以优先点为中心的Delaunay三角网生长算法

目的 Delaunay三角网具备的优良性质使其得到广泛的应用,构建Delaunay三角网是计算几何的基础问题之一,为了高效、准确地构建大规模点集的Delaunay三角网,提出一种基于优先点的改进三角网生长算法.方法 算法以逆时针次序的一条凸包边为初始基边,使用基边对角最大化并按照逆时针次序选定第3点构建一个Delaunay三角形,通过待扩展边列表中的数据判断新生成的两条边是否需要扩展,采用先进先出的方式从待扩展边列表中取边作为基边,以优先点为中心构建局部Delaunay三角网使优先点尽快成为封闭点,再从点集中删除此封闭点.结果 对于同一测试点集,改进算法运行时间与经典算法运行时间的比率不超过1/3,且此比率随点集规模增长逐步下降.相比经典算法,改进算法在时间效率上有较大提升.结论 本文改进算法对点集规模具有较好的自适应性与较高的构网效率,可用于大规模场景下Delaunay三角网的构建.     

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。     

一种快速三维散乱点云的三角剖分算法

改进了一种三维散乱点云三角剖分算法。三角剖分是点云数据曲面重构的主要算法之一,但针对三维散乱点云的三角剖分存在剖分效率不高,剖分得到的三角曲面形状无法控制,细节特征表现不足的问题。提出了基于空间栅格划分的三角剖分算法,并提出了一个新的评价函数,以控制三角网格曲面的生长。实验证明,改进后的算法极大的提高了剖分效率,而且能保证最终生成的三角网格曲面平滑而保有丰富的细节特征,适用于在虚拟现实、曲面重构等领域推广使用。     

基于曲面局平特性的散乱数据拓扑重建算法

提出了一种基于曲面局平特性的,以散乱点集及其密度指标作为输入,以三角形分片线性曲面作为输出的拓扑重建算法.算法利用曲面的局平特性,从散乱点集三维Delaunay三角剖分的邻域结构中完成每个样点周围的局部拓扑重建,并从局部重建的并集中删除不相容的三角形,最终得到一个二维流形拓扑曲面集作为重建结果.该算法适应于包括单侧曲面在内的任意不自交的拓扑曲面集,并且重建结果是相对优化的曲面三角形剖分,可以应用于科学计算可视化、雕塑曲面造型和反求工程等领域.     

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.     

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。     

Feature‐Preserving Reconstruction of Singular Surfaces

Reconstructing a surface mesh from a set of discrete point samples is a fundamental problem in geometric modeling. It becomes challenging in presence of ‘singularities’ such as boundaries, sharp features, and non‐manifolds. A few of the current research in reconstruction have addressed handling some of these singularities, but a unified approach to handle them all is missing. In this paper we allow the presence of various singularities by requiring that the sampled object is a collection of smooth surface patches with boundaries that can meet or intersect. Our algorithm first identifies and reconstructs the features where singularities occur. Next, it reconstructs the surface patches containing these feature curves. The identification and reconstruction of feature curves are achieved by a novel combination of the Gaussian weighted graph Laplacian and the Reeb graphs. The global reconstruction is achieved by a method akin to the well known Cocone reconstruction, but with weighted Delaunay triangulation that allows protecting the feature samples with balls. We provide various experimental results to demonstrate the effectiveness of our feature‐preserving singular surface reconstruction algorithm.     

Delaunay三角网构建方法比较研究

Delaunay三角网构建是3维场景可视化领域的一个热点也是难点问题。归纳总结了现有Delaunay三角网构建研究中的3类方法——逐点插入法、三角网生长法和分治法,以及在各自原理框架下的不同实现算法;比较分析了3种不同方法的优缺点和各自代表性算法的时间复杂度,并详细讨论了Delaunay三角网构建方法在大规模场景渲染和地形可视化领域中未来3个研究方向：混合算法研究、算法支撑技术研究和分布式并行算法研究。     

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。     

An Experimental Study of Sliver Exudation

We present results on a two-step improvement of mesh quality in three-dimensional Delaunay triangulations. The first step refines the triangulation by inserting sinks and eliminates tetrahedra with large circumradius over shortest edge length ratio. The second step assigns weights to the vertices to eliminate slivers. Our experimental findings provide evidence for the practical effectiveness of sliver exudation. ID="A1" Correspondence and offprint requests to: H. Edelsbrunner, Department of Computer Science, Duke University, Box 90129, Durham, NC, USA     

基于Loose r-sample的网格质量保持技术

为保证虚拟手术系统中的网格质量,提出一种基于Loose r-sample理论的快速表面网格重建算法。记录满足Loose r-sample采样定理的点集,用以描述物体的轮廓。通过约束Delaunay方法对该点集进行三角化,标记顶点和Delaunay单元,重构新的网格。实验结果表明,该算法能够保证生成网格的质量,简化仿真复杂度。     

The conformal alpha shape filtration

Conformal alpha shapes are a new filtration of the Delaunay triangulation of a finite set of points in ℝ^d. In contrast to (ordinary) alpha shapes the new filtration is parameterized by a local scale parameter instead of the global scale parameter in alpha shapes. The local scale parameter conforms to the local geometry and is motivated from applications and previous algorithms in surface reconstruction. We show how conformal alpha shapes can be used for surface reconstruction of non-uniformly sampled surfaces, which is not possible with alpha shapes.     

