Combinatorial manifold mesh reconstruction and optimization from unorganized points with arbitrary topology

In this paper, a novel approach is proposed to reliably reconstruct the geometric shape of a physically existing object based on unorganized point cloud sampled from its boundary surface. The proposed approach is composed of two steps. In the first step, triangle mesh structure is reconstructed as a continuous manifold surface by imposing explicit relationship among the discrete data points. For efficient reconstruction, a growing procedure is employed to build the 2-manifold directly without intermediate 3D representation. Local and global topological operations with ensured completeness and soundness are defined to incrementally construct the 2-manifold with arbitrary topology. In addition, a novel criterion is proposed to control the growing process for ensured geometric integrity and automatic boundary detection with a non-metric threshold. The reconstructed manifold surface captures the object topology with the built-in combinatorial structure and approximates the object geometry to the first order. In the second step, new methods are proposed to efficiently obtain reliable curvature estimation for both the object surface and the reconstructed mesh surface. The combinatorial structure of the triangle mesh is then optimized by changing its local topology to minimize the curvature difference between the two surfaces. The optimized triangle mesh achieves second order approximation to the object geometry and can serve as a basis for many applications including virtual reality, computer vision, and reverse engineering.     

Implicit Surface-Based Geometric Fusion

This paper introduces a general purpose algorithm for reliable integration of sets of surface measurements into a single 3D model. The new algorithm constructs a single continuous implicit surface representation which is the zero-set of a scalar field function. An explicit object model is obtained using any implicit surface polygonization algorithm. Object models are reconstructed from both multiple view conventional 2.5D range images and hand-held sensor range data. To our knowledge this is the first geometric fusion algorithm capable of reconstructing 3D object models from noisy hand-held sensor range data.This approach has several important advantages over existing techniques. The implicit surface representation allows reconstruction of unknown objects of arbitrary topology and geometry. A continuous implicit surface representation enables reliable reconstruction of complex geometry. Correct integration of overlapping surface measurements in the presence of noise is achieved using geometric constraints based on measurement uncertainty. The use of measurement uncertainty ensures that the algorithm is robust to significant levels of measurement noise. Previous implicit surface-based approaches use discrete representations resulting in unreliable reconstruction for regions of high curvature or thin surface sections. Direct representation of the implicit surface boundary ensures correct reconstruction of arbitrary topology object surfaces. Fusion of overlapping measurements is performed using operations in 3D space only. This avoids the local 2D projection required for many previous methods which results in limitations on the object surface geometry that is reliably reconstructed. All previous geometric fusion algorithms developed for conventional range sensor data are based on the 2.5D image structure preventing their use for hand-held sensor data. Performance evaluation of the new integration algorithm against existing techniques demonstrates improved reconstruction of complex geometry.     

基于SOM的散乱数据点集的B样条曲面重建

利用自组织映射神经网络(SOM)技术对散乱数据点集进行B样条曲面重建时,往往存在网络学习时间过长和学习效果不理想等问题。提出了一种新的神经元初始化方法和分块学习算法,该算法首先运用主元素分析方法(PCA)对散乱数据进行分块,将拓扑结构为四边形的输出层神经元初始化在每块散乱数据的最小二乘平面上进行网络学习和训练,将分块学习得到的各网格曲面拼接成一个整体;然后对该整体网格曲面的边界和内部单独学习,得到一张逼近待重建曲面的双线性B样条曲面;最后对该B样条曲面误差进行了修正。实例证明,该算法可以明显地减少SOM网络学习时间,并改善网络学习效果。     

Three-dimensional surface reconstruction using meshing growing neural gas (MGNG)

The neural network method, a relatively new method in reverse engineering (RE), has the potential to reconstruct 3D models accurately and fast. A neural network (NN) is a set of interconnected neurons, in which each neuron is capable of making autonomous arithmetic and geometric calculations. Moreover, each neuron is affected by its surrounding neurons through the structure of the network. This work proposes a new approach that utilizes growing neural gas neural network (GNG NN) techniques to reconstruct a triangular manifold mesh. This method has the advantage of reconstructing the surface of an n-genus freeform object without a priori knowledge regarding the original object, its topology or its shape. The resulting mesh can be improved by extending the MGNG into an adaptive algorithm. The proposed method was also extended for micro-structure modeling. The feasibility of the proposed method is demonstrated on several examples of freeform objects with complex topologies.     

