An extension on robust directed projection of points onto point clouds

Azariadis and Sapidis [Azariadis PN, Sapidis NS. Drawing curves onto a cloud of points for point-based modelling. Computer-Aided Design 2005;37(1):109-22] introduced a novel method of point directed projection (DP) onto a point cloud along an associated projection vector. This method is essentially based on an idea of least sum of squares by making use of a weight function for bounding the influence of noise. One problem with their method is the lack of robustness for outliers. Here, we present a simple, robust, and efficient algorithm: robust directed projection (RDP) to guide the DP computation. Our algorithm is based on a robust statistical method for outlier detection: least median of squares (LMS). In order to effectively approximate the LMS optimization, the forward search technique is utilized. The algorithm presented here is better suited to detect outliers than the DP approach and thus finds better projection points onto the point cloud. One of the advantages of our algorithm is that it automatically ignores outliers during the directed projection phase.     

Parameterization of clouds of unorganized points using dynamic base surfaces

In this paper a new method for parameterizing clouds of unorganized points is presented. The proposed method introduces the notion of dynamic base surfaces (DBS) which are dynamically adapted to the three-dimensional shape implied by the clouds of points. The only assumption regarding the cloud of points is the existence of a boundary defined by a closed path of four curves. The proposed method is based on an iterative procedure where a DBS is gradually improved approximating more faithfully the fundamental geometry of the cloud of points. Parameterization is achieved by orthogonally projecting the cloud of points onto the DBS. An application of the introduced parameterization method to the well-known surface least-squares fitting is presented which illustrates the effectiveness and the efficiency of the proposed approach.     

Drawing curves onto a cloud of points for point-based modelling

Point-based geometric models are gaining popularity in both the computer graphics and CAD fields. A related design/modelling problem is the focus of the reported research: drawing curves onto digital surfaces represented by clouds of points. The problem is analyzed and solved, and a set of ‘design tools’ are proposed which allow the user/designer to efficiently perform ‘product development’ (alternative name: ‘detail design’) tasks which require efficient processing of a ‘digital surface’. The primary tool is a robust and efficient point projection algorithm combined with a smoothing technique for producing smooth ‘digital curves’ lying onto the cloud surface. The new design tools are tested on a real-life industrial example with very satisfactory results, which are thoroughly presented in the paper.     

An accurate and fast point-to-plane registration technique

This paper addresses a registration refinement problem and presents an accurate and fast point-to-(tangent) plane technique. Point-to-plane approach is known to be very accurate for registration refinement of partial 3D surfaces. However, the computation complexity for finding the intersection point on a destination surface from a source control point is hindering the algorithm from real-time applications. We introduce a novel point-to-plane registration technique by combining the high-speed advantage of point-to-projection technique. In order to find the intersection point fast and accurately, we forward-project the source point to the destination surface and reproject the projection point to the normal vector of the source point. We show that iterative projections of the projected destination point to the normal vector converge to the intersection point. By assuming the destination surface to be a monotonic function in a new 2D coordinate system, we show contraction mapping properties of our iterative projection technique. Experimental results for several objects are presented for both pair-wise and multi-view registrations.     

基于局部指纹曲面片的点云三维物体识别

提出一种新的基于局部描述符的点云物体识别算法。算法根据点云的位置信息提取出邻域以及曲率信息,进而得到形状索引信息。根据形状索引提取到特征点,在每个特征点根据样条拟合原理得到测地距离和矢量夹角分割曲面得到曲面片集。每个曲面片的等距测地线构成了曲面片指纹,通过矢量和半径的变化描述,可以把每个模型物体得到的曲面片集描述存入数据库。对于给定的一个物体,根据上面步骤同样得到其曲面片集描述,通过和数据库中模型物体曲面片集的比对,得到初始识别结果。对每对初始识别结果进行对应滤波后,通过最近点迭代方法得到最终的识别结果。最后通过具体的实验说明了算法的有效性和高效性。     

点云模型适应性上采样算法

针对点云模型采样密度的不足,提出一种新的适应性上采样算法。算法首先采用均匀栅格法建立点云模型的拓扑关系,提高数据点K-邻域的查找效率,利用协方差矩阵求取点云模型中数据点的法向量,并用法向传播算法进行法向重定向,然后检测点云模型中采样点密度不足的区域,在采样密度不足区域的点的切向矩形平面内适应性均匀采样,并把这些采样点几乎垂直投影到点云模型所在的原始曲面上,由此得到的模型即为上采样模型。该算法得到的上采样模型可以较好地补充点云模型的细节信息,能够满足点云模型的绘制和后续几何处理的需求。     