A Delaunay-based region-growing approach to surface reconstruction from unorganized points

This paper presents a Delaunay-based region-growing (DBRG) surface reconstruction algorithm that holds the advantages of both Delaunay-based and region-growing approaches. The proposed DBRG algorithm takes a set of unorganized sample points from the boundary surface of a three-dimensional object and produces an orientable manifold triangulated model with a correct geometry and topology that is faithful to the original object. Compared with the traditional Delaunay-based approach, the DBRG algorithm requires only one-pass Delaunay computation and needs no Voronoi information because it improves the non-trivial triangle extraction by using a region-growing technique. Compared with the traditional region-growing methods, the proposed DBRG algorithm makes the surface reconstruction more systematic and robust because it inherits the structural characteristics of the Delaunay triangulation, which nicely complements the absence of geometric information in a set of unorganized points. The proposed DBRG algorithm is capable of handling surfaces with complex topology, boundaries, and even non-uniform sample points. Experimental results show that it is highly efficient compared with other existing algorithms.     

一个利用法矢的散乱点三角剖分算法

曲面上散乱点的三角剖分在曲面重建中发挥着重要作用,借助于曲面上的法矢信息和三维Delaunay三角剖分算法,该文给出了一种新的散乱点三角剖分算法,输入一组散乱点以及所在曲面S在这些散乱点处的一致定向的法矢信息,该算法将产生一张插值散乱点的三角网格曲面M,并且曲面M可以近似地看成是曲面S的三角剖分,算法的主要步骤分为两步：首先通过曲面S的一致定向的法矢信息,在曲面S的同一侧添加辅助点,利用这些辅助点来剔除Delaunay三角剖分中产生的不需要的三角片;然后将剩余的三角片连接成一张完整的网格曲面,与基于中轴的三角剖分算法相比,该文算法需要更少和更简单的计算,与局部三角剖分算法相比,该文算法可以更有效地避免重建后的曲面产生自交,该文的算法可用于任意拓扑的光滑曲面重建。     

Adaptive detection of spatial point event outliers using multilevel constrained Delaunay triangulation

Spatial outlier detection is a research hot spot in the field of spatial data mining. Because of the lack of specific research on spatial point events, this study presents an adaptive approach for spatial point events outlier detection (SPEOD) using multilevel constrained Delaunay triangulation. First, the spatial proximity relationships between spatial point events are roughly captured by Delaunay triangulation. Then, three-level constraints are described and used to refine spatial proximity relationships with the consideration of statistical characteristics. Finally, those spatial point events connected by remaining edges are gathered to form a series of subgraphs. Those subgraphs containing very few point events are regarded as spatial outliers. Experiments on both synthetic and real-world spatial data sets are used to show that the proposed SPEOD algorithm can detect various types of spatial point event outliers with high efficiency. Moreover, there is no need to input any parameter in SPEOD.     

A competitive study of the pseudoflow algorithm for the minimum <Emphasis Type="Italic">s</Emphasis>–<Emphasis Type="Italic">t</Emphasis> cut problem in vision applications

Rapid advances in image acquisition and storage technology underline the need for real-time algorithms that are capable of solving large-scale image processing and computer-vision problems. The minimum s–t cut problem, which is a classical combinatorial optimization problem, is a prominent building block in many vision and imaging algorithms such as video segmentation, co-segmentation, stereo vision, multi-view reconstruction, and surface fitting to name a few. That is why finding a real-time algorithm which optimally solves this problem is of great importance. In this paper, we introduce to computer vision the Hochbaum’s pseudoflow (HPF) algorithm, which optimally solves the minimum s–t cut problem. We compare the performance of HPF, in terms of execution times and memory utilization, with three leading published algorithms: (1) Goldberg’s and Tarjan’s Push-Relabel; (2) Boykov’s and Kolmogorov’s augmenting paths; and (3) Goldberg’s partial augment-relabel. While the common practice in computer-vision is to use either BK or PRF algorithms for solving the problem, our results demonstrate that, in general, HPF algorithm is more efficient and utilizes less memory than these three algorithms. This strongly suggests that HPF is a great option for many real-time computer-vision problems that require solving the minimum s–t cut problem.     

利用Voronoi协方差矩阵重建隐式曲面

目的 针对含少量离群点的噪声点云,提出了一种Voronoi协方差矩阵的曲面重建方法。方法 以隐函数梯度在Voronoi协方差矩阵形成的张量场内的投影最大化为目标,构建隐函数微分方程,采用离散外微分形式求解连续微分方程,从而将曲面重建问题转化为广义特征值求解问题。在点云空间离散化过程中,附加最短边约束条件,避免了局部空间过度剖分。并引入概率测度理论定义曲面窄带,提高了算法抵抗离群点能力,通过精细剖分曲面窄带,提高了曲面重建精度。结果 实验结果表明,该算法可以抵抗噪声点和离群点的影响,可以生成不同分辨率的曲面。通过调整拟合参数,可以区分曲面的不同部分。结论 提出了一种新的隐式曲面重建方法,无需点云法向、稳健性较强,生成的三角面纵横比好。     

A Note on Point Location in Delaunay Triangulations of Random Points

This short note considers the problem of point location in a Delaunay triangulation of n random points, using no additional preprocessing or storage other than a standard data structure representing the triangulation. A simple and easy-to-implement (but, of course, worst-case suboptimal) heuristic is shown to take expected time O(n ^1/3 ) . Received November 27, 1997; revised February 15, 1998.     

基于图片序列的三维表面重建

根据非透明物体内部不可见的实际,提出了一种基于图片序列的三维表面重建算法.该算法首先利用传统的八叉树算法重建出物体的三维模型,然后利用一种新颖的表面点提取算法提取出物体表面点,最后利用这些表面点进行三角网格剖分,进而重建出光滑的三维物体表面.在表面点的提取过程中,算法对处于不同状态(处于立方体的顶点、棱、面)的点赋予不...