Topology-Aware Surface Reconstruction for Point Clouds

We present an approach to incorporate topological priors in the reconstruction of a surface from a point scan. We base the reconstruction on basis functions which are optimized to provide a good fit to the point scan while satisfying predefined topological constraints. We optimize the parameters of a model to obtain a likelihood function over the reconstruction domain. The topological constraints are captured by persistence diagrams which are incorporated within the optimization algorithm to promote the correct topology. The result is a novel topology-aware technique which can (i) weed out topological noise from point scans, and (ii) capture certain nuanced properties of the underlying shape which could otherwise be lost while performing surface reconstruction. We show results reconstructing shapes with multiple potential topologies, compare to other classical surface construction techniques, and show the completion of real scan data.     

A Neural Network Based System for Efficient Semantic Segmentation of Radar Point Clouds

Neural Processing Letters - The last decade has witnessed important advancements in the field of computer vision and scene understanding, enabling applications such us autonomous vehicles. Radar is...     

稠密采样点模型的快速隐式曲面重建

算法以稠密采样点模型表面局部区域内的双边滤波函数值为依据,模型表面附近任意一点的函数值通过与该点最近的模型表面的K个采样点数据直接计算得到。与已有的隐式曲面重建方法相比,该方法既不用曲面内部或外部的支撑点,也不用求解线性和非线性方程,其重建速度快。此外,由于采用双边滤波函数作为其重建的隐式曲面的函数值,因此还能对带有噪声的采样点模型进行特征保持的表面重建。实验结果表明,对于稠密采样点模型,该方法可以快速重建出逼近程度高,效果好的曲面。     

A Survey of Surface Reconstruction from Point Clouds

The area of surface reconstruction has seen substantial progress in the past two decades. The traditional problem addressed by surface reconstruction is to recover the digital representation of a physical shape that has been scanned, where the scanned data contain a wide variety of defects. While much of the earlier work has been focused on reconstructing a piece‐wise smooth representation of the original shape, recent work has taken on more specialized priors to address significantly challenging data imperfections, where the reconstruction can take on different representations—not necessarily the explicit geometry. We survey the field of surface reconstruction, and provide a categorization with respect to priors, data imperfections and reconstruction output. By considering a holistic view of surface reconstruction, we show a detailed characterization of the field, highlight similarities between diverse reconstruction techniques and provide directions for future work in surface reconstruction.     

Robust Segmentation of Multiple Intersecting Manifolds from Unoriented Noisy Point Clouds

We present a method for extracting complex manifolds with an arbitrary number of (self‐) intersections from unoriented point clouds containing large amounts of noise. Manifolds are formed in a three‐step process. First, small flat neighbourhoods of all possible orientations are created around all points. Next, neighbourhoods are assembled into larger quasi‐flat patches, whose overlaps give the global connectivity structure of the point cloud. Finally, curved manifolds are extracted from the patch connectivity graph via a multiple‐source flood fill. The manifolds can be reconstructed into meshed surfaces using standard existing surface reconstruction methods. We demonstrate the speed and robustness of our method on several point clouds, with applications in point cloud segmentation, denoising and medial surface reconstruction.     

尖锐特征诱导的点云自动分片算法

点云模型的分片技术是数字几何处理领域的基础技术之一.提出一种尖锐特征诱导的点云模型自动分片算法.算法首先计算点云模型的局部微分属性,并以此来识别模型上的尖锐特征点;然后采用改进的折线生长算法生成并完善特征折线,并基于特征折线采用三次B样条曲线来逼近的尖锐特征点;最后采用区域生长方法将点云模型分割成多个几何特征单一、边界整齐的点云数据面片.实验表明,本文算法运行稳定,可以准确地分割点云模型.该算法可用于点云模型的形状匹配、纹理映射、CAD建模、以及逆向工程等应用中.     

Binary Orientation Trees for Volume and Surface Reconstruction from Unoriented Point Clouds

Given a complete unoriented point set, we propose a binary orientation tree (BOT) for volume and surface representation, which roughly splits the space into the interior and exterior regions with respect to the input point set. The BOTs are constructed by performing a traditional octree subdivision technique while the corners of each cell are associated with a tag indicating the in/out relationship with respect to the input point set. Starting from the root cell, a growing stage is performed to efficiently assign tags to the connected empty sub‐cells. The unresolved tags of the remaining cell corners are determined by examining their visibility via the hidden point removal operator. We show that the outliers accompanying the input point set can be effectively detected during the construction of the BOTs. After removing the outliers and resolving the in/out tags, the BOTs are ready to support any volume or surface representation techniques. To represent the surfaces, we also present a modified MPU implicits algorithm enabled to reconstruct surfaces from the input unoriented point clouds by taking advantage of the BOTs.     

