三维点云法向量估计综述

由于获取方便、表示简单、灵活等优势,点云逐渐成为常用的三维模型表示方法之一。法向量作为点云必不可少的属性之一,其估计方法在点云处理中具有重要的位置。另一方面,由于点云获取过程中不可避免的噪声、误差和遮挡,点云中通常含有噪声、外点和空洞,并且部分采样模型如CAD模型,也会存在尖锐特征,这些都给法向量估计提出了挑战。对当前已有的点云法向量估计算法进行综述,分析其原理及关键技术,着重分析它们在处理噪声、外点和尖锐特征等方面的能力并给出比较,最后为未来研究提供了一些建议。     

MF-Net：结合残差网络的多尺度特征点云补全网络

针对目前点云补全网络只关注全局特征造成的语义信息丢失问题，提出了一个基于残差网络的多尺度特征提取的点云补全网络。网络采用端到端的思想，为避免单一特征不全面问题，将原始输入采样为三种不同尺度的点云；利用级联方式递归式融合不同方法提取的低分辨率点云的全局特征和原始点云的局部特征，形成特征向量并输入全连接网络，实现粗点云的预测；将拼接后的原始点云和粗点云送入精细重构单元，再在精细重构单元中融合注意力机制并利用残差网络进行由粗略到精细的补全；通过计算粗点云、稠密点云与真实点云之间的联合损失函数以提高补全性能。在ShapeNet数据集和KITTI数据集上的实验证明，无论是定性比较还是定量比较，提出的方法对残缺点云均具有较好的补全效果，同时也体现了该方法具有泛化能力。     

基于标签分布学习的三维手部姿态估计

快速、可靠的手部姿态估计在人机交互等领域有着广泛的应用。为了解决光照强度变化、自身遮挡以及姿态变化幅度较大等情况对手部姿态估计的影响,提出了一种基于标签分布学习的深度网络结构。该网络将手部点云作为输入数据,首先通过最远点采样和定向边界框（OBB）对点云数据进行归一化处理,然后采用PointNet++提取手部点云数据特征。为了应对点云数据与手部关节点之间的高度非线性关系,通过标签分布学习网络预测手部关节点的位置信息。与传统的基于深度图的方法相比,该方法能够高效地提取高鉴别力的手部几何特征,并且计算复杂度较低、精确度较高。为了验证提出的手部姿态估计网络的有效性,在公共数据集MSRA上进行了一系列测试。实验结果表明,该网络估计出的手部关节点位置的平均误差为8.43 mm,平均每帧的处理时间为12.8 ms,而且姿态估计的误差相较于3D CNN算法降低了11.82%,相较于Hand PointNet算法降低了0.83%。     

点云鲁棒低秩联合估计重构

为了提高三维点云的质量,在抑制噪声的同时恢复尖锐特征,提出一种基于L₁稀疏优化的点云鲁棒低秩联合估计重构算法.首先使用鲁棒主成分分析进行点云局部区域低秩建模估计,避免离群点的影响,并根据法向场的变化调整模型,实现点云各向异性自适应降噪;为了提高算法求解效率,利用局部曲率进行尖锐特征辨识,将阈值迭代法与非精确增广拉格朗日乘子法相结合,用于点云不同区域低秩模型的求解;再根据每个优化后局部邻域交叠区域的冗余信息完成点云的全局联合估计重构;最后对尖锐特征点运用投影优化实现边缘特征恢复,解决尖锐特征退化以及边缘毛糙的问题.在公开仿真点云数据与多种典型算法的实验结果表明,所提算法无论是主观视觉效果,还是重构精度与效率均得到改善,与MRPCA算法相比,精度、时效分别提升10.22%和56.52%;在保留点云原有特征信息的同时,可以有效地抑制噪声并恢复尖锐特征,重构效果良好.     

基于多尺度动态图卷积网络的3D点云分类

3D点云数据是一种不规则性数据,传统卷积神经网络无法直接对3D点云数据进行处理.对此,提出一种基于多尺度动态图卷积网络的3D点云分类模型.利用最远点采样方法采样3D点云数据集的代表点,降低模型计算复杂度;利用不同尺度的k最邻近节点聚合方式,对图中每一个中心节点的k最邻近节点进行定位;利用边卷积操作对中心节点及其邻接节点的局部属性特征进行提取与聚合用于分类.实验表明,该模型在3D点云分类准确度上,达到了比当前主流模型更高的水平,并且大幅降低了模型生成参数的数量.     