On surface reconstruction: A priority driven approach

To reconstruct an object surface from a set of surface points, a fast, practical, and efficient priority driven algorithm is presented. The key idea of the method is to consider the shape changes of an object at the boundary of the mesh growing area and to create a priority queue to the advancing front of the mesh area according to the changes. The mesh growing process is then driven by the priority queue for efficient surface reconstruction. New and practical triangulation criteria are also developed to support the priority driven strategy and to construct a new triangle at each step of mesh growing in real time. The quality and correctness of the created triangles will be guaranteed by the triangulation criteria and topological operations. The algorithm can reconstruct an object surface from unorganized surface points in a fast and reliable manner. Moreover, it can successfully construct the surface of the objects with complex geometry or topology. The efficiency and robustness of the proposed algorithm is validated by extensive experiments.     

基于DDPG的三维重建模糊概率点推理

单视图物体三维重建是一个长期存在的具有挑战性的问题. 为了解决具有复杂拓扑结构的物体以及一些高保真度的表面细节信息仍然难以准确进行恢复的问题, 本文提出了一种基于深度强化学习算法深度确定性策略梯度 (Deep deterministic policy gradient, DDPG)的方法对三维重建中模糊概率点进行再推理, 实现了具有高保真和丰富细节的单视图三维重建. 本文的方法是端到端的, 包括以下四个部分: 拟合物体三维形状的动态分支代偿网络的学习过程, 聚合模糊概率点周围点的邻域路由机制, 注意力机制引导的信息聚合和基于深度强化学习算法的模糊概率调整. 本文在公开的大规模三维形状数据集上进行了大量的实验证明了本文方法的正确性和有效性. 本文提出的方法结合了强化学习和深度学习, 聚合了模糊概率点周围的局部信息和图像全局信息, 从而有效地提升了模型对复杂拓扑结构和高保真度的细节信息的重建能力.     

一种基于投影的散乱数据表面增量重建算法

针对3维散乱数据场提出了一种表面重建算法.根据空间曲面的局平特性和平面三角化的基本原则,在参考点的切平面上对邻域点按角度排序,应用可见性准则删除不可见点后,相邻邻域点和参考点形成三角网格.将平面上的网格关系对应到空间,以增量方式重建反映散乱数据场拓扑关系的空间曲面.设定角度阈值优化网格,判断空间曲面的边界和孔洞.对多个数据场进行重建并对结果进行分析.对多个数据场进行重建并对结果进行分析表明,算法具有原理简单,重建速度快,重建效果好的特点.     

基于细分方法的破裂曲面重构

曲面重构是计算机图形学中一个基本问题.目前研究的热点集中于使用各种方法构建细分曲面,以及进行网格的优化等方面,但其核心是光滑连续曲面的重构.为了对破裂曲面有效重构,提出了一种基于细分的重建破裂曲面的方法,该方法先使用Loop细分曲面对目标曲面进行逼近,再自适应处理不连续部分的网格.这种方法在3维地震数据可视化中得到了较好的应用.     

面向点云三维重建的空间感知对抗神经网络

为了解决由原始点云数据局部密度稀疏、不均匀或者法向量错误等制约因素引起的重建网格质量问题,利用对抗神经网络中权重共享的特性和对抗的训练过程,提出一种基于对抗网络的点云三维重建方法。首先,利用预测器对网格模型边的偏移量进行预测,从而得到每一个顶点的位移,并进行拓扑保持的顶点重定向,得到新的网格模型。然后,利用判别器中的点云分类器,提取原始点云数据和网格模型表面采样点集的高维特征,并基于高维特征进行空间感知的判别,用于区分原始点云与采样点集数据。最后,使用对抗的训练方式将预测器与判别器的输出数据关联起来,通过多次迭代优化网络模型,从而得到满足点云空间特征的三维网格模型。在不同的点云数据集上进行实验,并使用MeshLab软件进行效果展示,结果表明,该方法能够重建出满足点云空间信息的三维网格模型,同时能够解决粗劣的点云数据引起的网格质量问题。     