曲面重构中点云数据的区域分割研究

在曲面重构中，由于实际的曲面模型往往含有多个曲面几何特征，即由多张曲面组成，如果对使用激光法测量的“点云”数据直接进行拟合，将会造成曲面模型的数学表示和拟合算法处理的难度加大，甚至无法用较简单的数学表达式描述曲面模型，因此针对该问题，提出了一种基于数据点曲率变化的区域分割方法，即先对每一条扫描线上的数据点求取曲率值，然后将其中曲率值变化较大的点提取出来作为边界点，当边界确定后，再将云点数据分割成多个区域，由于每个区域一般具有较简单的几何特征，因此可用简单的数学模型来描述，并可重构单张曲面。该算法不仅原理简单、易于理解和编程，而且能提高曲面模型重构效率。     

隐式T样条实现封闭曲面重建

为了简化法向偏差约束条件和优化光滑能量项,提出一种隐式T样条曲面重建算法.首先利用八叉树及其细分过程从采样点集构造三维T网格,以确定每个控制系数对应的混合函数;然后基于隐式T样条曲面建立目标函数,利用偏移曲面点集控制法向,采用广义交叉检验(GCV)方法估计最优光滑项系数,并依据最优化原理将该问题转化为线性方程组求解得到控制系数,从而实现三角网格曲面到光滑曲面的重建.在误差较大的区域插入控制系数进行T网格局部修正,使得重建曲面达到指定精度.该算法使重建曲面C1连续条件得到松弛,同时给出最优的光顺项系数估计,较好地解决了封闭曲面的重建问题.实例结果表明,文中算法逼近精度高,运算速度快,仿真结果逼真.     

Robust and Efficient Surface Reconstruction From Range Data

We describe a robust but simple algorithm to reconstruct a surface from a set of merged range scans. Our key contribution is the formulation of the surface reconstruction problem as an energy minimisation problem that explicitly models the scanning process. The adaptivity of the Delaunay triangulation is exploited by restricting the energy to inside/outside labelings of Delaunay tetrahedra. Our energy measures both the output surface quality and how well the surface agrees with soft visibility constraints. Such energy is shown to perfectly fit into the minimum s ? t cuts optimisation framework, allowing fast computation of a globally optimal tetrahedra labeling, while avoiding the “shrinking bias” that usually plagues graph cuts methods. The behaviour of our method confronted to noise, undersampling and outliers is evaluated on several data sets and compared with other methods through different experiments: its strong robustness would make our method practical not only for reconstruction from range data but also from typically more difficult dense point clouds, resulting for instance from stereo image matching. Our effective modeling of the surface acquisition inverse problem, along with the unique combination of Delaunay triangulation and minimum s ? t cuts, makes the computational requirements of the algorithm scale well with respect to the size of the input point cloud.     

一种隐式曲面多相图像分割的变分水平集模型

隐式曲面上的图像处理,与曲面的性状和特征息息相关,运用多个函数标记不同区域来进行图像分割计算量大。针对上述问题首先借助遥感图像提出了一种隐式曲面构建方式,利用图像中的高程数据来构建山体曲面模型,进而计算山体区域的曲面面积。其次将基于一个水平集函数的多相图像分割的模型推广到隐式曲面上,并设计了相应的交替方向乘子法,通过求解一个函数的极值实现对图像多个区域的分割,最后多个数值实验对该方法和模型的高效性和鲁棒性进行了验证。     

隐曲面重建的极性场模型方法

通过隐函数拟合实现曲面重建是计算机图形学领域中一项重要而有挑战性的工作.受经典物理学中极性场模型及扩展点集思想的启发,提出一种称为"场拟合"的隐曲面重建方法.该方法将三维曲面表达为极性场的零等值面,极性场由许多粒子对产生,则曲面重建过程就转化为求粒子分布的过程,使用一种贪婪算法求解粒子的分布.实验结果表明,采用文中的场拟合方法的重建结果优于已有的隐曲面重建方法.     