基于采样汇集网络的场景深度估计

针对现有场景深度估计方法中,由于下采样操作引起的复杂物体边界定位不准确,而造成物体边界处的场景深度估计模糊的问题,受密集网络中特征汇集过程的启发,本文提出一种针对上;下采样过程的汇集网络模型.在下采样过程中,使用尺度特征汇集策略,兼顾不同尺寸物体的估计;在上采样过程中,使用上采样反卷积恢复图像分辨率;同时,引入采样跨层汇集策略,提供下采样过程中保存的物体边界的有效定位信息.本文提出的采样汇集网络(Sampling aggregate network,SAN)中使用的尺度特征汇集和采样跨层汇集,都可以有效缩短特征图到输出损失之间的路径,从而有利于避免模型的参数优化时陷入局部最优解.在公认场景深度估计NYU-Depth-v2数据集上的实验说明,本文方法能够有效改善复杂物体边界等干扰情况下的场景深度估计效果,并在深度估计误差和准确性上,优于当前场景深度估计的主流方法.     

MSP-Net:多尺度点云分类网络

针对传统点云分类网络难以充分发挥卷积神经网络优势的问题,提出一种多尺度点云分类网络MSP-Net.首先,基于局部区域划分的完备性、自适应性、重叠性及多尺度特性要求,提出了多尺度局部区域划分算法,并以点云及不同层次的特征为输入,得到多尺度局部区域;然后构建了包含单尺度特征提取、低层次特征聚合及多尺度特征融合等模块的多尺度点云分类网络.该网络充分地模拟了卷积神经网络的作用原理,具备随着网络尺度和深度的增加,局部感受野越来越大,特征抽象程度越来越高的基本特征.最后将该算法应用在标准公开数据集ModelNet10和ModelNet40上,分别取得了94.71%和91.73%的分类准确率,表明该算法在同类工作中处于领先或相当的水平,验证了算法思想的可行性及有效性.     

PointMLP-FD：基于多级自适应下采样的点云分类模型

针对受硬件条件、物体遮挡和背景杂波等客观因素的影响,传感器采集的目标点云具有较强的 稀疏性和密度不均匀性,导致分类模型对点云特征的学习效率低、分类泛化能力差的问题,提出了一种基于多 级自适应下采样的点云分类模型 PointMLP-FD。该模型设计了多个 MLP 模块作为网络分支,以点云的浅层特 征为输入得到每个点云类别维度上的特征表达,之后再根据特征表达进行排序,选择具有更强语义特征的点构 成下采样点集。通过过滤背景和与目标相关性低的信息来自适应保留反应目标本质特征的信息。最后分别计算 分支网络的损失,与骨干网络并行训练来优化点云特征,减少模型参数。该方法在 ScanObjectNN 数据集上进 行测试,结果表明相较于 PointMLP-elite 分类精度更高,mAcc 提升 1%,OA 提升 0.8%,以更少的参数量接近 SOTA 模型的性能。     

结合密集残差结构和多尺度剪枝的点云压缩网络

目的 点云是一种重要的三维数据表示形式,已在无人驾驶、虚拟现实、三维测量等领域得到了应用。由于点云具有分辨率高的特性,数据传输需要消耗大量的网络带宽和存储资源,严重阻碍了进一步推广。为此,在深度学习的点云自编码器压缩框架基础上,提出一种结合密集残差结构和多尺度剪枝的点云压缩网络,实现了对点云几何信息和颜色信息的高效压缩。方法 针对点云的稀疏化特点以及传统体素网格表示点云时分辨率不足的问题,采用稀疏张量作为点云的表示方法,并使用稀疏卷积和子流形卷积取代常规卷积提取点云特征;为了捕获压缩过程中高维信息的依赖性,将密集残差结构和通道注意力机制引入到点云特征提取模块;为了补偿采样过程的特征损失以及减少模型训练的动态内存占用,自编码器采用多尺度渐进式结构,并在其解码器不同尺度的上采样层之后加入剪枝层。为了扩展本文网络的适用范围,设计了基于几何信息的点云颜色压缩方法,以保留点云全局颜色特征。结果 针对几何信息压缩,本文网络在MVUB（Microsoft voxelized upper bodies）、8iVFB（8i voxelized full bodies）和Owlii（Owlii dynamic human mesh sequence dataset）3个数据集上与其他5种方法进行比较。相对MPEG（moving picture experts group）提出的点云压缩标准V-PCC（video-based point cloud compression）,BD-Rate（bjontegaard delta rate）分别增加了41%、54%和33%。本文网络的编码运行时间与G-PCC（geometry-based point cloud compression）相当,仅为V-PCC的2.8%。针对颜色信息压缩,本文网络在低比特率下的YUV-PSNR（YUV peak signal to noise ratio）性能优于G-PCC中基于八叉树的颜色压缩方法。结论 本文网络在几何压缩和颜色压缩上优于主流的点云压缩方法,能在速率较小的情况下保留更多原始点云信息。     

