一种人体三维Reeb图计算方法

提出一种人体三维Reeb计算方法。利用人体三维网格数据的顶点坐标,求取顶点的测地距离,构造Morse函数,依据顶点的三角面关系提取人体三维模型的Reeb图,给出基于Reeb图的一般人体骨架结构表示。通过计算Reeb图上弧的曲率,判断是否需要增加关节节点,从而能更准确地描述人体三维模型的拓扑结构。实验结果表明,该方法计算量小、适用性广。     

三维人体点云模型多约束肢体分割

针对人体点云模型的肢体分割这一动作识别和虚拟重建领域的重要问题,提出了一种基于分类骨架线、测地距离、特征点和姿态分析的多约束肢体分割算法,通过生成点云模型的分类骨架线,配合测地距离获得人体各部位粗分割点云集,利用测地路径方法实现关键特征点的定位,并利用曲线拟合方式进行定位优化,针对头颈、上肢、下肢和躯干之间关联部位的解剖学特征,构造多种约束条件,对各部位粗分割点云集进行了优化再分割。实验结果表明,所提算法对站姿条件下的不同动作、不同体型、不同精度人体点云模型均能取得与视觉理解相吻合的分割效果。通过该算法得到的肢体各部分点云数据可用于姿态分析等后续研究。     

基于骨架的网格模型变形

现有骨架驱动变形算法多以单一骨架驱动变形,且骨架预设十分复杂。为此,提出一种基于骨架的网格模型变形算法。结合多分辨率Reeb图方法提取模型的骨架结构,确定各骨架点对应的局部区域,将骨架点插值构造二次Bézier曲线,通过交互式拖动任意骨架点,计算与其相连多骨架点的动态变化情况,实现模型局部区域的自然形变。实验结果表明,该算法能获得较为自然平滑的变形结果。     

一种基于模型分割的三维人体骨架提取方法

针对当前三维骨架提取方法复杂度较高、提取结果不够准确,以及专门针对人体模型的方法较少等问题,提出一种基于模型分割的三维人体骨架提取方法。首先,根据模型顶点与末端特征点的最小测地距离将模型分割;然后由归一化的测地距离函数确定模型各顶点所属拓扑层次;接着在模型分割的基础上依据拓扑层次提取出原始骨架点;最后经过微调,将各骨架点按照拓扑关系连接得到较为精确的人体骨架。实验结果表明,该方法有效降低了骨架提取算法的复杂度,且对不同姿势的人体模型均可获得较为准确的提取结果。     

基于整数中轴骨架的3维模型检索算法

针对3维模型检索算法性能较低的问题,提出了一种基于整数中轴骨架的3维模型检索算法。在对3维模型进行姿态调整和各向同向性预处理后,提取模型的整数中轴骨架,并记录每个骨架点相应的几何信息,对提取的骨架按不同的空间区域划分,形成模型骨架二叉树。为了能够描述骨架二叉树的不同节点对模型整体相似性匹配的影响程度,为每个节点定义一个特征权值,其大小由该节点对应的骨架区域大小所决定。最后,采用由粗到细逐步淘汰的策略计算不同模型的相似度。对一个标准3维模型测试数据库的检索实验结果表明,由于将模型的拓扑结构和统计特征相结合,该算法可以得到较好的检索性能。     

保特征的点云骨架提取算法

三维模型的骨架提取是计算机图形学中一个重要的研究方向。对于有噪声的点云模型,曲线骨 架提取的难点在于保持正确的拓扑结构以及良好的中心性;对于无噪声的点云模型,曲线骨架提取的难点在于 对模型细节特征的保留。目前主流的点云骨架提取方法往往无法同时解决这 2 个难点。算法在最优传输理论的 基础之上结合聚类的思想,将点云骨架提取的问题转化为一个最优化问题。首先使用最优传输得到原始点云与 采样点云之间的传输计划。然后使用聚类的思想将原始点云进行分割,采样点即成为了簇的中心。接着通过簇 与簇之间的调整与合并减少聚类个数,优化聚类结果。最后通过迭代的方式得到粗糙的骨架并使用插点操作进 行优化。大量实验结果表明,该算法在有噪声与无噪声的三维点云模型上均能提取出质量良好的曲线骨架并保 留模型的特征。     

一种改进的基于特征点求解的骨架提取算法

基于特征点求解和Reeb图思想,实现了一种新的骨架提取算法。首先求取模型特征点集,以特征点为计算依据,根据三角网格中每个顶点与特征点的不同对应关系得到网格分支点,聚合成一系列骨架点,依据骨架点携带的拓扑信息,连接拓扑相邻的骨架点得到模型骨架。采用了改进的特征点提取算法,其时间复杂度由O（n^3）提高到了O（n^2log（n））,实验表明算法能够快速提取骨架,针对一般模型的骨架提取效果令人满意。     