点云数据集的隐式曲面重构研究进展

点云数据的曲面重建就是对扫描设备获得的物体散乱数据点重建三维物体表面,它被广泛应用于计算机动画、目标识别、数据可视化以及地理信息系统。点云的隐式曲面重建由于能够去除点云噪声,修补孔洞和裂缝,不需要拼接和平滑等后续处理,成为点云数据集曲面重构的重要方法。文中综述了目前一些主要的隐式曲面重构方法,就隐式模型以及相应的曲面重构算法的优缺点进行了分析比较,并对隐式曲面重构存在的问题和未来发展方向作了相应的分析和讨论。     

基于图像分割的三维重构

三维重构方法是医学图像可视化系统、治疗计划系统的重要技术。基于图像分割的三维重构方法结合了图像分割、等值面抽取、网格简化三种技术,是不同于传统Marching Cubes算法的一种三维重构方法。它首先将医学图像分割为二值图,然后利用Marching Cubes方法进行等值面抽取,最后对得到的网格模型进行简化。实验结果表明,基于图像分割的三维重构方法加快了Marching Cubes的运算速度,改善了重构的效果,有利于实现对基于三维重构的大型几何模型的实时绘制和交互。     

面向PET图像重建的结构先验导引的自适应点云方法

正电子发射断层成像(PET)重建的核心是解决重建精度和重建速度的问题.针对传统重建方法中以PET符合计数值表达待求图像的每个点像素值的规则点表达框架的问题,提出利用结构先验导引的自适应点云表达待求图像的点云表达框架的方法,从而可在保证重建精度的条件下有效地提高重建速度.该方法采用两步布点的方法引入点云表达框架:第一步基...     

Smoothing of Partition of Unity Implicit Surfaces for Noise Robust Surface Reconstruction

We propose a novel method for smoothing partition of unity (PU) implicit surfaces consisting of sets of non-conforming linear functions with spherical supports. We derive new discrete differential operators and Laplacian smoothing using a spherical covering of PU as a grid-like data structure. These new differential operators are applied to the smoothing of PU implicit surfaces. First, Laplacian smoothing is performed for the vector field defined by the gradient of the PU implicit surface, which is then updated to reflect the smoothing of the gradient field. This process achieves a method for noise robust surface reconstruction from scattered points.     

VASE: Volume‐Aware Surface Evolution for Surface Reconstruction from Incomplete Point Clouds

Objects with many concavities are difficult to acquire using laser scanners. The highly concave areas are hard to access by a scanner due to occlusions by other components of the object. The resulting point scan typically suffers from large amounts of missing data. Methods that use surface‐based priors rely on local surface estimates and perform well only when filling small holes. When the holes become large, the reconstruction problem becomes severely under‐constrained, which necessitates the use of additional reconstruction priors. In this paper, we introduce weak volumetric priors which assume that the volume of a shape varies smoothly and that each point cloud sample is visible from outside the shape. Specifically, the union of view‐rays given by the scanner implicitly carves the exterior volume, while volumetric smoothness regularizes the internal volume. We incorporate these priors into a surface evolution framework where a new energy term defined by volumetric smoothness is introduced to handle large amount of missing data. We demonstrate the effectiveness of our method on objects exhibiting deep concavities, and show its general applicability over a broader spectrum of geometric scenario.     

近似刚性的快速点云变形算法

针对大规模的复杂点云模型,提出了一种非线性变形算法.通过保持局部邻域的刚性使得点云模型进行近似刚性的变形,在大尺度变形时有效地保持几何细节和体积;为了保证求解过程的收敛性,对原始点云进行聚类,快速生成其简化点云,进而在稀疏的简化点云上完成变形,并将该变形作用给原始点云以得到合理的初始结果.此外,还给出一种动态重采样方法,以消除变形造成的冗余点和裂缝.实验结果和对比数据表明,文中算法简单高效,能够防止几何细节的扭曲和明显的体积变化,获得了令人满意的变形效果.     

三维重建中点云模型与纹理图像的配准

研究三维立体图像优化问题,实现高真实度的纹理图.由于立体图像重建过程产生累加误差,影响匹配精度.目前半自动和自动纹理贴图中三维扫描数据与高分辨率纹理图像对应点配准精度低、计算量大.为解决上述问题,在标准ICP(Iterative Closest Point)算法的基础上,提出一种改进的LM-ICP 2D和3D配准算法.通过法向量内积加权的最近点迭代,动态更新特征对应,减小误匹配点对配准精度的影响,并利用LM(Levenberg-Marquardt)算法优化投影矩阵.采用真实数据进行仿真.实验表明,提出的算法能得到精度高、真实性强的匹配图像效果,为设计提供参考.     

基于散乱点集的曲面重建

基于散乱点集的曲面重建是计算机图形学和虚拟现实等领域的研究热点.在对基于散乱点集的曲面重建经典算法进行综述的基础上,较详细地讨论了基于成长型神经网络的曲面重建方法和基于法向量场的曲面重建方法.