A surface reconstruction algorithm for topology optimization

For mechanical structural design, topology optimization is often utilized. During this process, a topologically optimized model must be converted into a parametric CAD solid model. The key point of conversion is that a discretized shape of a topologically optimized model must be smoothed, but features such as creases and corners must be retained. Thus, a surface reconstruction algorithm to produce the parametric CAD solid model from a topologically optimized model is proposed in this paper. Our presented algorithm consists of three parts: (1) an enclosed isosurface geometry from which the topologically optimized model is generated, (2) features detected and (3) the parametric CAD solid model reconstructed as biquartic surface splines. In order to generate an enclosed isosurface model effectively, we propose an algorithm based upon the marching cubes method to detect elements intersected by an isosurface. After generating an enclosed isosurface model, we produce biquartic surface splines. By applying our algorithm to an enclosed isosurface model, it is possible to produce smoothed biquartic surface splines with features retained. Some examples are shown and the effectiveness of our algorithm is discussed in this paper.     

多尺度图割曲面重建算法

针对图割曲面重建算法计算量过大的难题, 根据代数多栅理论对图割计算过程进行多尺度分解, 仅对最后一级进行最大流计算, 其他级的标记值通过插值得到。首先, 根据点云法向和重建曲面法向的一致性构建能量函数; 其次, 将能量函数映射到三维权重图的顶点和边上; 然后, 定义顶点间的一致性并由此构造抽取矩阵, 以决定哪些图的顶点参与图割运算; 之后, 构造插值矩阵, 将最后一级图割计算结果逐级插值到第一级; 最后, 利用步进立方体算法得到重建曲面的三角网格表示。实验结果表明, 与窄带图割算法相比, 本方法计算速度更快, 当图的顶点数越多时速度提高得越多; 对于不均匀采样的点云数据, 重建效果更好; 其他情况下两者效果相当。     

面向非均匀采样点集的3维表面重建算法

针对非均匀采样点集,提出一种改进的3维表面重建方法。该方法将整个点集进行空间划分,缩小近邻点的搜索范围,减少搜索时间;在确定近邻点时,先计算几何近邻点,然后通过求方向性点并构造最小生成树的方法,确定拓扑近邻点;最后通过将拓扑近邻点投影到局部切平面上,利用约束条件对投影点进行三角剖分,并将剖分得到的顶点连接关系映射到3维空间中,实现3维表面重建。实验结果表明,改进后的算法运行效率高、重建效果好、广泛适用于非均匀采样点集的表面重建。     

A new mesh-growing algorithm for fast surface reconstruction

This paper presents a new high-performance method for triangular mesh generation based on a mesh-growing approach. Starting from a seed triangle, the algorithm grows the triangular mesh by selecting a new point based on the Gabriel 2—Simplex criterion. This criterion can be considered to be a good approximation of the 2D Delaunay if the point cloud is well-sampled and not too rough. The performance of the proposed method is compared with that of the Cocone family and that of Ball Pivoting as regards the tessellation rate and the quality of the surface being generated from some benchmark point clouds and artificially noised test cases. The results are analysed and critically discussed.     

A greedy Delaunay-based surface reconstruction algorithm

In this paper, we present a new greedy algorithm for surface reconstruction from unorganized point sets. Starting from a seed facet, a piecewise linear surface is grown by adding Delaunay triangles one by one. The most plausible triangles are added first and in such a way as to prevent the appearance of topological singularities. The output is thus guaranteed to be a piecewise linear orientable manifold, possibly with boundary. Experiments show that this method is very fast and achieves topologically correct reconstruction in most cases. Moreover, it can handle surfaces with complex topology, boundaries, and nonuniform sampling.     

三维散乱点云快速曲面重建算法

提出了一种基于Delaunay三角剖分的三维散乱点云快速曲面重建算法。算法首先计算点云的Delaunay三角剖分, 从Delaunay四面体提取初始三角网格, 根据Voronoi体元的特征构造优先队列并生成种子三角网格, 然后通过区域生长的方式进行流形提取。实验结果表明, 该算法可以高效、稳定地重构具有复杂拓扑结构、非封闭曲面甚至是非均匀采样的点云数据。与传统的基于Delaunay的方法比较, 该算法仅需要进行一次Delaunay三角剖分, 无须极点的计算, 因此算法的重构速度快。     

A novel rapid point-cloud surface reconstruction algorithm for laser imaging radar

