一种基于凸包近似的快速体积计算方法

体积是物体的基本几何属性,在许多应用场合需要频繁地被计算。目前基本上通过重构物体曲面而间接求取体积,增加了许多不必要的工作。提出一种快速求取点云模型体积的方法,使用增量式算法计算点云的凸包用来近似物体,将凸包分解成上下两个三角网格面,使用正投影法分别求取它们的投影体积,它们两者之差即是所求模型体积。实验表明该算法实现简单,可快速地求解处理具有任何几何和拓扑复杂性的点云模型。     

Visible neighborhood graph of point clouds

In this paper we present a new neighborhood graph definition of point clouds, called visible neighborhood graph. A local construction scheme using visibility information near each sample point is developed, and the neighbors are defined based on a convex hull computation in a dual space. Our method is able to approximate the underlying surface on which the point cloud was sampled, and can provide accurate neighborhoods in regions of close-by surface sheets. The theoretical guarantees of our method are proved, and the accuracy and efficiency of the graph are verified by experimental results. Its usefulness for applications such as geodesic computation and point cloud segmentation is also demonstrated.     

Incorporating object-centered sampling and Delaunay tetrahedrization for visual hull reconstruction

In this paper we present a novel shape from silhouette algorithm. For an object to be modeled, the algorithm first computes a cloud of points located on a pencil of rays and distributed evenly on the visual hull surface, inside and outside the visual hull. Then Delaunay tetrahedrization is applied to the point cloud to partition its convex hull into a set of tetrahedrons. Finally, outlier tetrahedrons are removed by tetrahedron peeling, and a mesh model of the visual hull is extracted. The algorithm is robust, free from discretization artifacts, and produces a mesh model composed of well-shaped triangles.     

图像点模式匹配的一种凸包序列的图谱方法

利用点集的凸包具有仿射不变性和局部可控性,针对图谱方法难以精确匹配旋转角度较大图像的问题,提出了图像点模式匹配的一种凸包序列的图谱方法,使得匹配在图像旋转角度较大的情形下仍具有稳定性。构建图像特征点集新的图模型（凸包）,利用改进的图谱方法对凸包进行匹配,并减小原始特征点集,迭代上述过程,通过构造凸包序列,自特征点集的外围到内部逐步匹配,得到较精确的匹配对。实现基于凸包序列的图谱方法的图像点模式匹配。实验结果表明,该方法不但能精确匹配旋转角度较小的图像,而且对于旋转角度大的图像以及多光谱图像匹配精度也较高。     

基于凸壳与有向包围盒的骨架提取方法

为获取三维模型的几何及拓扑信息,提出一种基于凸壳与有向包围盒(OBB)的线性骨架提取方法.首先将三维网格模型进行分割生成多个子网格模型;然后对各子网格中的点集求取凸壳作为该子网格点集的近似,由凸壳顶点的形心构成原始骨架点;再用OBB进行重叠计算求出相交点集,以生成关节骨架点;最后对原始骨架点与关节骨架点进行连接,经冗余检测后形成完整骨架.实验结果表明,该方法快速、有效,提取出的骨架能保证连通性与中心性且能很好地提取关节骨架点,为蒙皮关节动画、模型形状分析等提供有效信息.     

An efficient algorithm for minimum zone flatness based on the computation of the largest inscribed ball in a symmetric polyhedron

This paper presents an algorithm for the minimum zone flatness tolerance of a finite point set, which is defined to be the minimum Euclidean distance between two parallel planes that sandwich the point set. The algorithm is based on the observation that the flatness tolerance is equal to the radius of the largest inscribed ball in the convex hull of the Minkowski difference of the point set and itself, which is a symmetric polyhedron with respect to the origin. Then, an iterative procedure is developed to adaptively grow another symmetric polyhedron inside the convex hull of the Minkowski difference such that the radius of its inscribed ball monotonically increases and converges to the flatness tolerance. The algorithm is guaranteed to compute the globally minimum solution within finite iterations. Moreover, there is no need to compute the Minkowski difference or the convex hull of the point set, so the proposed algorithm is very fast and takes only several milliseconds for hundreds of thousands of points on a normal computer, such as a desktop computer with an Intel Xeon 3.70 GHz CPU and 16GB RAM used in this work.     

