基于曲线和曲面控制的多边形物体变形反走样

基于参数曲线和曲面控制的空间变形是重要的几何外形编辑和柔性物体动画实现手段．当这两类变形方法的对象是多边形物体时,如何对变形物体进行重采样以得到高质量结果,是计算机动画和几何造型领域中的一个重要问题．该文针对B-样条曲线和曲面控制的空间变形方法,提出了面向多边形物体的空间变形反走样方法．在该方法中,利用等距技术将B-样条曲线或曲面所张成的变形空间近似表示为张量积B-样条参数体,结合作者提出的多边形物体精确B-样条自由变形方法,实现了参数曲线和曲面控制的多边形物体变形反走样．     

基于微分不变量和区域增长法的深度图分割

用深度图(点云)直接对曲面物体进行识别,将会加大曲面物体的数学表示的难度。该文提出一种对深度图进行自动分割的方法,基于微分不变量进行初始分割,得到初始的核区域,用区域增长法进行曲面片增长,将深度图分割成多个区域。该算法原理简单、易于理解和编程。通过一个米老鼠头部深度图实例证明了该方法的有效性。     

基于Level Set算法的医学图像分割的研究与实现

提出了一种改进的结合基于阈值分割特点的Level Set方法.首先用滤波器对原始图像进行平滑,然后根据当前曲线找到区域的统计特性,最后根据区域之间的统计特性的相似度重新定义了Level Set方法的演化停止准则,从而提高了算法的准确性和自动性.实验结果表明,该方法具有较好的分割效果和较高的分割效率.     

结合快速步进法的Level Set人体足部图像分割

针对Level set算法运算速度较慢和易产生边缘泄露的不足,引入了结合快速步进的Level Set算法,提出了一套完整的分割人体足部骨骼图像技术路线.修正了原始"光切片"图像噪声多的不足,通过预处理去除噪声,增强边缘;设定分割初始点和运算参数,运行改进的Level set算法提取骨骼区域;运行形态学开操作进行边缘断裂和毛刺修复.实验结果表明,该处理流程具有较好的准确度和鲁棒性,与经典Level Set算法相比,改进的算法能提高19%～36%的运行速度.     

基于Level Set方法的曲线演化

Level Set方法是一种描述曲线以曲率相关的速度演化的有力工具,最近几年在医学图像处理、自然现象的模拟以及计算机视觉等领域得到了广泛的应用.其中,曲线演化后的平滑算法和轮廓跟踪方法是Level Set方法实际应用中的两个关键算法.给出了一种平滑Level Set距离函数的简单方法.该方法只采用内插值的方式,消除平面上的全部孤立点以及部分可能产生歧义的点,在允许存在部分冗余点的情况下,利用曲线轮廓跟踪算法,得到平面上所有曲线的轮廓.经过实验验证,该方法简单、高效,适应范围广.     

点云模型自适应增加采样点算法

提出一种新的点集模型自适应增加啊采样算法.算法利用最小二乘法求出点云模型上每个点的局部光滑曲面片,并由所求得的曲面多项式计算点集曲面上每个点的曲率.通过对每个点及其邻点进行Voronoi剖分,求取每个点所控制的有效采样区域,然后根据曲率在有效区域内建立采样栅格,求取有效区域内的栅格点在曲面上的投影点即为新增采样点.该方法得到的增加采样模型可以较好地保持原点云模型曲面的几何性质,同时还可以通过选择不同的栅格得到适用于不同处理要求的点云模型.     