点云表面曲线的手绘构造方法

为了勾勒点云的骨架或在点云上标记符号,提出一种基于手绘的点云表面曲线构造方法．首先将手绘的二维草图识别成二次曲线;然后将其均匀离散化并分别投影到点云表面;最后判断投影点是否接近于同一平面,如果是,则将二次曲线重新投影到该拟合平面;否则,将投影点连接成B样条曲线并对其平滑去噪．实验结果表明,利用该方法可以快速勾勒出点云轮廓,并在点云表面高效地绘制出二次曲线或者平滑的B样条曲线．     

A quasi-Monte Carlo method for computing areas of point-sampled surfaces

A novel and efficient quasi-Monte Carlo method for computing the area of a point-sampled surface with associated surface normal for each point is presented. Our method operates directly on the point cloud without any surface reconstruction procedure. Using the Cauchy-Crofton formula, the area of the point-sampled surface is calculated by counting the number of intersection points between the point cloud and a set of uniformly distributed lines generated with low-discrepancy sequences. Based on a clustering technique, we also propose an effective algorithm for computing the intersection points of a line with the point-sampled surface. By testing on a number of point-based models, experiments suggest that our method is more robust and more efficient than those conventional approaches based on surface reconstruction.     

关键点匹配三维人脸识别方法*

提出了一种新颖的三维人脸识别算法,其基本思路是,把代表人脸的三维点云沿X、Y或Z轴旋转,反复多次把3D人脸关键点投影到2.5D图像上,然后提取2.5D图像的关键点并进行标记,而用这些比原来小得多的关键点代替原来的面扫描。面对未知的待测人脸首先通过执行相同的多视角特征点提取技术提取关键点,然后应用一个新的加权特征点匹配算法进行识别。通过用GavabDB三维面部识别数据集进行试验评估,这个方法对中性表情人脸可获得高达94％的识别精度,对人脸表情辨识（如微笑）的准确率也超过了88％。实验结果表明,此方法在识别精     

Projecting registration error for accurate registration of overlapping range images

In this paper, we propose a novel algorithm for the automatic registration of two overlapping range images. Since it is relatively difficult to compare the registration errors of different point matches, we project them onto a virtual image plane for more accurate comparison using the classical pin-hole perspective projection camera model. While the traditional ICP algorithm is more interested in the points in the second image close to the sphere centred at the transformed point, the novel algorithm is more interested in the points in the second image as collinear as possible to the transformed point. The novel algorithm then extracts useful information from both the registration error and projected error histograms for the elimination of false matches without any feature extraction, image segmentation or the requirement of motion estimation from outliers corrupted data and, thus, has an advantage of easy implementation. A comparative study based on real images captured under typical imaging conditions has shown that the novel algorithm produces good registration results.     

基于移动最小二乘曲面的点云拼接算法

针对现有点云拼接方法受被测零件复杂外形和测量噪声影响的问题,提出基于移动最小二乘( Moving Least-Squares,MLS)曲面的点云拼接算法.该算法利用一种极值投影方法来有效计算点到MLS曲面的对应点,并结合迭代最近点(Iterative Closest Point,ICP)算法将各个视角的点云统一到该ML...     

结构光视觉三维点云逐层三角网格化算法

针对结构光视觉恢复的大规模三维点云的可投影特点,提出一种基于投影网格的底边驱动逐层网格化曲面重建算法。该算法首先将点云投影到一个二维平面上;然后基于点云投影区域建立规则投影网格,并将投影点映射到规则二维投影网格上,建立二维网格点与三维点云间的映射关系;接着对投影网格进行底边驱动的逐层网格化,建立二维三角网格;最后根据二维投影点与三维点的对应关系及二维三角网格拓扑关系获得最终的三维网格曲面。实验结果表明,算法曲面重建速度快,可较好地保持曲面细节特征。     

一种无标记点三维点云自动拼接技术

基于相位投影和双目的三维光学测量系统已经广泛应用于各领域.受投影光测量系统单次测量范围大小的限制,对大型物体的测量需要在表面粘贴圆形标记点进行多次拼接的缺点,探讨一种基于SIFT的无标记点自动拼接技术.该技术采用SIFT方法获取两次测量的特征点,其次结合RANSAC求出图像特征点的匹配关系,再根据立体匹配中图像特征点与三维点云之间的对应关系,将二维特征点的对应关系映射到三维点云的对应关系上,最后由SVD奇异值分解算法求得旋转和平移矩阵实现拼接.实验证明:该方法可以避免在被测量对象上粘贴标记点,能够快速准确地实现自动拼接.     

