融合形状特征的MRG骨架树三维检索方法

提出一种基于MRG骨架树的三维模型检索方法。根据多分辨率Reeb图(MRG)的原理,提取反映模型拓扑特征的Reeb图骨架并且映射成树形结构,分析了节点的拓扑属性。针对拓扑属性在形状特征上的表达能力不足,在节点相应区域提取离散曲率和面积比例描绘局部的形状特征。有效地结合了模型的拓扑特征和形状特征计算模型的相似度。该方法突出了模型的整体拓扑特征和形状特征,实验结果表明了该方法的高效性和鲁棒性。     

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。     

三角网格模型骨架提取算法

骨架图能够直观表达三维模型几何形状,很好地反映模型的拓扑特征,在工业机器人抓取、特征识别等领域有着广泛的应用。针对三角网格表达的工业零件给出一种骨架提取算法,该算法采用Reeb图对三角网格进行骨架的抽取运算。首先读取三角网格文件,并对复杂的三角网格进行简化处理,然后遍历所有的三角网格,采用Dijkstra算法抽取基本点集,根据定义的连续函数计算每个顶点的函数值,最后根据函数值得出模型的基本骨架。实验表明,该算法具有良好的计算效果和效率,提取出的骨架图较好地保存了三维模型拓扑结构和姿态,可作为后续研究三维模型搜索的特征描述符。     

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。     

关节特征约束的3维模型骨架提取算法

根据多分辨率Reeb图（MRG）的原理,提出一种基于关节特征约束的骨架优化算法。它克服了基于曲率约束提取骨架方法中逐点计算顶点的曲率约束轮廓的低效性,通过分析网格顶点的离散高斯曲率,获取模型表面上具有凹陷特性的双曲极值点作为约束点, 进行关节特征区域的有效提取。进而增加关节特性点,优化MRG骨架。实验结果表明,本方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。     

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.     

拓扑和形状特征相结合的三维模型检索

针对整体相似性检索算法在局部细节特征上的表达能力不足,提出了一种将拓扑和形状特征相结合的三维模型相似性比较方法.首先提取三维模型的骨架,获得模型的整体拓扑特征;然后根据骨架节点将模型分解为多个子部分,并利用球面谐波算法提取每一个子部分的形状特征.模型的匹配分为3步进行:整体骨架的拓扑特征相似性比较,相对应的子部分的局部形状特征相似性比较,模型总的相似性是整体骨架相似性与对应子部分局部形状相似性的加权和.实验结果表明:该方法从整体到局部、由粗到精,综合考虑了拓扑和形状特征,较传统的考虑单一拓扑或形状特征的检索算法有较高的检索精度,同时又支持基于局部特征的相似性检索.     

基于优化DRG的三维人体点云骨架提取方法

针对离散Reeb图（Discrete Reeb Graph,DRG）描述人体骨架时分支部位骨架线偏离中轴的问题,采用了能量函数最小化的方法对DRG曲线进行优化。将人体模型的DRG曲线作为初始骨架,定义其能量函数,在点云模型的距离场梯度的作用下,迭代地调整偏离中轴目标段的曲线位置使其逐渐逼近中轴,能量函数最小时得到优化的骨架。将该算法应用于同一模特四个不同姿势和四个不同模特同一姿势的人体点云模型,并与基于拉普拉斯算子的点云收缩的骨架提取方法进行了比较。结果表明,该算法能够很好地适应各种不同姿势和体型,模型分叉部位的特征得到更加完善的描述,得到的骨架曲线更接近模型的中轴。     

改进的多分辨率Reeb图骨架抽取算法

针对实际应用中的模型可能包含多个连通分量的情形,改进了多分辨率Reeb图中的骨架创建算法,并对多种不连通的模型进行了实验。生成的骨架可为三维检索提供特征描述符。     

交互式轮廓线骨架的提取

为精确抽取自由绘制的二维轮廓线骨架,提出了一种新的自适应骨架提取方法.将用户绘制的轮廓线,采用离散曲率约束,自适应调整步长,提取样点,进行最小二乘法实现样条曲线拟合,有效地突出了曲线形状特征;依据曲线模型的特征点,改进约束化三角剖分方法,高效地重建三角网格的拓扑结构;基于Voronoi图优化提取轮廓线骨架.实验结果表明了该算法的高效性和鲁棒性.     