快速非刚体人体运动三维重建

为了实现基于单目深度传感器的快速非刚体人体运动三维重建,提出一种基于骨架的非刚体人体运动点云融合算法.首先利用分割的人体局部点云配准,对深度传感器提取的人体骨架进行修正,提高了骨架提取的准确性;当相邻2帧之间存在较大人体运动时,利用骨架驱动人体表面点云进行点云粗配准;在粗配准的基础上,利用非刚体点云融合算法进行点云的精细配准,得到精确的表面重建.实验结果表明,该算法能够鲁棒地重建快速非刚体三维人体运动.     

高斯曲率约束的MRG骨架提取优化算法

三维模型的骨架保持了模型的拓扑特性,并被广泛应用于模型相似性比较、计算机动画及压缩等领域.根据多分辨率Reeb图的原理,提出了一种基于离散高斯曲率约束的骨架提取优化算法.通过计算网格顶点的离散高斯曲牢判断曲面局部凸凹特性,以获取模型表面的双曲极值点作为约束点;并依据约束点及其邻域的μ函数值产生的分裂线进行区域细分,获得子连通区域、确定关节点、形成优化的骨架结构.实验结果表明,该算法有效地突出了模型的拓扑分支特征以及模型表面的细节,提高了骨架提取的精度和效率.     

自适应三维美工树木骨架提取算法

提出了一种自适应三维美工树木骨架提取算法。该算法主要由前处理、骨架提取和后处理三个步骤组成。前处理阶段依次完成预计算操作,包括对具有几何相似性的子枝进行聚类,自适应生成每个子枝点云的聚类长度阈值,确定子枝之间的父子关系等;骨架提取阶段实现对每个子枝点云的聚类,及其对应骨架点、骨架曲线的生成等操作;后处理阶段完成孤立骨架节点去除,整棵树所有骨架曲线光滑化等处理。该树木骨架提取过程完全由计算机自动完成,不需要用户的任何干预。实验结果表明,采用该算法得到的美工树木骨架既能完整地保持树木模型的形状,又能正确地实现树木模型的拓扑结构。     

约束方程能量最小化提取3维血管图像中轴线

3维血管中轴线提取是血管量化的第一步,同时也是最重要的一步。为此,提出一种动态提取3维血管图像中轴线的方法。首先构造具有3维血管特征的能量约束方程,通过细化方法或人工构造方式得到血管图像初始骨架线,在能量约束方程的作用下,沿着血管图像距离场梯度的方向不断向血管中轴线位置逼近。当方程能量达到最小值时,初始骨架线也就固定在中轴线位置。实验结果表明,提取出来的血管中轴线位置准确,且保持拓扑结构和连通性。     

Piecewise linear skeletonization using principal curves

Proposes an algorithm to find piecewise linear skeletons of handwritten characters by using principal curves. The development of the method was inspired by the apparent similarity between the definition of principal curves (smooth curves which pass through the "middle" of a cloud of points) and medial axes (smooth curves that run equidistantly from the contours of a character image). The central fitting-and-smoothing step of the algorithm is an extension of the polygonal line algorithm, which approximates principal curves of data sets by piecewise linear curves. The polygonal line algorithm is extended to find principal graphs and complemented with two steps specific to the task of skeletonization: an initialization method to capture the approximate topology of the character, and a collection of restructuring operations to improve the structural quality of the skeleton produced by the initialization method. An advantage of our approach over existing methods is that we optimize the skeleton graph by minimizing an intuitive and explicit objective function that captures the two competing criteria of smoothing the skeleton and fitting it closely to the pixels of the character image. We tested the algorithm on isolated handwritten digits and images of continuous handwriting. The results indicated that the proposed algorithm can find a smooth medial axis in the great majority of a wide variety of character templates and that it substantially improves the pixel-wise skeleton obtained by traditional thinning methods     

Skeletonization based on error reduction

The accuracy of a non-pixel-based skeletonization method is largely dependent on the contour information chosen as input. When using a Constrained Delaunay Triangulation to construct an object's skeleton, a number of contour pixels must be chosen as a basis for triangulation. This paper presents a new method of selecting these contour pixels. A new method for measuring skeletonization error is proposed, which quantifies the deviation of a skeleton segment from the true medial axis of a stroke in an image. The goal of the proposed algorithm is to reduce this error to an acceptable level, whilst retaining the superior efficiencies of previous non-pixel-based techniques. Experimental results show that the proposed method is adept at following the medial axis of an image, and is capable of producing a skeleton that is confirmed by a human's perception of the image. It is also computationally efficient and robust against noise.     

