Sparse Iterative Closest Point

Rigid registration of two geometric data sets is essential in many applications, including robot navigation, surface reconstruction, and shape matching. Most commonly, variants of the Iterative Closest Point (ICP) algorithm are employed for this task. These methods alternate between closest point computations to establish correspondences between two data sets, and solving for the optimal transformation that brings these correspondences into alignment. A major difficulty for this approach is the sensitivity to outliers and missing data often observed in 3D scans. Most practical implementations of the ICP algorithm address this issue with a number of heuristics to prune or reweight correspondences. However, these heuristics can be unreliable and difficult to tune, which often requires substantial manual assistance. We propose a new formulation of the ICP algorithm that avoids these difficulties by formulating the registration optimization using sparsity inducing norms. Our new algorithm retains the simple structure of the ICP algorithm, while achieving superior registration results when dealing with outliers and incomplete data. The complete source code of our implementation is provided at http://lgg.epfl.ch/sparseicp .     

Efficiently registering scan point clouds of 3D printed parts for shape accuracy assessment and modeling

One popular approach to assess the geometric differences between a part produced by additive manufacturing (AM) and its intended design is the use of a 3D scanner to produce a point cloud. This digital scan is then aligned against the part’s intended design, allowing for quantification of print accuracy. One of the most common methods for achieving this alignment is the Iterative Closest Point (ICP) algorithm. This paper evaluates several potential pitfalls that can be encountered when applying ICP for assessment of dimensional accuracy of AM parts. These challenges are then illustrated using simulated data, allowing for quantification of their impact on the accuracy of deviation measurements. Each of these registration errors was shown to be significant enough to noticeably affect the measured deviations. An efficient and practical method to address several of these errors based on engineering informed assumptions is then presented. Both the proposed method and traditional unconstrained ICP are used to produce alignments of real and simulated measurement data. A real designed experiment was conducted to compare the results obtained by the two registration methods using a linear mixed effects modeling approach. The proposed method is shown to produce alignments that were less sensitive to variation sources, and to generate deviation measurements that will not underestimate the true shape deviations as the unconstrained ICP algorithm commonly does.     

同态滤波下RGB-D点云配准方法

目的 为了提高彩色物体配准的精度,针对3维点云颜色信息易受光照条件影响的问题,提出一种基于光照补偿的RGB-D（RGB Depth）点云配准方法。方法 引入同态滤波算法,并将模型对象的3维点云转化成线性点序列,从而对颜色信息进行光照补偿,以提高颜色信息的一致性;获取模型的颜色和几何特征并加权组合成混合特征,以此定义源点云的特征点,并运用K近邻算法搜索其对应点;用奇异值分解（SVD）得到配准的刚性变换矩阵。结果 进行传统的迭代最近点法（ICP）算法、深度信息与色调相结合的算法以及本文算法在不同的光照强度组合的模型配准对比实验,结果显示,在网面凹凸均匀的大卫模型上,配准时间及特征点匹配平均误差方面均约减少到对比方法的1/2;在网面光滑的barrel模型和网面凹凸不一致的阿基米德模型上,特征点匹配平均误差约分别减少到对比方法的1/6和1/8。此外,与Super 4-Points Congruent Set（Super 4PCS）、彩色点云配准算法在不同组合光照强度下进行对比实验,针对4种不同的网面结构模型,本文算法的SIFT特征点距离平均误差全距约减少到对比方法的1/5。结论 利用同态滤波算法抑制光照影响,提高了颜色信息的一致性,在一定效果上消除了光照强度不均匀对3维点云配准精度的干扰。     

Robust Non-rigid Registration Based on Affine ICP Algorithm and Part-Based Method

The classical affine iterative closest point (ICP) algorithm is fast and accurate for affine registration between two point sets, but it is easy to fall into a local minimum. As an extension of the classical affine registration algorithm, this paper first proposes an affine ICP algorithm based on control point guided, and then applies this new method to establish a robust non-rigid registration algorithm based on local affine registration. The algorithm uses a hierarchical iterative method to complete the point set non-rigid registration from coarse to fine. In each iteration, the sub data point sets and sub model point sets are divided, meanwhile, the shape control points of each sub point set are updated. Then we use the control point guided affine ICP algorithm to solve the local affine transformation between the corresponding sub point sets. Next, the local affine transformation obtained by the previous step is used to update the sub data point sets and their shape control point sets. Experimental results demonstrate that the accuracy and convergence of our algorithm are greatly improved compared with the traditional point set non-rigid registration algorithms.     