Reeb graph path dissimilarity for 3D object matching and retrieval

We introduce a skeletal graph for topological 3D shape representation using Morse theory. The proposed skeletonization algorithm encodes a 3D shape into a topological Reeb graph using a normalized mixture distance function. We also propose a novel graph matching algorithm by comparing the relative shortest paths between the skeleton endpoints. Experimental results demonstrate the feasibility of the proposed topological Reeb graph as a shape signature for 3D object matching and retrieval.     

骨架驱动的三维模型变形方法

为发展三维网格模型的变形技术,研究了多种三维模型变形算法,通过对骨架驱动变形算法的深入研究,针对现行算法多是以单一骨架驱动变形的不足,提出了一种新的基于多骨架点驱动的交互式局部变形方法.有效结合模型的骨架图结构,确定各骨架点对应的局部区域.并将骨架点拟合为二次Bézier曲线,通过交互式拖动任意骨架点计算与之相连的多骨架点的动态变化,实现模型局部区域的自然形变.实验结果表明了该算法的有效性和直观性.     

Partial 3D Shape Retrieval by Reeb Pattern Unfolding

This paper presents a novel approach for fast and efficient partial shape retrieval on a collection of 3D shapes. Each shape is represented by a Reeb graph associated with geometrical signatures. Partial similarity between two shapes is evaluated by computing a variant of their maximum common sub-graph.
By investigating Reeb graph theory, we take advantage of its intrinsic properties at two levels. First, we show that the segmentation of a shape by a Reeb graph provides charts with disk or annulus topology only. This topology control enables the computation of concise and efficient sub-part geometrical signatures based on parameterisation techniques. Secondly, we introduce the notion of Reeb pattern on a Reeb graph along with its structural signature. We show this information discards Reeb graph structural distortion and still depicts the topology of the related sub-parts. The number of combinations to evaluate in the matching process is then dramatically reduced by only considering the combinations of topology equivalent Reeb patterns.
The proposed framework is invariant against rigid transformations and robust against non-rigid transformations and surface noise. It queries the collection in interactive time (from 4 to 30 seconds for the largest queries). It outperforms the competing methods of the SHREC 2007 contest in term of NDCG vector and provides, respectively, a gain of 14.1% and 40.9% on the approaches by Biasotti et al. [ BMSF06 ] and Cornea et al. [ CDS*05 ].
As an application, we present an intelligent modelling-by-example system which enables a novice user to rapidly create new 3D shapes by composing shapes of a collection having similar sub-parts.     

SkelTre

Terrestrial laser scanners capture 3D geometry of real world objects as a point cloud. This paper reports on a new algorithm developed for the skeletonization of a laser scanner point cloud. The skeletonization algorithm proposed in this paper consists of three steps: (i) extraction of a graph from an octree organization, (ii) reduction of the graph to a skeleton, and (iii) embedding of the skeleton into the point cloud. For these three steps, only one input parameter is required. The results are validated on laser scanner point clouds representing 2 classes of objects; first on botanic trees as a special application and secondly on popular arbitrary objects. The presented skeleton found its first application in obtaining botanic tree parameters like length and diameter of branches and is presented here in a new, generalized version. Its definition as Reeb Graph, proofs the usefulness of the skeleton for applications like shape analysis. In this paper we show that the resulting skeleton contains the Reeb Graph and investigate the practically relevant parameters: centeredness and topological correctness. The robustness of this skeletonization method against undersampling, varying point density and systematic errors of the point cloud is demonstrated on real data examples.     

Volume data mining using 3D field topology analysis

This article proposes a novel approach to automating the settings of visualization parameter values for volume data mining. To this end, we extended the conventional Reeb graph-based approach to topological modeling of 3D surfaces to capture the topological skeleton of a volumetric field. The analyzed results take the form of hyper Reeb graphs which give the basic reference structure for designing comprehensible volume visualization     

Constructing a Reeb graph automatically from cross sections

The Reeb graph represents the topological skeleton of a 3-D object and shows between which contours the surface patches should be generated. To construct the graph automatically, a weight function is defined for a pair of contours with each contour lying on the adjacent cross sections. First, the algorithm automatically generates the major parts of the edges of the Reeb graph where the number of contours does not change. Then the rest of the graph is determined by using the weight function and prior knowledge of the number of holes the object has. Specifically, the graph is completed by adding edges that do not contradict the known number of holes in descending order of the weight