基于NURBS曲面拟合的三角网格曲率计算

针对三角网格提出了一种基于NURBS曲面拟合的计算Gauss曲率和平均曲率的算法。首先选取边界检测后的二阶邻点作为局部拟合数据,采用直接投影法实现参数化,由二次NURBS曲面进行最小平方拟合反算控制点矩阵,最后由拟合曲面计算曲率。并从三角网格分辨率和噪声两方面进行了比较,实验结果表明本文算法精度高、较其他算法稳定,因而更具通用性。     

点云模型自适应增加采样点算法

提出一种新的点集模型自适应增加啊采样算法.算法利用最小二乘法求出点云模型上每个点的局部光滑曲面片,并由所求得的曲面多项式计算点集曲面上每个点的曲率.通过对每个点及其邻点进行Voronoi剖分,求取每个点所控制的有效采样区域,然后根据曲率在有效区域内建立采样栅格,求取有效区域内的栅格点在曲面上的投影点即为新增采样点.该方法得到的增加采样模型可以较好地保持原点云模型曲面的几何性质,同时还可以通过选择不同的栅格得到适用于不同处理要求的点云模型.     

噪声鲁棒的分水岭网格分割算法

提出一种对逆向工程网格噪声鲁棒的分水岭分割算法.该算法在计算网格离散曲率时,针对曲率计算对网格噪声特别敏感的问题,根据拟合曲面的曲面误差估计,动态地调整拟合曲面的顶点个数,提高了曲率计算的精确性,增强了基于曲率的分水岭算法对噪声的鲁棒性;通过后续的标识、聚类和分割后处理方法,提高了算法的分割精度和效果.该算法在大量的噪声网格模型上获得了较好的分割结果,适用于逆向工程中的二次曲面识别和NURBS曲面逼近.     

散乱点云数据特征信息提取算法

针对散乱点云特征提取过程中效率低和噪声敏感性差的问题,提出一种双阈值点云特征信息提取算法。采用主成分分析法和局部二次曲面拟合法对点云模型进行微分几何信息估算,得到k邻域内采样点平均法矢夹角和平均曲率的特征权值,并利用双阈值检测方法对散乱点云的特征信息进行提取。实验结果表明,该算法能够快速准确地对散乱以及含有噪声的点云模型进行特征信息提取,具有较高的鲁棒性。     

基于模板采样和MLS能量函数的曲率计算

针对传统的曲率计算方法通常在顶点的k-阶邻域(k=1,2,3)内进行,会不可避免地受到三角化质量和细密程度影响的问题,提出一种基于模板采样和移动最小二乘法(MLS)能量函数的曲率计算方法.该方法采用测地圆盘作为邻域,并根据离散指数映射和事先指定的二维模板快速采样;然后借助MLS能量函数直接给出计算高斯曲率和平均曲率的公式,得到相应的曲率值.实验结果表明,文中方法得到的曲率能够稳定地提取几何体的局部弯曲信息,与三角化的好坏和细密程度无关,对噪声不敏感.     

点模型的多边滤波器降噪算法

为了更好地去除噪声,并保持模型的突出特征,提出了一种鲁棒的点模型多边滤波器降噪算法,该算法充分考虑了模型表面的法向量、曲率等内蕴几何量和噪声之间的关系。首先通过自适应选取最优邻域控制函数来将滤波窗口限制在顶点法向量相近的区域,以防止滤波后模型的收缩和过光顺;然后运用协方差矩阵分析的方法,在最优邻域内计算出各采样点的法向量和曲率;最后以采样点滤波参考平面为基准,分别平滑采样点的法向量和位置,即先对采样点的法向量进行多边平滑,然后根据新的法向量来多边平滑输出各采样点的位置偏移量,最后在法向方向上移动该顶点,以达到降噪的目的。实验结果表明,多边滤波器在有效地去除噪声的同时,还能较好地保持点模型表面的几何特征。     

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.     

