the discrete collocation method. The proposed method is meshless, since it does not require any background mesh or domain elements. An error bound is obtained to ensure the convergence and reliability of the method. Numerical results approve the efficiency and applicability of the proposed method.     

Topology‐aware moving least square deformation for 2D characters

Deformation method based on moving least squares (MLS) allows the user to manipulate 2D characters using either sets of points or line segments in real time. However, the traditional MLS deformation spreads the deformation of the controls with respect to the spatial distance, but oblivious to the shape topology, which would possibly lead to distortion. In this paper, we present a topology‐aware MLS deformation approach for 2D characters. First, a Laplace equation is solved to obtain a set of weights, which are called harmonic weights. Then, the MLS deformation is performed by using the harmonic weights as the deformation influence of the user‐specified controls. Finally, the possible distortion in the traditional MLS deformation can be effectively avoided, as the harmonic weights spread the deformation of the controls in a localized and topology‐aware way. In addition, a simple but effective area‐preserving variant of MLS deformation is proposed, which is suitable for the editing of incompressible objects. Copyright © 2015 John Wiley & Sons, Ltd.     

Dynamic Sampling and Rendering of Algebraic Point Set Surfaces

Algebraic Point Set Surfaces (APSS) define a smooth surface from a set of points using local moving least‐squares (MLS) fitting of algebraic spheres. In this paper we first revisit the spherical fitting problem and provide a new, more generic solution that includes intuitive parameters for curvature control of the fitted spheres. As a second contribution we present a novel real‐time rendering system of such surfaces using a dynamic up‐sampling strategy combined with a conventional splatting algorithm for high quality rendering. Our approach also includes a new view dependent geometric error tailored to efficient and adaptive up‐sampling of the surface. One of the key features of our system is its high degree of flexibility that enables us to achieve high performance even for highly dynamic data or complex models by exploiting temporal coherence at the primitive level. We also address the issue of efficient spatial search data structures with respect to construction, access and GPU friendliness. Finally, we present an efficient parallel GPU implementation of the algorithms and search structures.     

基于无网格自然邻接点Petrov-Galerkin法求解带源参数瞬态热传导问题

基于无网格自然邻接点Petrov-Galerkin法,本文建立了一种求解带源参数瞬态热传导问题的新方法.为了克服移动最小二乘近似难以准确施加本质边界条件的缺点,采用了自然邻接点插值构造试函数.在局部多边形子域上采用局部Petrov-Galerkin方法建立瞬态热传导问题的积分弱形式.这些多边形子域可由Delaunay三角形创建.时间域则通过传统的两点差分法进行离散.最后通过算例验证了该数值算法的有效性和正确性.     

基于移动最小二乘法的气动力数据建模方法

针对一体化飞行器高度耦合的非线性气动问题,提出了一种基于移动最小二乘法的气动力数据建模方法;首先,对影响模型精度的因素进行了分析;接着,在构建移动最小二乘模型时采用遗传算法获取最佳支撑域半径以及最佳影响因子β,提高近似精度从而达到减少样本点的目的;得到泛化能力较强的气动力模型,并与偏最小二乘方法的建模结果进行对比;实验结果表明:移动最小二乘法的建模效果优于偏最小二乘方法,预测误差较小,证明了将该方法应用于气动数据建模是可行的。