基于包围盒和空间分解的碰撞检测算法

文中提出一种基于包围盒和空间分解的碰撞检测算法,用以解决软体的碰撞检测。算法使用AABB包围盒做初步检测,确定可能发生碰撞的物体。再根据包围盒的重叠情况缩小可能发生碰撞的区域,利用哈希表作为数据储存结构进行空间分解,将物体包围盒重叠区域的基本几何元素的空间网格映射到哈希表中,将碰撞区域缩小到基本几何元素,最后用基元碰撞检测找出具体碰撞点。由于前期AABB包围盒的处理减少了空间分解阶段需要映射的基本几何元素数量,该算法具有较高的运算速度。     

用神经网络实现NURBS曲面重构

曲面重构问题是几何逆向工程中的首要问题,为了获得物体的几何模型(某些物体可能发生部分损坏)需要从大量的测量点构造曲面。该文采用了一个神经网络模型和相应的快速学习算法应用于曲面重建。该模型可以有效地逼近曲面并剔除输入数据点中的“坏”点。     

基于Level Set曲面的蛋白质分子场特征分析

阐述了利用Level Set模型抽取并分析蛋白质分子场特征方面的工作.从蛋白质分子结构出发,基于分子力学和分子动力学理论计算得到蕴含丰富生化信息的分子场数据;设计了一种有效的Level Set模型揭示分子场能量突变区域;进而构造体特征函数,抽取并分析Level Set曲面的拓扑结构特征;最后对同一蛋白质不同状态下的LevelSet曲面进行多属性比对.采用文中方法可成功地抽取蛋白质分子场的重要特征,所抽取的特征与已有生物学结论一致,如DPS蛋白质与铁离子结合的空腔区域、HIV-1蛋白酶内部的水分子排出通道,以及HIV-1蛋白酶在水溶液中进行SMD模拟时的生物活性变化等.     

海量散乱点的曲面重建算法研究

基于海量散乱点的曲面重建在机械产品测量造型、计算机视觉、根据切片数据的医学图像重建等领域中有重要应用.给出了一种以物体表面上不附加任何几何和拓扑信息(包括测点法矢、曲面边界信息)的散乱点集为处理对象,自动生成物体表面的三角网格模型的算法.该算法首先根据测点的邻近测点估算曲面在该测点处的法矢,并采用优化的顺序对法矢方向进行调整以使各测点处的法矢都指向曲面外侧,最后用步进立方体算法输出三角网格模型.采用新的方法计算切平面,不但进一步提高了效率,而且改善了曲面边界及尖锐棱边区域的重建效果.还提出并解决了法矢方向传播中可能出现的局部“孤岛”问题.同时,提出了一种对海量数据进行空间划分的算法,从而大大提高了海量数据的处理效率.应用实例表明,算法效果良好     

基于变形与测地距离一致性约束的3D面皮点对应

针对三维面皮生理点对应关系建立这一难题,充分考虑测地距离在描述复杂几何体表面形状方面的优势,提出了基于变形与测地距离一致性约束的3D面皮生理点对应方法。首先在Frankfurt坐标变换后标定面皮特征点集,利用特征点对应关系进行TPS变形;然后根据特征点几何特征向量建立初始点对应关系集,并利用测地距离一致性约束对其进行修剪以生成对应关系核心集;最后扩展对应关系核心集,直至确定源模型上每一顶点的对应关系。实验表明,该方法提高了点对应关系准确度,可有效建立三维面皮生理点对应关系。     

以目标节点为导向的XML路径查询处理

XML查询语言将复杂路径表达式作为核心内容.为了加速路径表达式处理,基于路径分解和结构连接操作的处理策略需要更深入的研究.以目标节点为导向的XML路径查询处理框架被提了出来.该方法利用了扩展基本操作来减少连接操作的数目.在路径分解和查询计划选择的过程中,利用查询树中的目标节点来避免中间结果的传递.除了分解规则和策略以外,提出了一组扩展的基本操作和实现算法.初步的实验结果显示,该方法具有良好的性能.它为路径查询处理提供了更多的选择.     

