Designing 2D Vector Fields of Arbitrary Topology

We introduce a scheme of control polygons to design topological skeletons for vector fields of arbitrary topology. Based on this we construct piecewise linear vector fields of exactly the topology specified by the control polygons. This way a controlled construction of vector fields of any topology is possible. Finally we apply this method for topology‐preserving compression of vector fields consisting of a simple topology.     

三维矢量场的流动拓扑结构抽取

提出一种基于关键点分类的三维矢量场流动拓扑结构抽取算法,可应用于三维曲线网格、结构化网格和分块网格中.在许多计算流体力学计算中,存在非滑移边界,这种边界上流体的速度为0.通过分析流场边界的表面摩擦场的拓扑,展示绕壁面流体的流动结构;使用图标定位关键点,可交互式地标记和显示涡核区域,并通过选择暗示螺旋流动的图标,沿着该关键点的实特征值对应的特征矢量方向积分流线来完成.测试结果清晰地展示了关键特征区域的流体流动特征.     

与物理特征相关的平面向量场的拓扑简化及压缩

针对现有拓扑简化方法忽略物理特征保持的缺陷,提出一种对物理特征敏感的平面向量场拓扑简化算法,其中心思想是使用为应用定制的物理判据分类向量场区域,将向量场的特征检出与拓扑简化关联起来.通过合并次要物理特征所在区域上的网格及在新网格布局下重新提取向量场拓扑,该算法不仅能完好地保持场内的重要特征,还能同时实现向量场的数据压缩.实验结果表明,该算法在复杂流场的特征提取方面可发挥重要的作用.     

平面时变向量场Hopf分岔的精确定位与可视化

分岔是指动力系统在演化过程中定性行为发生质变的现象．分岔研究对揭示复杂流场的不稳定过程有重要意义．文中提出一个平面时变向量场Hopf分岔的榆出、定位与可视化算法．通过精密跟踪场内全体临界点的变化以及用一个颜色模型图画般地记述这些变化的演化路径,新算法不仅实现了对平面时变向量场中全部Hopf分岔点的检出和定位,还能详尽显示分岔的发展过程,文中方法原则上也适用于其它局部分岔类型的检出,为用数据可视化技术观察和研究分岔现象开辟了新的途径。     

Selective Visualization of Vector Fields

In this paper, we present an approach to selective vector field visualization. This selective visualization approach consists of three stages: selectdon creation, selection processing and selective visualization mapping. It is described how selected regions, called selections, can be represented and created, how selections can be processed and how they can be used in the visualization mapping. Combination of these techniques with a standard visualization pipeline improves the visualization process and offers new facilities for visualization. Examples of selective visualization of fluid flow datasets are provided.     

Multilevel Robustness for 2D Vector Field Feature Tracking,Selection and Comparison

Critical point tracking is a core topic in scientific visualization for understanding the dynamic behaviour of time-varying vector field data. The topological notion of robustness has been introduced recently to quantify the structural stability of critical points, that is, the robustness of a critical point is the minimum amount of perturbation to the vector field necessary to cancel it. A theoretical basis has been established previously that relates critical point tracking with the notion of robustness, in particular, critical points could be tracked based on their closeness in stability, measured by robustness, instead of just distance proximity within the domain. However, in practice, the computation of classic robustness may produce artifacts when a critical point is close to the boundary of the domain; thus, we do not have a complete picture of the vector field behaviour within its local neighbourhood. To alleviate these issues, we introduce a multilevel robustness framework for the study of 2D time-varying vector fields. We compute the robustness of critical points across varying neighbourhoods to capture the multiscale nature of the data and to mitigate the boundary effect suffered by the classic robustness computation. We demonstrate via experiments that such a new notion of robustness can be combined seamlessly with existing feature tracking algorithms to improve the visual interpretability of vector fields in terms of feature tracking, selection and comparison for large-scale scientific simulations. We observe, for the first time, that the minimum multilevel robustness is highly correlated with physical quantities used by domain scientists in studying a real-world tropical cyclone dataset. Such an observation helps to increase the physical interpretability of robustness.     