In order to obtain the fast three-dimensional surface reconstruction from given scattered point clouds, a novel improved point-cloud surface reconstruction algorithm for laser imaging radar is proposed so as to reconstruct the three-dimensional depth surface from the depth data and image data in this paper. Firstly, the three-dimensional space is partitioned into voxels with local distance points and finds outliers with point histogram features; then the Gaussian process (GP) regression is adopted to generate a plane similar to a Gaussian distribution; finally, the high-resolution gray data and three-dimensional interpolation points are fused by using Markov random fields to build a dense three-dimensional depth surface. Experimental results show that our proposed algorithm will greatly improve the robustness and reconstruction accuracy of three-dimensional surface reconstruction algorithm and can be used to assist unmanned driving in complex urban scenes.

     

三维空间散乱点集快速曲面重建的研究与实现

提出了一种快速曲面重建方法。针对Power crust算法提出一种不均匀降采样技术,根据曲面的局部特征大小对采样点进行削减,从而在不破坏原曲面拓扑特性的情况下,使参与曲面重建的采样点数目降低。实验结果表明,改进后的算法运行效率有所提高。     

基于快速Delaunay三角化的散乱点曲面重建算法

针对现有三维重建算法速度较慢的问题,提出了一种基于快速Delaunay三角化的散乱数据点的三维重建算法。首先,提出一种新的平面Delaunay三角化插入点目标三角形定位算法,利用插入点的方向搜索线与三角形是否相交以及交点个数加速目标三角形定位,不用额外判断点是否在三角形内;其次,自动检测曲面漏洞,利用凸壳的边界拼接方法进行漏洞弥补。实验结果表明,本算法不仅能较好地重建出三维模型,而且有较高的效率。     

基于RBF神经网络的点云数据曲面重建快速算法

在分析现有重构方法局限性的基础上,给出了一种基于神经网络的点云数据重构三维网格形状的快速算法。首先对点云数据进行归一化处理;然后进行特征线提取,并以特征线为基础对曲面进行分割。该方法能直接从神经网络的权值矩阵得到曲线的控制顶点或曲面的控制网格,通过神经网络的权值约束实现曲线段或曲面片之间的连接。实验结果表明,使用该方法能快速获得形状良好的网格曲面。     

基于Delaunay剖分的心内膜表面动态三维重建算法

心内膜表面三维重建技术在三维标测系统起着手术导航和靶点定位的作用。针对心内科手术中实时采集的散乱心内膜点云,提出了一种基于Delaunay剖分的表面动态三维重建算法。以CGAL非递归方式实现的逐点插入计算Delaunay剖分算法为基础,在剖分过程中,用关联采样点的伞局部替换原来表面中不满足Gabriel准则表面面片的集合,心内膜表面结构随着点云Delaunay剖分的变化而进行动态地更新。同时为了有效地表达心内膜表面及其点云的Delaunay剖分,并能够快速地索引四面体网格和表面三角面片,提出了一种以vtkDataArray为基础的几何数据结构。最后,实验表明该方法在重建结果和重建时间上可以满足心内科手术中的临床应用。     

A pointwise smooth surface stereo reconstruction algorithm without correspondences

This paper describes an algorithm for 3D reconstruction of a smooth surface with a relatively dense set of self-similar point features from two calibrated views. We bypass the usual correspondence problem by triangulating a point in space from all pairs of features satisfying the epipolar constraint. The surface is then extracted from the resulting point cloud by taking advantage of the statistical and geometric properties of the point distribution on the surface. Results are presented for computer simulations and for a laboratory experiment on a silicon gel phantom used in a breast cancer screening project.     

GPU Local Triangulation: an interpolating surface reconstruction algorithm

A GPU capable method for surface reconstruction from unorganized point clouds without additional information, called GLT (GPU Local Triangulation), is presented. The main objective of this research is the generation of a GPU interpolating reconstruction based on local Delaunay triangulations, inspired by a pre‐existing reconstruction algorithm. Current graphics hardware accelerated algorithms are approximating approaches, where the final triangulation is usually performed through either marching cubes or marching tetrahedras. GPU‐compatible methods and data structures to perform normal estimation and the local triangulation have been developed, plus a variation of the Bitonic Merge Sort algorithm to work with multi‐lists. Our method shows an average gain of one order of magnitude over previous research.     