基于三维点云模型的特征线提取算法

针对以往算法存在无法区分尖锐和非尖锐特征点、提取的特征点与视角有关、特征点未连线等问题, 提出一种基于高斯映射和曲率值分析的三维点云模型尖锐特征线提取算法。该算法先进行点云数据点的离散高斯映射, 并将映射点集聚类; 然后使用自适应迭代过程得到两个或多个面的相交线上曲率值和法向量发生突变的尖锐特征点, 这些点与视角无关; 最后, 用改进的特征折线生长算法, 将特征点连接, 得到光顺特征线。实验证明, 该算法具有良好的自适应性、抗噪性和准确性, 是一种有效的三维模型特征线提取算法。     

Deep Learning for Robust Normal Estimation in Unstructured Point Clouds

Normal estimation in point clouds is a crucial first step for numerous algorithms, from surface reconstruction and scene understanding to rendering. A recurrent issue when estimating normals is to make appropriate decisions close to sharp features, not to smooth edges, or when the sampling density is not uniform, to prevent bias. Rather than resorting to manually‐designed geometric priors, we propose to learn how to make these decisions, using ground‐truth data made from synthetic scenes. For this, we project a discretized Hough space representing normal directions onto a structure amenable to deep learning. The resulting normal estimation method outperforms most of the time the state of the art regarding robustness to outliers, to noise and to point density variation, in the presence of sharp edges, while remaining fast, scaling up to millions of points.     

Feature Preserving Point Set Surfaces based on Non-Linear Kernel Regression

Moving least squares (MLS) is a very attractive tool to design effective meshless surface representations. However, as long as approximations are performed in a least square sense, the resulting definitions remain sensitive to outliers, and smooth-out small or sharp features. In this paper, we address these major issues, and present a novel point based surface definition combining the simplicity of implicit MLS surfaces [ SOS04 , Kol05 ] with the strength of robust statistics. To reach this new definition, we review MLS surfaces in terms of local kernel regression, opening the doors to a vast and well established literature from which we utilize robust kernel regression. Our novel representation can handle sparse sampling, generates a continuous surface better preserving fine details, and can naturally handle any kind of sharp features with controllable sharpness. Finally, it combines ease of implementation with performance competing with other non-robust approaches.     

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。     

An adaptive normal estimation method for scanned point clouds with sharp features

Normal estimation is an essential task for scanned point clouds in various CAD/CAM applications. Many existing methods are unable to reliably estimate normals for points around sharp features since the neighborhood employed for the normal estimation would enclose points belonging to different surface patches across the sharp feature. To address this challenging issue, a robust normal estimation method is developed in order to effectively establish a proper neighborhood for each point in the scanned point cloud. In particular, for a point near sharp features, an anisotropic neighborhood is formed to only enclose neighboring points located on the same surface patch as the point. Neighboring points on the other surface patches are discarded. The developed method has been demonstrated to be robust towards noise and outliers in the scanned point cloud and capable of dealing with sparse point clouds. Some parameters are involved in the developed method. An automatic procedure is devised to adaptively evaluate the values of these parameters according to the varying local geometry. Numerous case studies using both synthetic and measured point cloud data have been carried out to compare the reliability and robustness of the proposed method against various existing methods.     

Fast and Robust Normal Estimation for Point Clouds with Sharp Features

This paper presents a new method for estimating normals on unorganized point clouds that preserves sharp features. It is based on a robust version of the Randomized Hough Transform (RHT). We consider the filled Hough transform accumulator as an image of the discrete probability distribution of possible normals. The normals we estimate corresponds to the maximum of this distribution. We use a fixed‐size accumulator for speed, statistical exploration bounds for robustness, and randomized accumulators to prevent discretization effects. We also propose various sampling strategies to deal with anisotropy, as produced by laser scans due to differences of incidence. Our experiments show that our approach offers an ideal compromise between precision, speed, and robustness: it is at least as precise and noise‐resistant as state‐of‐the‐art methods that preserve sharp features, while being almost an order of magnitude faster. Besides, it can handle anisotropy with minor speed and precision losses.     

结合多尺度与可变形卷积的自监督图像特征点提取网络

特征点提取是图像处理领域的一个重要方向,在视觉导航、图像匹配、三维重建等领域具有广泛的应用价值。基于卷积神经网络的特征点提取方法是目前的主流方法,但由于传统卷积层的感受野大小不变、采样区域的几何结构固定,在尺度、视角和光照变化较大的情况下,特征点提取的精度和鲁棒性较差。为解决以上问题提出了一种结合多尺度与可变形卷积的自监督特征点提取网络。本文以L2-NET为网络骨干,在深层网络中引入多尺度卷积核,增强网络的多尺度特征提取能力,获得细粒度尺度信息的特征图;使用单应矩阵约束的可变形卷积以提取不规则的特征区域,同时降低运算量,并采用归一化约束单应矩阵的求解,均衡不同采样点对结果的影响,配合在网络中增加的卷积注意力机制和坐标注意力机制,提升网络的特征提取能力。文章在HPatches数据集上进行了对比试验和消融实验,与R2D2等7种主流方法进行对比,本文方法的特征点提取效果最好,相比于次优数据,特征点重复度指标（Rep）提升了约1%,匹配分数（M.s.）提升了约1.3%,平均匹配精度（MMA）提高了约0.4%。本文提出的方法充分利用了可变形卷积提供的深层信息,融合了不同尺度的特征,使特征点提取结果更加准确和鲁棒。     