Parallel and adaptive surface reconstruction based on implicit PHT-splines

We present a new surface reconstruction framework, which uses the implicit PHT-spline for shape representation and allows us to efficiently reconstruct surface models from very large sets of points. A PHT-spline is a piecewise tri-cubic polynomial over a 3D hierarchical T-mesh, the basis functions of which have good properties such as nonnegativity, compact support and partition of unity. Given a point cloud, an implicit PHT-spline surface is constructed by interpolating the Hermitian information at the basis vertices of the T-mesh, and the Hermitian information is obtained by estimating the geometric quantities on the underlying surface of the point cloud. We take full advantage of the natural hierarchical structure of PHT-splines to reconstruct surfaces adaptively, with simple error-guided local refinements that adapt to the regional geometric details of the target object. Examples show that our approach can produce high quality reconstruction surfaces very efficiently. We also present the multi-threaded algorithm of our approach and show its parallel scalability.     

一种基于三维Delaunay三角化的曲面重建算法

提出一种基于三维Delaunay三角化的区域增长式曲面重建方法。该方法以空间点云的Delaunay三角化为基础,结合局部区域增长的曲面构造,较以往方法具有人为参与更少、适用范围更广的优点。算法采用增量式插入点的方式构建空间Delaunay划分,采用广度优先算法,以外接圆最小为准则从Delaunay三角化得到的四面体中抽取出合适的三角片构成曲面。该算法的设计无须计算原始点集的法矢,且孔洞系数对重建的结果影响很小,重建出的三角网格面更符合原始曲面的几何特征。无论待建曲面是否是封闭曲面,本算法均可获得较好的重建效果。     

一种保持纹理的网面简化算法

在计算机视觉领域,三维网面的简化不仅要求保持物体形状和拓扑关系,还要求保持物体表面法线,纹理,颜色和边缘等物体特征,以使计算机视觉系统能有效地表示,描述,识别和理解物体和场景,为此讨论了一种基于边操作（边收缩,边分裂）,并具有颜色或灰度纹理特征保持的三维网面的简化算法,该算法将网面不对称最大距离作为形状改变测度,将邻域内颜色或灰度最大改变量作为纹理改变测试,从而在大量简化模型数据的同时,有效地保持了模型的几何形状,拓扑关系,颜色或灰度特征,以及网面顶点均匀分布。     

Generating 3D Faces using Multi‐column Graph Convolutional Networks

In this work, we introduce multi‐column graph convolutional networks (MGCNs), a deep generative model for 3D mesh surfaces that effectively learns a non‐linear facial representation. We perform spectral decomposition of meshes and apply convolutions directly in the frequency domain. Our network architecture involves multiple columns of graph convolutional networks (GCNs), namely large GCN (L‐GCN), medium GCN (M‐GCN) and small GCN (S‐GCN), with different filter sizes to extract features at different scales. L‐GCN is more useful to extract large‐scale features, whereas S‐GCN is effective for extracting subtle and fine‐grained features, and M‐GCN captures information in between. Therefore, to obtain a high‐quality representation, we propose a selective fusion method that adaptively integrates these three kinds of information. Spatially non‐local relationships are also exploited through a self‐attention mechanism to further improve the representation ability in the latent vector space. Through extensive experiments, we demonstrate the superiority of our end‐to‐end framework in improving the accuracy of 3D face reconstruction. Moreover, with the help of variational inference, our model has excellent generating ability.     

From A Medial Surface To A Mesh

Medial surfaces are well‐known and interesting surface skeletons. As such, they can describe the topology and the geometry of a 3D closed object. The link between an object and its medial surface is also intuitively understood by people. We want to exploit such skeletons to use them in applications like shape creation and shape deformation. For this purpose, we need to define medial surfaces as Shape Representation Models (SRMs). One of the very first task of a SRM is to offer a visualization of the shape it describes. However, achieving this with a medial surface remains a challenging problem. In this paper, we propose a method to build a mesh that approximates an object only described by a medial surface. To do so, we use a volumetric approach based on the construction of an octree. Then, we mesh the boundary of that octree to get a coarse approximation of the object. Finally, we refine this mesh using an original migration algorithm. Quantitative and qualitative studies, on objects coming from digital modeling and laser scans, shows the efficiency of our method in providing high quality surfaces with a reasonable computational complexity.     