点到隐式曲面的正交投影计算

针对点到隐式曲面的正交投影问题,提出一种稳定的几何迭代算法.首先构造初始点处的一条特殊的法截线,并给出沿着该法截线追踪投影点的二阶泰勒迭代方法;然后将给定点向初始点处的法截线的曲率圆作投影,提出基于曲率的步长控制策略,在此基础上给出了基于梯度的迭代误差矫正方法.仿真结果表明,该算法具有良好的收敛性、鲁棒性以及精确性.     

Fully Automatic Registration of Image Sets on Approximate Geometry

The photorealistic acquisition of 3D objects often requires color information from digital photography to be mapped on the acquired geometry, in order to obtain a textured 3D model. This paper presents a novel fully automatic 2D/3D global registration pipeline consisting of several stages that simultaneously register the input image set on the corresponding 3D object. The first stage exploits Structure From Motion (SFM) on the image set in order to generate a sparse point cloud. During the second stage, this point cloud is aligned to the 3D object using an extension of the 4 Point Congruent Set (4PCS) algorithm for the alignment of range maps. The extension accounts for models with different scales and unknown regions of overlap. In the last processing stage a global refinement algorithm based on mutual information optimizes the color projection of the aligned photos on the 3D object, in order to obtain high quality textures. The proposed registration pipeline is general, capable of dealing with small and big objects of any shape, and robust. We present results from six real cases, evaluating the quality of the final colors mapped onto the 3D object. A comparison with a ground truth dataset is also presented.     

规则特征曲面点云法向估计

目的 针对特征曲面点云法矢估计不准确,点云处理时容易丢失曲面的细节特征等问题,提出基于高斯映射的特征曲面散乱点云法向估计法。方法 首先,用主成分分析法粗略地估算点云法向和特征点;其次,将特征点的各向同性邻域映射到高斯球,用K均值聚类法对高斯球上的数据分割成多个子集,以最优子集对应的各向异性邻域拟合曲面来精确估算特征点的法向量;最后,通过测试估计法向与标准法向的误差来评价估计法矢的准确性,并且将估计的法向应用到点云曲面重建中来比较特征保留效果。结果 本文方法估计的法向最小误差接近0,对噪声有较好的鲁棒性,重建的曲面能保留曲面的尖锐特征,相比于其他法向估计法,所提出的方法估计的法向更准确。结论 本文方法能够比较准确的估算尖锐特征曲面法向量,对噪声鲁棒性强,具有较高的适用性。     

Gauss map computation for free-form surfaces

The Gauss map of a smooth doubly-curved surface characterizes the range of variation of the surface normal as an area on the unit sphere. An algorithm to approximate the Gauss map boundary to any desired accuracy is presented, in the context of a tensor-product polynomial surface patch, r(u,v) for (u,v)[0,1]×[0,1]. Boundary segments of the Gauss map correspond to variations of the normal along the patch boundary or the parabolic lines (loci of vanishing Gaussian curvature) on the surface. To compute the latter, points of vanishing Gaussian curvature are identified with the zero-set of a bivariate polynomial, expressed in the numerically-stable Bernstein basis—the subdivision and variation-diminishing properties then govern an adaptive quadtree decomposition of the (u,v) parameter domain that captures the zero-set of this polynomial to any desired accuracy. Loci on the unit sphere corresponding to the patch boundaries and parabolic lines are trimmed at their mutual or self-intersection points (if any), and the resulting segments are arranged in a graph structure with the segment end-points as nodes. By appropriate traversal of this graph, the Gauss map boundary segments may then be identified in proper order, and extraneous segments (lying in the Gauss map interior) are discarded. The symmetrization of the Gauss map (by identification of antipodal points) and its stereographic projection onto a plane are also discussed.     

Vector projection method for unclassifiable region of support vector machine

Unclassifiable region (UR) in conventional multi-classification support vector machine (MSVM) decreased the classification capacity and generalization ability of MSVM. To overcome the disadvantage, vector projection method (VPM) was presented. VPM first projects the samples in UR onto the line linking every two class centers, then computes the feature distance between each projecting point and corresponding class center. For one sample, the class with smaller feature distance will be voted one time and the sample belongs to the class which owns the most votes. Experimental results on synthetic and benchmark datasets show that VPM resolved the UR problem effectively and improved the classification capacity and generalization ability of MSVM.     

不平衡支持向量机的调整方法

针对两类不平衡数据的分离超平面的偏移问题提出一种调整方法.首先对两类样本数据进行初步训练,产生一个初步分离超平面的法向量,然后把高维样本投影到该法向量上得到一维数据,然后由一维投影数据所提供的信息利用非参数密度估计,根据误差率最小准则,得到一个修正的偏置.几个真实数据试验表明,该方法不仅能保持标准支持向量机的良好性能,而且能平衡或减少总的错分率.