A Continuum Mechanical Approach to Geodesics in Shape Space

In this paper concepts from continuum mechanics are used to define geodesic paths in the space of shapes, where shapes are implicitly described as boundary contours of objects. The proposed shape metric is derived from a continuum mechanical notion of viscous dissipation. A geodesic path is defined as the family of shapes such that the total amount of viscous dissipation caused by an optimal material transport along the path is minimized. The approach can easily be generalized to shapes given as segment contours of multi-labeled images and to geodesic paths between partially occluded objects. The proposed computational framework for finding such a minimizer is based on the time discretization of a geodesic path as a sequence of pairwise matching problems, which is strictly invariant with respect to rigid body motions and ensures a 1–1 correspondence along the induced flow in shape space. When decreasing the time step size, the proposed model leads to the minimization of the actual geodesic length, where the Hessian of the pairwise matching energy reflects the chosen Riemannian metric on the underlying shape space. If the constraint of pairwise shape correspondence is replaced by the volume of the shape mismatch as a penalty functional, one obtains for decreasing time step size an optical flow term controlling the transport of the shape by the underlying motion field. The method is implemented via a level set representation of shapes, and a finite element approximation is employed as spatial discretization both for the pairwise matching deformations and for the level set representations. The numerical relaxation of the energy is performed via an efficient multi-scale procedure in space and time. Various examples for 2D and 3D shapes underline the effectiveness and robustness of the proposed approach.     

Geodesic Distance and Curves Through Isotropic and Anisotropic Heat Equations on Images and Surfaces

This paper proposes a method to extract geodesic distance and geodesic curves using heat diffusion. The method is based on Varadhan’s formula that helps to obtain a numerical approximation of geodesic distance according to metrics based on different heat flows. The heat equation can be utilized by regarding an image or a surface as a medium for heat diffusion and letting the user set at least one source point in the domain. Both isotropic and anisotropic diffusions are considered here to obtain geodesics according to their respective metrics. (1) In the part of the paper where we deal with the isotropic case, we use gray-level intensity to compute the conductivity, i.e., those pixels with gray-levels similar to the source point would have higher conductivity. The model of Perona and Malik, which inhibits heat from diffusing out of homogeneous regions, is also used for geodesic computations in this paper. The two methods are combined and used for more complicated cases. We can also use the norm of the gradient of an image as the feature in the Perona and Malik model to make the heat diffuse along boundaries and edges. (2) For the anisotropic case, we use different eigenvectors and eigenvalues to compose the diffusion tensors to concentrate heat flow along chosen directions. Furthermore, to automate the process of extracting geodesic lines, we propose two automatic methods: a new voting method and a key point method, which are both especially designed for the heat-based method. Our algorithms are tested on synthetic and real images as well as on a mesh. The results are very promising and demonstrate the robustness of the algorithms.     

基于DRLSE模型的运动目标跟踪

高斯粒子滤波不能处理曲线的拓扑变化,而基于水平集的几何活动轮廓模型能较好地适应拓扑变化,为了跟踪和提取刚体和非刚体运动目标精确的轮廓信息,提出基于距离规则化的水平集演化(DRLSE)模型和高斯粒子滤波(GPF)相结合的运动目标跟踪方法.首先用高斯粒子滤波对目标跟踪得到目标的运动区域,然后把水平集规则项引入到测地线活动轮廓模型中,以外接轮廓的中心为基础进行DRLSE.距离规则化不仅消除了水平集重新初始化的需要,而且避免了因此而导致的数值错误,在水平集演化过程中保持了水平集函数的规则化.最后,将获得的精确轮廓信息反馈到跟踪框架.实验结果表明,该方法适用于刚体和非刚体目标,在实际交通环境中跟踪结果更加精确.     