平面点集凸包快速构建算法的研究

文章提出了一种提高构建凸包速度的新方法。该算法生成一个网格来管理离散点,在淘汰明显不位于凸包上的点时,将对离散点的取舍转换为对格的取舍,计算工作量只与离散点的范围及网格的密度有关,与离散点的数目无关;同时对点集也进行了初略的排序。在求取剩余点集的凸包时,采用了一种先分段求取凸包边界,最后将这些边界合并成凸包的方法,该方法充分利用了剩余点集所具有的有序性。     

基于点云数据的单木三维绿量估算方法

针对不同树种的树叶疏密及空间结构不同,提出基于激光点云数据,顾及冠层叶面积密度的树木三维绿量（Living Vegetation Volume, LVV）计算方法。该方法首先根据树木局部点云的主方向相似度和局部点云轴向分布密度分离枝干与树叶,剔除非光合作用成分,提取树叶点云;然后建立体元模型,引入Graham算法确定分层树冠边界,获取激光接触频率,从而基于体元冠层分析（Voxel-based Canopy Profiling, VCP）方法求出冠层叶面积密度（Leaf Area Density, LAD）;最后分层棱柱体积乘以叶面积密度,累加得到树木的三维绿量。利用Riegl VZ-400地面激光扫描仪获取13棵不同形状和树种的树木点云数据,利用该方法估算各树木三维绿量,并与传统的凸包法和台积法的结果对比。实验结果表明,台积法计算的三维绿量值最大,凸包法计算的三维绿量次之,顾及冠层叶面积密度的树木三维绿量方法计算的三维绿量值最小,为台积法的36.69%,为凸包法的47.80%。相比传统方法,顾及冠层叶面积密度的树木三维绿量计算方法侧重光合作用组分叶片点云的统计,并考虑了树冠内部树叶分布情况,更符合树木的实际情况,能充分利用三维点云数据特性,反映树冠内部三维绿量分布。     

基于有序简单多边形的平面点集凸包快速求取算法

凸包问题是计算几何的基本问题之一，在许多领域均有应用。传统平面点集凸包算法和简单多边形凸包算法平行发展，互不相干。本文将改进的简单多边形凸包算法应用于平面点集凸包问题中，提出了新的点集凸包算法。该算法首先淘汰掉明显不位于凸包上的点，然后对剩余点集排序，再将点集按照一定顺序串联成有序简单多边形，最后利用前瞻回溯方法搜索多边形凸包，从而得到点集的凸包。本文算法不仅达到了Ｏ的理论时间复杂度下限，而且算法     

改进的三维点集凸包求取算法

为提高三维点集凸包的求取效率,提出充分利用凸包极值点和性质改进的三维点集凸包求取算法.首先,求出三维点集中的极值点,并由它们形成初步凸包;其次,根据初步凸包与点的位置关系,排除其内部点;最后,依次考察其外部点,求出符合要求的点集、棱边集和面集,并对凸包进行扩展,得到凸包的点集、棱边集和面集.与普通算法进行时间的复杂度分析比较及实验表明,该算法效率较高.     

基于凸壳技术求解二维点集对称轴的方法

通过物体的对称性,人们可以推断物体的结构并估计它的形状,从而恢复被遮挡或丢失部分的信息。针对二维点集,提出了一种新的求解信息完整和不完整点集对称轴的方法。首先根据凸壳算法求出点集的凸壳,对于信息完整点集,点集的对称轴必是凸壳的对称轴,因此可以借助求解凸壳的对称轴来求解点集的对称轴;对于信息不完整点集,当遗失的点为凸壳内部点时,点集的对称轴也必为凸壳对称轴,当凸壳上的点有遗失时,则可通过求凸壳边的中垂线,以及长度相等两邻边组成角的角平分线来确定点集的对称轴。该方法解决了现有算法只能求解封闭和信息完整图形的对称轴的不足,实验结果表明该方法是高效、可行的。     

Volumetric stereo and silhouette fusion for image-based modeling

This paper presents a volumetric stereo and silhouette fusion algorithm for acquiring high quality models from multiple calibrated photographs. Our method is based on computing and merging depth maps. Different from previous methods of this category, the silhouette information is also applied in our algorithm to recover the shape information on the textureless and occluded areas. The proposed algorithm starts by computing visual hull using a volumetric method in which a novel projection test method is proposed for visual hull octree construction. Then, the depth map of each image is estimated by an expansion-based approach that returns a 3D point cloud with outliers and redundant information. After generating an oriented point cloud from stereo by rejecting outlier, reducing scale, and estimating surface normal for the depth maps, another oriented point cloud from silhouette is added by carving the visual hull octree structure using the point cloud from stereo to restore the textureless and occluded surfaces. Finally, Poisson Surface Reconstruction approach is applied to convert the oriented point cloud both from stereo and silhouette into a complete and accurate triangulated mesh model. The proposed approach has been implemented and the performance of the approach is demonstrated on several real data sets, along with qualitative comparisons with the state-of-the-art image-based modeling techniques according to the Middlebury benchmark.     