一种深度图像中的表面曲率估计算法

曲率估计在深度图像分析中占有重要地位,传统的有限差分或局部拟合方法未考虑到表面上可能出现的不连续性,因而会不可避免地出现错误,为了得到有效可靠的曲率估计,本文提出了基于自适应局部表面拟合和鲁棒最大似然的估计的曲率估计算法,首先,提出曲面是分片光滑的假设,表面曲率需从该像素所属的光滑曲面片来估计,其次,定义了能量函数来度量拟合窗的平滑度,在局部表面拟合时,依据最小化能量函数的原则来自适应移动拟合窗的中心,以使拟合窗达到最“光滑”,最后,采用鲁棒最大似然估计以消除仍然存在的“局外点”的影响,理论分析和实验结果证明估计算法是稳健,可靠,有效的且计算复杂度小。     

空间曲线基于内在几何量的高质量采样和B样条拟合

为解决均匀参数采样在许多情况下得到质量不高的采样点,进而生成不理想的B样条拟合曲线,提出空间曲线基于内在几何量的均匀采样方法,以获得给定总数且具有代表性的采样点.首先定义基于弧长、曲率和挠率加权组合的特征函数,通过调整组合参数更好匹配不同的曲线形状;然后提出空间曲线基于内在几何量的自适应采样方法,迭代生成满足给定距离阈值的采样点.采用最大绝对误差和均方根误差作为评价指标,与均匀弧长采样方法和基于弧长和曲率平均的均匀采样方法进行对比,并通过实例进行验证.结果表明,文中方法在采样质量和B样条拟合结果上获得明显改善.     

空间曲线的特征识别与高质量非均匀采样

为避免传统均匀采样方法因忽视曲线重要特征而生成不理想的采样结果,获得给定数量且由特征点和辅助点组成的采样点序列,提出基于特征识别的高质量空间曲线非均匀采样方法.首先使用抛物线插值法得到曲线上所有曲率极大值点和挠率极大值点的近似位置,经筛选后产生特征点,以更好地抓住空间曲线的轮廓特征.然后定义基于弧长、曲率和挠率加权组合的特征函数,并以此自适应地选取曲线上的辅助点.与3种主流采样方法比较的实验结果表明,该方法能够获得更高质量的采样结果且具有更好的实用性,从而进一步改善空间曲线的B样条拟合效果.     

保特征的三维模型的三边滤波去噪算法

随着三维物体扫描仪的广泛应用,如何对扫描出来的模型进行有效、鲁棒、快速的操作已经成为当今计算机图形学中的一个热门话题.通过在扫描模型每个采样点处拟合一个二次型曲面,设计了一个鲁棒的滤波函数--三边滤波函数;应用该函数分别对模型表面上每个点的法线、曲率和位置进行滤波;通过对曲率的滤波结果进行优化,可有效地保持三维模型表面上的特征.该算法不要求已知模型中顶点之间的连接关系,并可应用于网格模型或点模型的光顺去噪处理.     

基于最小代价路径的血管中心线提取

为解决传统最小代价路径算法提取血管中心线时存在偏向血管侧壁的问题,提出一种基于点的中心线校正方法。应用最小代价路径算法初步提取中心线,然后根据血管剖面灰阶值呈高斯分布的特点对每个中心点进行校正,再利用三次B样条将离散的中心点拟合为一条连续的中心线。实验结果表明,该算法提取的中心线更靠近血管的中心处,且对噪声具有鲁棒性。此外,将该算法用于起点、终点位置的校正,则提取的中心线对用户定义点的位置不敏感。     

基于曲率的点云数据配准算法

为了实现不同视角下测得的数据的多视定位,提出一种点云数据配准算法。该算法针对近邻内的点,采用二次曲面逼近的方法来求得每个点的曲率,并根据曲率的Hausdorff距离来寻找有效点集,建立名义上的对应关系,最后用四元组法来求得坐标变换,把数据统一到一个坐标系下。该算法利用曲率的性质准确判断对应点集,解决了任意多视点云的拼合问题,试验结果验证了其有效性和精度。     

A high-accuracy method for fine registration of overlapping point clouds

This paper presents a high-accuracy method for fine registration of two partially overlapping point clouds that have been coarsely registered. The proposed algorithm, which is named dual interpolating point-to-surface method, is principally a modified variant of point-to-surface Iterative Closest Point (ICP) algorithm. The original correspondences are established by adopting a dual surface fitting approach using B-spline interpolation. A novel auxiliary pair constraint based on the surface fitting approach, together with surface curvature information, is employed to remove unreliable point matches. The combined constraint directly utilizes global rigid motion consistency in conjunction with local geometric invariant to reject false correspondences precisely and efficiently. The experimental results involving a number of realistic point clouds demonstrate that the new method can obtain accurate and robust fine registration for pairwise 3D point clouds. This method addresses highest accuracy alignment with less focus on recovery from poor coarse registrations.     