Bilateral normal filtering for mesh denoising

Decoupling local geometric features from the spatial location of a mesh is crucial for feature-preserving mesh denoising. This paper focuses on first order features, i.e., facet normals, and presents a simple yet effective anisotropic mesh denoising framework via normal field denoising. Unlike previous denoising methods based on normal filtering, which process normals defined on the Gauss sphere, our method considers normals as a surface signal defined over the original mesh. This allows the design of a novel bilateral normal filter that depends on both spatial distance and signal distance. Our bilateral filter is a more natural extension of the elegant bilateral filter for image denoising than those used in previous bilateral mesh denoising methods. Besides applying this bilateral normal filter in a local, iterative scheme, as common in most of previous works, we present for the first time a global, noniterative scheme for an isotropic denoising. We show that the former scheme is faster and more effective for denoising extremely noisy meshes while the latter scheme is more robust to irregular surface sampling. We demonstrate that both our feature-preserving schemes generally produce visually and numerically better denoising results than previous methods, especially at challenging regions with sharp features or irregular sampling.     

Shape classification and normal estimation for non-uniformly sampled, noisy point data

We present an algorithm for robustly analyzing point data arising from sampling a 2D surface embedded in 3D, even in the presence of noise and non-uniform sampling. The algorithm outputs, for each data point, a surface normal, a local surface approximation in the form of a one-ring, the local shape (flat, ridge, bowl, saddle, sharp edge, corner, boundary), the feature size, and a confidence value that can be used to determine areas where the sampling is poor or not surface-like.We show that the normal estimation out-performs traditional fitting approaches, especially when the data points are non-uniformly sampled and in areas of high curvature. We demonstrate surface reconstruction, parameterization, and smoothing using the one-ring neighborhood at each point as an approximation of the full mesh structure.     

用于三维点集形状模型的水印算法

对定义在一系列无方向点集上的3D形状模型提出一种新的数字水印方案。首先应用神经网络的方法对点集模型进行学习,根据在学习过程中神经网格法线的变化情况,找到特征点。最后对已加水印的点集模型应用不同的攻击,比如剪切、（模拟）简化和附加随在特征点附近嵌入水印信息机噪声之后,结果显示通过这种方案嵌入的水印,在某种程度上仍可以被检测到。     

Robust normal estimation and region growing segmentation of infrastructure 3D point cloud models

Modern remote sensing technologies such as three-dimensional (3D) laser scanners and image-based 3D scene reconstruction are in increasing demand for applications in civil infrastructure design, maintenance, operation, and as-built construction verification. The complex nature of the 3D point clouds these technologies generate, as well as the often massive scale of the 3D data, make it inefficient and time consuming to manually analyze and manipulate point clouds, and highlights the need for automated analysis techniques. This paper presents one such technique, a new region growing algorithm for the automated segmentation of both planar and non-planar surfaces in point clouds. A core component of the algorithm is a new point normal estimation method, an essential task for many point cloud processing algorithms. The newly developed estimation method utilizes robust multivariate statistical outlier analysis for reliable normal estimation in complex 3D models, considering that these models often contain regions of varying surface roughness, a mixture of high curvature and low curvature regions, and sharp features. An adaptation of Mahalanobis distance, in which the mean vector and covariance matrix are derived from a high-breakdown multivariate location and scale estimator called Deterministic MM-estimator (DetMM) is used to find and discard outlier points prior to estimating the best local tangent plane around any point in a cloud. This approach is capable of more accurately estimating point normals located in highly curved regions or near sharp features. Thereafter, the estimated point normals serve a region growing segmentation algorithm that only requires a single input parameter, an improvement over existing methods which typically require two control parameters. The reliability and robustness of the normal estimation subroutine was compared against well-known normal estimation methods including the Minimum Volume Ellipsoid (MVE) and Minimum Covariance Determinant (MCD) estimators, along with Maximum Likelihood Sample Consensus (MLESAC). The overall region growing segmentation algorithm was then experimentally validated on several challenging 3D point clouds of real-world infrastructure systems. The results indicate that the developed approach performs more accurately and robustly in comparison with conventional region growing methods, particularly in the presence of sharp features, outliers and noise.