基于密度缩放因子的ISOMAP算法

等度量映射(ISOMAP)算法是一种被广泛应用的非线性无监督降维算法,通过保持各个观测样本间的测地距离进行等距嵌入,从而实现高维空间向低维空间的坐标转换。但在实际应用中,观测数据无可避免地会存在噪声,由于测地距离的计算对噪声比较敏感,并且也没有考虑数据集的密度分布,导致ISOMAP算法降维后低维坐标表示存在几何变形。针对这一缺点,根据局部密度的思想,提出一种基于密度缩放因子的ISOMAP(Density Scaling Factor Based ISOMAP,D-ISOMAP)算法。在传统的ISOMAP算法框架下,首先,针对每个观测样本计算一个局部密度缩放因子;然后,在测地距离的计算过程中,将直接相邻的两个样本之间的测地距离除以这两个样本密度缩放因子的乘积;最后,通过最短路径算法求得改进后的距离矩阵,并对其进行降维处理。改进的测地距离在密度较大的区域被缩小,而在密度较小的区域被放大,这样可以减小噪声对降维效果的影响,提升可视化和聚类效果。人工数据集和UCI数据集上的实验结果表明,在数据集的可视化和聚类效果方面, D-ISOMAP算法较经典的无监督降维算法具有一定的优势。     

基于代数张量积B样条的隐式曲面重构

提出一种以代数张量积B-样条曲面作为几何表示形式的方式,采用Sampson距离来度量数据点与曲面之间的误差,它不仅是几何距离的很好近似且具有齐性和刚体不变的良好性质.建立了近似几何误差和薄板能量极小化的最优化隐式曲面重构模型.同时结合最优化理论中的信赖域思想和拟牛顿法,给出自适应的选代求解算法及其实现.理论上由信赖域法的收敛性分析,迭代算法具有总体收敛性.最后基于散乱点数据集,给出曲面重构的实例,并作简单的讨论.     

Shape of Elastic Strings in Euclidean Space

We construct a 1-parameter family of geodesic shape metrics on a space of closed parametric curves in Euclidean space of any dimension. The curves are modeled on homogeneous elastic strings whose elasticity properties are described in terms of their tension and rigidity coefficients. As we change the elasticity properties, we obtain the various elastic models. The metrics are invariant under reparametrizations of the curves and induce metrics on shape space. Analysis of the geometry of the space of elastic strings and path spaces of elastic curves enables us to develop a computational model and algorithms for the estimation of geodesics and geodesic distances based on energy minimization. We also investigate a curve registration procedure that is employed in the estimation of shape distances and can be used as a general method for matching the geometric features of a family of curves. Several examples of geodesics are given and experiments are carried out to demonstrate the discriminative quality of the elastic metrics.     

Geometric characterization and clustering of graphs using heat kernel embeddings

In this paper, we investigate the use of heat kernels as a means of embedding the individual nodes of a graph in a vector space. The reason for turning to the heat kernel is that it encapsulates information concerning the distribution of path lengths and hence node affinities on the graph. The heat kernel of the graph is found by exponentiating the Laplacian eigensystem over time. In this paper, we explore how graphs can be characterized in a geometric manner using embeddings into a vector space obtained from the heat kernel. We explore two different embedding strategies. The first of these is a direct method in which the matrix of embedding co-ordinates is obtained by performing a Young–Householder decomposition on the heat kernel. The second method is indirect and involves performing a low-distortion embedding by applying multidimensional scaling to the geodesic distances between nodes. We show how the required geodesic distances can be computed using parametrix expansion of the heat kernel. Once the nodes of the graph are embedded using one of the two alternative methods, we can characterize them in a geometric manner using the distribution of the node co-ordinates. We investigate several alternative methods of characterization, including spatial moments for the embedded points, the Laplacian spectrum for the Euclidean distance matrix and scalar curvatures computed from the difference in geodesic and Euclidean distances. We experiment with the resulting algorithms on the COIL database.     

实时三维超声心动图中二尖瓣的提取

二尖瓣的复杂结构和不规则运动特性使得自动提取非常困难，因而依据二尖瓣解剖形状的先验知识，采用人机交互方式构造符合二尖瓣生理形状的柱状区域，把该区域作为测地活动轮廓模型的区域约束项，在levelset框架下对二尖瓣进行分割提取。该方法通过对大量三维超声瓣膜进行实验，取得了良好的分割效果，能够直接准确提取三维心脏二尖瓣。