基于边界检测的三维散乱点快速曲面重建算法

针对Power Crust算法提出一种带边界检测的不均匀降采样算法。曲面重建前先通过该算法减少参与运算的采样点,表面特征丰富的区域削减的采样点数远小于特征不丰富的区域,再进行曲面重建。通过实例表明该算法大大加快了散乱点数据的重建速度,而且很好地保持了模型表面的特征,能够较为真实地重建出曲面模型。     

动态调节圆半径曲面重建算法的改进

为实现对散乱数据点划分三角形网格的曲面重建,克服实体表面存在阶跃边缘而难以确定圆半径的问题,改进用动态调节圆半径产生三角形网格并实现曲面重建的算法,将散乱数据点转化为二维图像数据,并进行三角形网格划分.实验结果表明,虽然改进算法效率有所下降,但对表面存在阶跃边缘的实体有较好的重建效果.     

月面地形重构系统中的并行Delaunay算法设计

三角剖分过程是影响三维重建系统实时性的瓶颈之一,为提高三角剖分速度,基于共享内存多核计算机设计并实现了并行Delaunay算法。该算法在分治三角剖分算法的基础上,通过改进子三角网归并过程及Delaunay三角网优化过程避免了并行计算中的数据竞争问题。利用月面仿真实验场真实地形数据在50万到500万不同规模的点云数据集上进行了实验,加速比最高可达6.44。除此之外,对算法复杂度、加速比以及并行效率进行了全面分析,并将算法实际应用于月面地形重构系统,实现了虚拟地形的快速构建。     

三维物体表面重建的分支处理算法研究

根据平面点集Delaunay三角剖分的特性,将Delaunay三角剖分应用到分支问题上,改进和实现了一种分支问题处理算法。将相邻层轮廓线投影到同一个剖面上形成一个带约束边的平面点集,并将它们Delaunay三角化,根据这些三角形组来生成新的轮廓线,使轮廓线一一对应。实验结果表明该算法实现的效果较符合实际情况,能有效地处理各种不同情况。     

Implicit meshes for surface reconstruction

Deformable 3D models can be represented either as traditional explicit surfaces, such as triangulated meshes, or as implicit surfaces. Explicit surfaces are widely accepted because they are simple to deform and render, but fitting them involves minimizing a nondifferentiable distance function. By contrast, implicit surfaces allow fitting by minimizing a differentiate algebraic distance, but are harder to meaningfully deform and render. Here, we propose a method that combines the strength of both approaches. It relies on a technique that can turn a completely arbitrary triangulated mesh, such as one taken from the Web, into an implicit surface that closely approximates it and can deform in tandem with it. This allows both automated algorithms to take advantage of the attractive properties of implicit surfaces for fitting purposes and people to use standard deformation tools they feel comfortable for interaction and animation purposes. We demonstrate the applicability of our technique to modeling the human upper-body, including face, neck, shoulders, and ears, from noisy stereo and silhouette data.     

Generalized reconstruction algorithm for compressed sensing

Compressed sensing (CS) is considered as a promising signal processing technique, and successful applications of the CS theory depend mainly on the accuracy and speed of the reconstruction algorithms. In this paper, a generalized objective functional, which has been developed using the combinational estimation and an extended stabilizing functional, is proposed. An efficient iterative scheme, which integrates the beneficial advantages of the homotopy method, the shuffled frog-leaping (SFL) algorithm and the harmony search (HS) algorithm, is designed for searching a possible global optimal solution. Numerical simulations are implemented to evaluate the numerical performances and effectiveness of the proposed algorithm. Excellent numerical performances and encouraging results are observed. For the cases considered in this paper, a dramatic improvement in the reconstruction accuracy is achieved, which indicates that the proposed algorithm is a promising candidate for solving CS inverse problem.     

Computational topology for isotopic surface reconstruction

New computational topology techniques are presented for surface reconstruction of 2-manifolds with boundary, while rigorous proofs have previously been limited to surfaces without boundary. This is done by an intermediate construction of the envelope   (as defined herein) of the original surface. For any compact C²$C^2$-manifold M$M$ embedded in R³${\mathbf{R}}^3$, it is shown that its envelope is C^1,1$C^{1,1}$. Then it is shown that there exists a piecewise linear (PL) subset of the reconstruction of the envelope that is ambient isotopic to M$M$, whenever M$M$ is orientable. The emphasis of this paper is upon the formal mathematical proofs needed for these extensions. (Practical application examples have already been published in a companion paper.) Possible extensions to non-orientable manifolds are also discussed. The mathematical exposition relies heavily on known techniques from differential geometry and topology, but the specific new proofs are intended to be sufficiently specialized to prompt further algorithmic discoveries.