平面点集凸壳的快速算法

提出一种计算平面点集凸壳的快速算法。利用极值点划分出四个矩形,它们包含了所有凸壳顶点,通过对矩形中的点进行扫描,排除明显不是凸壳顶点的点,剩余的点构成一个简单多边形。再利用极点顺序法判断多边形顶点的凹凸性并删除所出现的凹顶点,最终得到一个凸多边形即为点集的凸壳。整个算法简洁明了,避免了乘法运算（除最坏情况外）,从而节省计算时间。     

利用正负划分性求平面点集凸包的最优算法

求平面点集的凸包是计算几何的一个基本算法。目前的算法较多,但这些算法均较复杂,为降低算法复杂性,首先从分析直线的正负划分性入手,利用其来对平面点集进行分类,以简化点到直线的距离计算;然后进一步详细地给出了一种改进的求平面任意散乱点集凸包的新算法。该算法在搜索凸包时,较目前流行的算法中所采用的前瞻回溯法既简单又速度快,该算法较传统的算法更是优越,尤其他不需要计算角度和欧氏距离。结果表明,利用该算法求任意平面散乱点集凸包不仅计算准确,而且计算过程中仅仅用到加、减、乘、比较运算。这样不仅使算法的每一步骤的时间复杂性大大降低,而且也使得整个算法的时间复杂性大大降低。经过分析,该算法也是一个最优的算法。     

基于最大基线倾角智能逼近的凸壳新算法

本文评述了有代表性的折半分治递归凸壳算法,并利用同构化凸壳基本定理提出效率更高的最大倾角智能逼近凸壳新算法。本新算法的同构化特点是：1）找出给定二维点集最外点（指最左、最右、最高、最低点）,即其X轴、Y轴坐标值最大、最小的四个初始极点;2）用该初始极点,把原二维点集分布域划分为四个子分布域;3）分别在这四个子分布域中,各基于自身最新所得极点依次动态构造其基线倾角最大的当前极点,并用这些极点作凸边,来逐步智能逼近和最终生成该给定二维点集的凸壳。     

Dynamics and balance of a humanoid robot during manipulation tasks

In this paper, we analyze the balance of a humanoid robot during manipulation tasks. By defining the generalized zero-moment point (GZMP), we obtain the region of it for keeping the balance of the robot during manipulation. During manipulation, the convex hull of the supporting points forms the 3-D convex polyhedron. The region of the GZMP is obtained by considering the infinitesimal displacement and the moment about the edges of the convex hull. We show that we can determine whether or not the robot may keep balance for several styles of manipulation tasks, such as pushing and pulling an object. The effectiveness of our proposed method is demonstrated by simulation.     

论二维点集或线段集凸壳生成算法改进与优化的同构化方向

本文指出了迄今为止的现行二维点集或线段集（包括：多边形、封闭折线、半封闭折线、开放线段集等）凸壳生成算法的共同弱点;提出了可改进与优化凸壳算法的同构化凸壳构造基本定理。进而,基于同构化凸壳构造基本定理,阐明了有限二维点集或线段集凸壳生成算法改进与优化的同构化方向,应当是：第一,使凸壳极点（或称顶点）分布域极小化,即让包含凸壳极点的判定区域尽可能小;使极点判定对象直接化,即让所判定对象尽可能接近当前所寻极点。第二,尽力对有可改造潜力的优秀串行凸壳算法施以并行化改造和创新。     

基于双域双向水平倾角最小化圈绕的凸壳新算法

本文依据同构化凸壳构造基本定理,提出效率更高的双域双向水平倾角最小化圈绕凸壳新算法.本新算法的同构化特点是:1)"初始顶点与双域生成"处理:找出给定二维点集S的最低点和最高点,即Y轴坐标值最小点(若有多个最小点,则只取最左的最小点)和Y轴坐标值最大点(若有多个最大点,则只取最左的最大点),作为凸壳(逆时针围绕的)A向初始顶点、(顺时针圈绕的)B向初始顶点;并以这两个初始顶点为端点的线段,把原二维点集划分为两个独立的子点集S右、S左.2)在S右内,进行双向"圈绕寻找下一新顶点"即凸壳A向、B向最新顶点寻找处理:分别过自己的最近新顶点,作X轴正向射线,并A向或B向找出当前点集内对该顶点正向射线(为始边的)倾角最小的点;删除对已得各顶点所构成的子凸壳内点,当所剩当前点集非空时继续作"2)"逐边圈绕,直到为空.3)同理,在子点集S左内,进行双向"圈绕寻找下一新顶点"即凸壳A向、B向最新顶点寻找处理.     

基于区域正交化分割的平面点集凸包算法EI北大核心CSCD

为解决实际工程应用中具有超大规模的平面点集的凸包计算问题,提出了一种基于点集所在区域正交化分割的新算法.利用点集几何结构的部分极点对平面点集进行正交化分割,以获取不相干的点集子集簇,再对所有点集子集分别计算其凸包极点,最后合并极点得到凸包点集.在不同层级的正交化分割过程中,根据已知极点的信息,逐层舍去对于凸包极点生成没有贡献的无效点,进而提高算法运行效率.在与目前常用凸包算法的对比实验中,该算法处理超大规模的平面点集时稳定性高且速度更快.