基于特征点和改进ICP的三维点云数据配准算法

在光学非接触三维测量中,复杂对象的重构需要多组测量数据的配准。最近点迭代(ICP)算法是三维激光扫描数据处理中点云数据配准的一种经典的数学方法,为了获得更好的配准结果,在ICP算法的基础之上,提出了结合基于特征点的等曲率预配准方法和邻近搜索ICP改进算法的精细配准,自动进行点云数据配准的算法,经对牙齿点云模型实验发现,点云数据量越大,算法的配准速度优势越明显,采用ICP算法的运行时间(194.58 s)远大于本算法的运行时间(89.13 s)。应用实例表明:该算法具有速度快、精度高的特点,算法效果良好。     

Towards a general multi-view registration technique

We present an algorithm that reduces significantly the level of the registration errors between all pairs in a set of range views. This algorithm refines initial estimates of the transformation matrices obtained from either the calibrated acquisition setup or a crude manual alignment. It is an instance of a category of registration algorithms known as iterated closest-point (ICP) algorithms. The algorithm considers the network of views as a whole and minimizes the registration errors of all views simultaneously. This leads to a well-balanced network of views in which the registration errors are equally distributed, an objective not met by previously published ICP algorithms which all process the views sequentially. Experimental results show that this refinement technique improves the calibrated registrations and the quality of the integrated model for complex multi-part objects. In the case of scenes comprising man-made objects of very simple shapes, the basic algorithm faces problems common to all ICP algorithms and so must be extended     

A Correntropy-based Affine Iterative Closest Point Algorithm for Robust Point Set Registration

The iterative closest point (ICP) algorithm has the advantages of high accuracy and fast speed for point set registration, but it performs poorly when the point set has a large number of noisy outliers. To solve this problem, we propose a new affine registration algorithm based on correntropy which works well in the affine registration of point sets with outliers. Firstly, we substitute the traditional measure of least squares with a maximum correntropy criterion to build a new registration model, which can avoid the influence of outliers. To maximize the objective function, we then propose a robust affine ICP algorithm. At each iteration of this new algorithm, we set up the index mapping of two point sets according to the known transformation, and then compute the closed-form solution of the new transformation according to the known index mapping. Similar to the traditional ICP algorithm, our algorithm converges to a local maximum monotonously for any given initial value. Finally, the robustness and high efficiency of affine ICP algorithm based on correntropy are demonstrated by 2D and 3D point set registration experiments.      

加入迭代因子的层次化颅骨配准方法

目的 在基于知识的颅面复原中,为了对未知颅骨的面貌进行复原,需要在颅骨库里寻找相似颅骨,将相似颅骨的面皮作为参考。寻找相似颅骨的过程即颅骨配准,配准的精度和效率是两个重要性能指标。本文提出一种基于特征区域和改进ICP（iterative closest point）算法的层次化颅骨配准方法。方法 首先,将颅骨模型去噪、简化并归一化,通过计算体积积分不变量,确定每个点的凹凸性;使用K-means方法,将颅骨上的点聚类为多个或凹或凸的特征区域。然后,通过主成分分析法来计算两个颅骨的相似特征区域,对每一个可能的匹配计算3维变换,将两个颅骨粗略对齐;最后,采用加入迭代因子的方法对ICP算法进行改进,使用改进的ICP算法对颅骨进行精配准。结果 将本文方法用于颅骨模型、兵马俑模型以及公共数据集中的3维模型配准,经典ICP算法的配准时间分别为6.23 s、7.61 s、4.17 s,改进的ICP算法配准时间分别为3.02 s、3.23 s、2.83 s,算法效率提高了约2倍,配准效果也有明显提高。实验中通过对迭代因子的测试,发现不同的数据集需要设定不同的迭代因子。结论 本文所提出的基于区域特征的层次化配准方法提高了颅骨配准的精度和效率,整个过程不需要人工干预,该算法具有一定的普适性,可用于相似3维模型配准。     

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.     

Simultaneous Registration of Multiple Corresponding Point Sets

We present a new technique for the simultaneous registration of multiple corresponding point sets with rigid 3D transformations. This class of problems is a generalization of the classic pairwise point set registration task, involving multiple views with multiple correspondences existing between them. The proposed technique requires the computation of a constant matrix which encodes the point correspondence information, followed by an efficient iterative algorithm to compute the optimal rotations. The optimal translations are then recovered directly through the solution of a linear equation system. The algorithm supports weighting of data according to confidence, and we show how it may be incorporated into two robust estimation frameworks to detect and reject outlier data. We have integrated our method into a generalized multiview ICP surface matching system and tested it with synthetic and real data. These tests indicate that the technique is accurate and efficient. The algorithm also compares favorably to another multiview technique from the literature.     