基于聚类的二维向量场可视化

已有的二维流场可视化中,鞍点等临界点是最重要的特征之一.文中从一个新的角度提出一种基于流线聚类的二维向量场可视化方法.首先生成采样流线集合,然后将流线聚类,最后引入共轭法向量场和流线密度矩阵对同一个类的流线进行加速排序.在此基础上,提出3种可视化应用:抽取每一类的代表流线进行向量场的流线简洁表达;根据流线之间距离进行多分辨率均匀流线表达;生成权值图,增强基于纹理的向量场可视化.实验结果表明,该方法具有良好的鲁棒性,可视化效果优于已有的方法.     

Time-Dependent 2-D Vector Field Topology: An Approach Inspired by Lagrangian Coherent Structures

This paper presents an approach to a time-dependent variant of the concept of vector field topology for 2-D vector fields. Vector field topology is defined for steady vector fields and aims at discriminating the domain of a vector field into regions of qualitatively different behaviour. The presented approach represents a generalization for saddle-type critical points and their separatrices to unsteady vector fields based on generalized streak lines, with the classical vector field topology as its special case for steady vector fields. The concept is closely related to that of Lagrangian coherent structures obtained as ridges in the finite-time Lyapunov exponent field. The proposed approach is evaluated on both 2-D time-dependent synthetic and vector fields from computational fluid dynamics.     

利用临界点聚类的平面向量场极限环的检出及可视化

检出和可视化极限环已经成为向量场拓扑分析中日益重要的研究课题．提出了一个基于临界点聚类的检出算法,将向量场的全部临界点以几何距离为相似性判据聚类成一棵二叉树,通过只检查临界点指数和为＋1的少数树结点,以及在算法中增加检测和剔除中心型闭轨的部分,获得了比Wischgoll算法更好的结果．     

纹理流线:一种有效的二维向量场可视化方法

向量场可视化是可视化研究的一个焦点.流线能够很好地表现向量场的局部信息,并被用于二维向量场的全局显示.从信号分析的角度讨论了基于流线的全局向量场可视化方法的频域特点,指出其结果图像视觉效果的优缺点.在此基础上提出和分析了一种新的方法:纹理流线方法.新方法的频域意义更为明确,计算简单且开销小.     

Toward a Lagrangian Vector Field Topology

In this paper we present an extended critical point concept which allows us to apply vector field topology in the case of unsteady flow. We propose a measure for unsteadiness which describes the rate of change of the velocities in a fluid element over time. This measure allows us to select particles for which topological properties remain intact inside a finite spatio‐temporal neighborhood. One benefit of this approach is that the classification of critical points based on the eigenvalues of the Jacobian remains meaningful. In the steady case the proposed criterion reduces to the classical definition of critical points. As a first step we show that finding an optimal Galilean frame of reference can be obtained implicitly by analyzing the acceleration field. In a second step we show that this can be extended by switching to the Lagrangian frame of reference. This way the criterion can detect critical points moving along intricate trajectories. We analyze the behavior of the proposed criterion based on two analytical vector fields for which a correct solution is defined by their inherent symmetries and present results for numerical vector fields.     

Demons非刚性配准算法拓扑保持性的研究

在基于配准的图像分割应用中, 拓扑保持性是非刚性图像配准算法的一个重要约束. 本文从矢量场特性出发, 分析了Demons非刚性图像配准算法导致目标拓扑改变时变形场的特点. 根据变形场特点与其雅可比行列式之间的关系, 给出了校正该算法拓扑保持性的方法. 实验表明, 改进后的变形场具有了拓扑保持性.     

基于链模型的分布式小波压缩算法

针对任意支撑长度的小波函数,提出一种基于链模型的分布式数据压缩算法,在数据传送到簇头前去除传感数据的相关性,避免冗余数据的传输。设计一个适合于小波变换的链模型,选择小波系数在链上存放的最佳传感器节点位置,确定进行分布式小波变换的链。基于此链给出一个适合任意支撑长度小波函数的分布式小波压缩算法。从网络耗能和数据重构精度的角度设计模拟实验,验证了算法具有较好的性能。     

WebGIS系统中矢量数据的压缩与化简方法综述

空间数据的压缩对于空间数据网络传输以及提高整个WebGIS系统的效率来说是一项很重要的工作。该文针对WebGIS系统中矢量数据压缩问题进行了总结与综述。首先分析了矢量数据压缩的重要性,并对矢量数据压缩技术进行了详细的分类,然后重点分析与比较了Douglas-Peucker压缩方法与小波技术压缩方法,最后简单讨论了WebGIS系统中矢量数据的网络传输策略。     