Iterative curved surface fitting algorithm using a raster-scanning window

In this paper, an iterative curved surface fitting method using a small sliding window is first proposed to smooth the original organized point cloud data (PCD) with noise and fluctuation. Samples included in a small sliding window positioned in PCD are successively fitted to a quadratic surface from upper left to lower right using a least squares method. In the iterative process, outliers of samples are asymptotically removed based on an evaluation index. This proposed method allows original PCD to be smoothed keeping its own shape feature. Then, the already developed stereolithography (STL) generator is used to produce triangulated patches from the smoothed PCD. The process allows to reconstruct 3D digital data of a real object written with STL format for reverse engineering from original PCD with noise. The effectiveness and usefulness of the proposed curved surface fitting method are demonstrated through actual smoothing experiments.     

Extracting lines of curvature from noisy point clouds

We present a robust framework for extracting lines of curvature from point clouds. First, we show a novel approach to denoising the input point cloud using robust statistical estimates of surface normal and curvature which automatically rejects outliers and corrects points by energy minimization. Then the lines of curvature are constructed on the point cloud with controllable density. Our approach is applicable to surfaces of arbitrary genus, with or without boundaries, and is statistically robust to noise and outliers while preserving sharp surface features. We show our approach to be effective over a range of synthetic and real-world input datasets with varying amounts of noise and outliers. The extraction of curvature information can benefit many applications in CAD, computer vision and graphics for point cloud shape analysis, recognition and segmentation. Here, we show the possibility of using the lines of curvature for feature-preserving mesh construction directly from noisy point clouds.     

Contour curve reconstruction from cloud data for rapid prototyping

In this study, a method for generation of sectional contour curves directly from cloud point data is given. This method computes contour curves for rapid prototyping model generation via adaptive slicing, data points reducing and B-spline curve fitting. In this approach, first a cloud point data set is segmented along the component building direction to a number of layers. The points are projected to the mid-plane of the layer to form a 2-dimensional (2D) band of scattered points. These points are then utilized to construct a boundary curve. A number of points are picked up along the band and a B-spline curve is fitted. Then points are selected on the B-spline curve based on its discrete curvature. These are the points used as centers for generation of circles with a user-define radius to capture a piece of the scattered band. The geometric center of the points lying within these circles is treated as a control point for a B-spline curve fitting that represents a boundary contour curve. The advantage of this method is simplicity and insensitivity to common small inaccuracies. Two experimental results are included to demonstrate the effectiveness and applicability of the proposed method.     

Establishing a balanced neighborhood of discrete points for local quadric surface fitting

This paper presents a novel algorithm to establish a balanced neighborhood of points for reliable local quadric surface fitting, a common task in point cloud data processing. The underlying smooth surface geometry of a point cloud in the vicinity of a point can be locally approximated by the best fitted quadric surface at the point. The quality of the fitted surface considerably depends on what neighboring points are selected for the fitting. Specifically, if the selected neighboring points carry a biased distribution, the fitted geometry becomes biased, resulting in loss of accuracy in the fitting. The presented algorithm in this paper is able to reliably select neighboring points considering measures of both distance and direction. The main feature is the development of a geometric relationship, named as Territory Claiming, between the selected and the candidate neighboring points. The fundamental principle is for the selected point set to cover the whole neighborhood domain without redundancy. The selection procedure starts with a distance-based sequence of neighboring points with the territory claiming relationship functioning as a filter to establish a well-balanced neighborhood. The neighborhood can be expanded to incorporate sufficient number of points for the quadric surface fitting while maintaining the balance of the overall neighborhood. The implementation results have demonstrated that the presented method is robust and selects local neighboring points with superior fitting performance in comparison with the distance-based neighbors, mesh neighbors, and elliptic Gabriel graph neighbors.     

Feature line extraction from unorganized noisy point clouds using truncated Fourier series

The detection of feature lines is important for representing and understanding geometric features of 3D models. In this paper, we introduce a new and robust method for extracting feature lines from unorganized point clouds. We use a one-dimensional truncated Fourier series for detecting feature points. Each point and its neighbors are approximated along the principal directions by using the truncated Fourier series, and the curvature of the point is computed from the approximated curves. The Fourier coefficients are computed by Fast Fourier Transform (FFT). We apply low-pass filtering to remove noise and to compute the curvature of the point robustly. For extracting feature points from the detected potential feature points, the potential feature points are thinned using a curvature weighted Laplacian-like smoothing method. The feature lines are constructed through growing extracted points and then projected onto the original point cloud. The efficiency and robustness of our approach is illustrated by several experimental results.