Multi-View Point Clouds Registration without Feature Extraction for Use in Reverse Engineering of CAD Models

For reverse engineering a CAD model, it is necessary to integrate measured points from several views of an object into a common reference frame. Given a rough initial alignment of point cloud in different views with point-normal method, further refinement is achieved by using an improved iterative closest point (ICP) algorithm. Compared with other methods used for mult-view registration, this approach is automatic because no geometric feature, such as line, plane or sphere needs to be extracted from the original point cloud manually. A good initial alignment can be acquired automatically and the registration accuracy and efficiency is proven better than the normal point-point ICP algorithm both experimentally and theoretically.     

基于3D-Harris 与FPFH 改进的3D-NDT 配准算法

针对传统点云配准三维正态分布变换(3D-NDT)、迭代最近点(ICP)算法在未给定初 始配准估计的情况下配准效果不佳、配准时间长、误差较大的缺陷,提出了精准且相对高效的 点云匹配算法。首先,运用3D-Harris 算法识别每一幅点云的关键点,并以此为基本点建立局 部参考框架,计算快速点特征直方图(FPFH)描述子;之后,使用最小中值法(LMeds)中的对应 估计算法排除不准确的点对应关系,得到含有对应三维特征关系的特征点对。计算粗配准所需 的变换矩阵,完成初步匹配。随后,根据3D-NDT 算法将点云数据空间体素化,运用概率分布 函数完成最终的点云进行精确地匹配。使用改进配准将3 组分别从网络下载的较少噪声、大规 模与Kinect V2.0 采集的较多噪声、大规模的2 组重叠度不同的点云数据匹配到同一个空间参考 框架中,并通过精度分析对比经典3D-NDT,ICP 等算法。实验结果证明,该算法在迭代次数 较低时,可使室内场景点云数据完成精度较高的配准且受噪声影响较小,但如何将算法的复杂 度适当降低,缩短配准时间需要更进一步的研究。     

改进ICP算法实现多视点云精确配准研究

复杂面形的三维整体测量能否顺利完成取决于不同视下测得的三维点云的配准精度。研究表明:采用点到点,点到三角面配准方法易受噪声干扰,采用面形比较计算量大,且在平面和标准球面情况下容易失效。以粗配准标记点所在的立方体区域为重合区域,使用点到点的多邻接三角面距离最近的点对作为初始匹配点,并根据几何结构最大相似原则对所求得的多个粗匹配点对进行筛选,再对筛选后的点对应用最近点迭代(ICP)算法。改进后的ICP算法实现了重合区域的快速自动定位,实现了不同视下点云的快速精确配准,在多个实例下获得了配准精度优于0.01 mm的实验结果。     

基于Kinect的点云配准方法

Kinect采集的点云存在点云数量大、点云位置有误差,直接使用迭代最近点(ICP)算法对点云进行配准时效率低.针对该问题,提出一种基于特征点法向量夹角的改进点云配准算法.首先使用体素栅格对Kinect采集的原始点云进行下采样,精简点云数量,并使用滤波器移除离群点.然后使用SIFT算法提取目标点云与待配准点云公共部分的特征点,通过计算特征点法向量之间的夹角调整点云位姿,完成点云的初始配准.最后使用ICP算法完成点云的精细配准.实验结果表明,该算法与传统ICP算法相比,在保证点云配准精度的同时,能够提高点云的配准效率,具有较高的适用性和鲁棒性.     