向量相似度可复原三维点云压缩算法

针对三维点云数据压缩中细节特征不易保留,模型平缓部位存在过度压缩以及压缩后的点云模型不易复原等问题,提出一种基于向量相似度的三维点云压缩算法和复原算法CVS。向量相似性度量采用提出的L3A进行度量。CVS把每个三维坐标点看作是连接其坐标和原点的三维向量,按照三维坐标点的读入顺序选取参考向量,生成覆盖整个点云区域的采样区域,进行分区压缩。在采样区域中使用最小二乘曲面拟合算法对包含其中的点云进行曲面拟合,设置曲率阈值剔除坐标点,并存储曲面方程参数用于复原。通过控制L3A向量相似度中的长度和角度的变化阈值,使得密集点云区域的压缩率高于非密集区域的压缩率,通过控制曲率阈值,使得低曲率区域的压缩率高于高曲率区域的压缩率,最大程度保留模型细节特征。CVS使用压缩阶段产生的复原信息生成点云来恢复模型的细节特征,使得模型特征更加明显。     

Topology in Raster and Vector Representation

Egenhofer's nine-intersection, well-known for vector representations, is defined here on a raster, using a hybrid raster model, and then systematically transformed to yield functions which can be used in a convolution operation applied to a regular raster representation. Applying functions, the hybrid raster elements need not be stored. It becomes thus possible to determine the topological relation of two regions, given in raster representation, with the same reasoning as in vector representations. This contributes to the merging of raster and vector operations. It demonstrates how the same conceptual operations can be used for both representations, thus hiding in one more instance the difference between them.     

三维无旋矢量场的一种新的可视化方法

提出了三维无旋矢量场的一种新的可视化方法,即构造空间曲面,使得矢量场在曲面上任意一点处垂直于该曲面。首先找到曲面所满足的偏微分方程组,通过采用类似于经典四阶龙格―库塔方法的数值解法对其求解,得到曲面上的离散点,然后进行三角剖分,从而得到逼近于曲面的空间三角网格。论文的偏微分方程组的求解借鉴了常微分方程求解算法的设计思想,构造出的曲面与传统的点图标和线图标相比,在更大程度上揭示了矢量场本身的连续性。     

Variable-resolution Compression of Vector Data

The compression of spatial data is a promising solution to reduce the space of data storage and to decrease the transmission time of spatial data over the Internet. This paper proposes a new method for variable-resolution compression of vector data. Three key steps are encompassed in the proposed method, namely, the simplification of vector data via the elimination of vertices, the compression of removed vertices, and the decoding of the compressed vector data. The proposed compression method was implemented and applied to compress vector data to investigate its performance in terms of the compression ratio, distortions of geometric shapes. The results show that the proposed method provides a feasible and efficient solution for the compression of vector data, is able to achieve good compression ratios and maintains the main shape characteristics of the spatial objects within the compressed vector data.

基于小波变换和形状-增益矢量量化的3维图像压缩

数据压缩是高光谱图像处理应用中的一个关键问题。为了对高光谱图像进行有效压缩，在2维小波变换的基础上，提出了一种分组矢量量化的高光谱图像有损压缩方案。该方案首先按照谱段类型对高光谱图像进行分组，然后对每个谱段分别进行2维小波变换，最后变换系数再使用一种Kronecker-Product形状-增益矢量量化方法来进行量化编码。计算机仿真结果证明．该算法在取得高压缩率的同时，不仅能很好地保持数据的谱特征，并能降低运算量。     

基于流线纹理合成的2D矢量场可视化

针对科学试验数据可视化问题,提出了一种2D矢量场可视化的方法－流线纹理合成方法,即通过将1D纹理映射到流线上,再利用流线纹理来合成可视化图象,因为移动1D纹理很容易形成矢量场动画。该方法是利用局部区域内流线的近似平行性,首先依据临界点来设定流线宽度,然后把流线绘制成多条平行流线,再分别将多条不同的1D纹理映射到流线上,从而能够加快计算。实际结果表明,由于流线纹理合成的纹理图象上清楚地显示了流线,因而反映了矢量场的方向信息,同时,该方法计算速度快,可以达到交互可视化的要求。