Computation of medial axis and offset curves of curved boundaries in planar domain

In this paper, we begin our research from the generating theory of the medial axis. The normal equidistant mapping relationships between two boundaries and its medial axis have been proposed based on the moving Frenet frames and Cesaro’s approach of the differential geometry. Two pairs of adjoint curves have been formed and the geometrical model of the medial axis transform of the planar domains with curved boundaries has been established. The relations of position mapping, scale transform and differential invariants between the curved boundaries and the medial axis have been investigated. Based on this model, a tracing algorithm for the computation of the medial axis has been generated. In order to get the accurate medial axis and branch points, a Two_Tangent_Points_Circle algorithm and a Three_Tangent_Points_Circle algorithm have been generated, which use the results of the tracing algorithm as the initial values to make the iterative process effective. These algorithms can be used for the computation of the medial axis effectively and accurately. Based on the medial axis transform and the envelope theory, the trimmed offset curves of curved boundaries have been investigated. Several numerical examples are given at the end of the paper.     

Total curvature variation fairing for medial axis regularization

We present a new fairing method for planar curves, which is particularly well suited for the regularization of the medial axis of a planar domain. It is based on the concept of total variation regularization. The original boundary (given as a closed B-spline curve or several such curves for multiply connected domains) is approximated by another curve that possesses a smaller number of curvature extrema. Consequently, the modified curve leads to a smaller number of branches of the medial axis. In order to compute the medial axis, we use the state-of-the-art algorithm from [1] which is based on arc spline approximation and a domain decomposition approach. We improve this algorithm by using a different decomposition strategy that allows to reduce the number of base cases from 13 to only 5. Moreover, the algorithm reduces the number of conic arcs in the output by approx. 50%.     

圆角化的图形区域直骨架及其算法

在直骨架定义的基础上提出了一种新的图形区域骨架,它仅包含直线边,在结构上比基于Voronoi图的圆骨架更简单,在区域形状描述上比直骨架更接近圆骨架;还提出了一种计算该骨架的算法,在原有直骨架算法的基础上加入了一个对边界凸点的圆角化的预处理过程,并且对实际计算中的特殊碰撞问题进行了处理,以提高计算的鲁棒性.实验结果表明了文中算法的鲁棒性和有效性.     

基于LeapMotion的个体化手部建模与实时交互

虚拟人手的实时建模是以人机交互为核心的VR/AR系统中的重要技术难点，传统的基于LeapMotion的手部跟踪视觉反馈仅展示骨架动画信息，缺少应用演示的真实感。由此，提出了一个快速高效的个体化手部建模与实时交互系统，重点阐述了该系统的的工作原理以及算法。以含有骨架信息的静止手模型为模板，使用LeapMotion跟踪用户手的骨架数据作为输入，提出了基于骨骼尺寸的手部模型自动个体化建模算法。提供了一种基于不完整骨骼运动数据的线性蒙皮技术的改进算法，可快速计算不同手部姿势下骨架之间的变换矩阵，动态更新虚拟手的姿势。实验结果表明，此系统在实验的硬件平台上运行速度可以达到60 f/s，误差稳定在4 mm以内，能为人机交互任务实时提供真实可靠的视觉反馈。     

基于最大偏差相似性准则的交通流聚类算法

针对常用聚类算法对随机性强、波动频繁的交通流聚类效果不理想的问题,提出了一种新的交通流相似性度量准则——最大偏差相似性准则,并提出了一种基于最大偏差相似性准则的交通流聚类算法。最大偏差相似性准则能够有效刻画频繁波动交通流曲线的形态相似性,具有简明、合理、灵活等特点;聚类算法无需预先指定类别数,能够保证类间曲线的明显差异性和类内曲线的高度相似性。实验表明,所提出的算法聚类效果明显优于常用聚类算法,聚类结果能够较好地满足实际应用的需要。     

Research on 3D medial axis transform via the saddle point programming method

The present paper investigates the 3D medial axis transform of objects bounded by freeform surfaces via the saddle point programming method, a mathematical programming approach used to identify the saddle points of a function. After exploring the local geometry and saddle point property of 3D medial axis transform, the mathematical programming method is employed to construct the saddle point programming models. Based on the optimality conditions that the optimal solutions should satisfy, a generic algorithm for computing various medial axis points is developed. In order to identify the junction points and localize the problem, the boundary and the skeletal curves are divided into skeletal segments, and it is proved to be efficient and accurate by numerical examples.