OpenGL在逆向工程三维重构中的应用研究

研究了在MFC中运用OpenGL进行编程，重构三维物体的方法，对于逆向工程三维重构的杂乱离散点云，在进行排序重组和三角网格化后，运用OpenGL对三角网格进行消隐，设定法线，光照和材质的处理，重构原始物体，具体的应用实例说明了所提方法的有效性。     

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。     

海量数据的曲面分层重建算法

从二维图像序列进行表面重建的问题由来已久.传统的重建方法通常是先重建或先等值面抽取,再简化数据量.随着处理数据量的增长,传统算法的中间过程会因为存储空间的限制不能进行下去.如何利用有限的存储空间对大数据量进行处理,从而完成曲面的重建曾是要研究的问题.针对大数据量的已分割的医学切片图像,利用逐层重建、即时简化的基本思想,给出一个易于操作实现、数据量可控制的算法.这样可以在硬件条件不太高的计算机(如内存不太大的个人微机)上实现大数据量的医学图像表面重建.     

结合Delaunay 三角面分离法与搜索球策略的三维曲面重建算法

基于曲面重建在计算机图形学、三维GIS、逆向工程等领域有重要应用,结合区 域生长法与Delaunay 三角剖分的优势,提出了一种新的散乱点云曲面重建算法。首先根据曲面 中轴性质提出了分离角定义并推导了相关结论,利用局部Delaunay 三角形分离角性质抽取大量 位于模型表面三角形,从而构建种子三角网增加初始区域的生长面积其次运用自适应搜索球法 加快邻域三角形搜索并识别曲面边界。对比传统的基于Delaunay 法和传统区域生长法,该方法 只需要一次三角剖分,无需极点与法向量计算,重建速度快,具有Delaunay 三角网格的优良结 构特性,孔洞数量少,重建出的三维模型几何信息与拓扑关系准确。实验表明,结合Delaunay 三角剖分与区域生长法重构有向的流形三角网格模型,能够提高三维模型的重建效果与速度, 有效地自动识别曲面边界。     

A spherical representation for recognition of free-form surfaces

Introduces a new surface representation for recognizing curved objects. The authors approach begins by representing an object by a discrete mesh of points built from range data or from a geometric model of the object. The mesh is computed from the data by deforming a standard shaped mesh, for example, an ellipsoid, until it fits the surface of the object. The authors define local regularity constraints that the mesh must satisfy. The authors then define a canonical mapping between the mesh describing the object and a standard spherical mesh. A surface curvature index that is pose-invariant is stored at every node of the mesh. The authors use this object representation for recognition by comparing the spherical model of a reference object with the model extracted from a new observed scene. The authors show how the similarity between reference model and observed data can be evaluated and they show how the pose of the reference object in the observed scene can be easily computed using this representation. The authors present results on real range images which show that this approach to modelling and recognizing 3D objects has three main advantages: (1) it is applicable to complex curved surfaces that cannot be handled by conventional techniques; (2) it reduces the recognition problem to the computation of similarity between spherical distributions; in particular, the recognition algorithm does not require any combinatorial search; and (3) even though it is based on a spherical mapping, the approach can handle occlusions and partial views     

Generating subdivision surfaces from profile curves

The construction of freeform models has always been a challenging task. A popular approach is to edit a primitive object such that its projections conform to a set of given planar curves. This process is tedious and relies very much on the skill and experience of the designer in editing 3D shapes. This paper describes an intuitive approach for the modeling of freeform objects based on planar profile curves. A freeform surface defined by a set of orthogonal planar curves is created by blending a corresponding set of sweep surfaces. Each of the sweep surfaces is obtained by sweeping a planar curve about a computed axis. A Catmull-Clark subdivision surface interpolating a set of data points on the object surface is then constructed. Since the curve points lying on the computed axis of the sweep will become extraordinary vertices of the subdivision surface, a mesh refinement process is applied to adjust the mesh topology of the surface around the axis points. In order to maintain characteristic features of the surface defined with the planar curves, sharp features on the surface are located and are retained in the mesh refinement process. This provides an intuitive approach for constructing freeform objects with regular mesh topology using planar profile curves.