面向RGBD深度数据的快速点云配准方法

目的 真实物体的3维重建一直是计算机图形学、机器视觉等领域的研究热点。针对基于RGBD数据的非匀速非固定角度旋转物体的3维重建问题,提出一种利用旋转平台重建物体3维模型的配准方法。方法 首先通过Kinect采集位于旋转平台上目标物的深度数据和颜色数据,对齐融合并使用包围盒算法去除背景噪声和不需要的外部点云,获得带有颜色信息的点云数据。并使用基于标定物不同角度上的点云数据标定出旋转平台中心轴的位置,从而获得Kinect与旋转平台之间的相对关系;然后通过曲率特征对目标点云进行特征点提取并寻找与相邻点云的对应点;其中对于特征点的选取,首先针对点云中的任意一点利用kd-tree搜寻其k个邻近点,对这些点进行曲面拟合,进而计算其高斯曲率,将高斯曲率绝对值较大的n个点作为点云的特征点。n的取值由点云的点个数、点密度和复杂度决定,具体表现为能反映物体的大致轮廓或表面特征信息即可。对于对应点的选取,考虑到欧氏距离并不能较好反映点云中的点对在旋转过程中的对应关系,在实际配准中,往往会因为点云重叠或距离过远等原因找到大量错误的对应点。由于目标物在扫描过程中仅绕旋转轴进行旋转,因此采用圆弧最小距离寻找对应点可有效减少错误点对。随后,使用二分迭代寻找绕中心轴的最优旋转角度以满足点云间的匹配误差最小;最后,将任意角度获取的点云数据配准到统一的坐标系下并重建模型。结果 使用斯坦福大学点云数据库和自采集数据库分别对该方法和已有方法在算法效率和配准结果上进行对比实验,实验结果显示在拥有平均75 000个采样点的斯坦福大学点云数据库上与传统ICP算法和改进ICP算法相比,迭代次数分别平均减少86.5%、57.5%,算法运行时间分别平均减少87%、60.75%,欧氏距离误差平方和分别平均减少70%、22%;在具有平均57000个采样点的自采集点云数据库上与传统ICP算法和改进ICP算法相比,迭代次数分别平均减少94%、75%,算法运行时间分别平均减少92%、69%,欧氏距离误差平方和分别平均减少61.5%、30.6%;实验结果显示使用该方法进行点云配准效率较高且配准误差更小;和KinectFusion算法相比在纹理细节保留上也表现出较好的效果。结论 本文提出的基于旋转平台标定的点云配准算法,利用二分迭代算法能够有效降低算法复杂度。与典型ICP和改进的ICP算法的对比实验也表明了本文算法的有效性。另外,与其他方法在具有纹理的点云配准对比实验中也验证了本文配准方法的优越性。该方法仅采用单个Kinect即可实现对非匀速非固定角度旋转物体的3维建模,方便实用,适用于简单快速的3维重建应用场合。     

一种应用于大角度变换点云的配准方法

针对传统配准法不能很好解决大角度变换点云的配准这一问题,提出一种基于精 确对应特征点对及其 K 邻域点云的配准方法。首先分别计算两组点云的 FPFH 值,根据特征值 建立点云间的对应关系;然后通过 RANSAC 滤除其中错误的匹配点对,得到相对精确的特征点 对集合;之后通过 KD-tree 搜索的方式分别找出特征点对 R 半径邻域内的点,应用 ICP 算法得 到两部分点云的最优收敛;最后将计算得到的相对位置关系应用到原始点云上得到配准结果。 通过对斯坦福大学点云库中 Dragon、Happy Buddha 模型以及 Kinect 采集的石膏像数据进行配 准和比较,实验表明该方法能够有效解决大角度变换点云的配准问题,是一种具有高精度和高 鲁棒性的三维点云配准方法。     

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.     

一种高程相关的机载LiDAR点云配准方法

针对现有配准方法难以提取大范围机载LiDAR点云特征信息的问题,提出了一种基于2片待配准机载LiDAR点云高程数据相关的点云自动配准方法。首先,将待配准点一定范围内的点云拟合局部曲面;然后,在另一点云片中确定搜索区域,利用拟合结果求解搜索区域内的点云在拟合曲面上的高程;最后,通过计算拟合高程与实际高程的相关系数,选择搜索区域内相关系数最大位置作为配准的关键点参与点云配准,反复迭代直到完成配准。文章用实际采集的机载LiDAR数据进行了实验分析,并与传统的ICP算法进行了对比。实验结果表明,该方法在配准精度上能达到较高的水准,能够满足机载LiDAR点云配准的要求。     

基于特征点匹配的排水管道声点云模型配准算法

三维重建技术逐渐成为获取全面、完备、准确的排水管道信息的关键手段。而实际检测受到管道堵塞等工况与管道检测规程等因素限制,造成所获得的管道声呐点云模型会出现位姿不同、部分重叠或空缺等情况,需要通过配准获取完整管道模型。同时,传统ICP算法针对管道模型存在效率低、精度差的问题。因此,该文提出基于特征点匹配的粗配准与改进的ICP精细配准相结合的点云配准算法。首先,利用ISS特征点检测法检测出模型特征点,通过FPFH对特征点进行进一步的描述;其次,采用RANSAC算法筛选出正确特征匹配点集,利用四元数法解算出初始变换参数完成粗配准;最后,在粗配准基础上,通过改进最近对应点查询的ICP算法完成精细配准。实验结果表明了该文算法的可行性与优越性,能为后续排水管道缺陷检测提供高完备、全面、准确的点云模型。