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.     

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.     

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．     

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。     

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.     

Complete Tensor Field Topology on 2D Triangulated Manifolds embedded in 3D

This paper is concerned with the extraction of the surface topology of tensor fields on 2D triangulated manifolds embedded in 3D. In scientific visualization topology is a meaningful instrument to get a hold on the structure of a given dataset. Due to the discontinuity of tensor fields on a piecewise planar domain, standard topology extraction methods result in an incomplete topological skeleton. In particular with regard to the high computational costs of the extraction this is not satisfactory. This paper provides a method for topology extraction of tensor fields that leads to complete results. The core idea is to include the locations of discontinuity into the topological analysis. For this purpose the model of continuous transition bridges is introduced, which allows to capture the entire topology on the discontinuous field. The proposed method is applied to piecewise linear three‐dimensional tensor fields defined on the vertices of the triangulation and for piecewise constant two or three‐dimensional tensor fields given per triangle, e.g. rate of strain tensors of piecewise linear flow fields.     

二维和三维矢量场的可视化

矢量场可视化用来帮助人们直观理解二维和三维矢量场。由于目前的矢量场可视化方法只能展示二维矢量场的方向而不能展示强度,并且对于三维矢量场可视化的效果不太令人满意,因此本文提出了用线积分卷积来实现二维平面矢量场可视化,以及三维空间矢量场可视化的方法。对于线积分卷积中的流线跟踪,利用扩展的Bresenham画线算法的思想,实现了二维平面和三维空间流线的跟踪,并且通过建立一个二维表和三维表来分别存储二维平面矢量场和三维空间矢量场中每个点在流线中的上一个点和下一点的位置,来避免传统流线跟踪方法的冗余计算,提高了效率。对于二维平面矢量场,把线积分卷积的结果和矢量的强度进行加权平均,从而利用输出图像的纹理和颜色,共同来表现矢量场的方向和强度。对于三维空间矢量场,利用体线积分卷积（Volume Line Integral Convolution, Volume LIC）的方法来得到输出体纹理,并且用光线投射的体渲染方法来展示三维空间矢量场。结果显示出本文的方法能够清晰直观的看到二维平面矢量场和三维空间矢量场。     

基于平面矢量场的可视化方法的研究

平面矢量场可视化是科学计算可视化的重要研究内容。矢量场以直观的图形图像显示场的运动,透过抽象数据有效洞察其内涵本质和变化规律,广泛应用于计算流体力学、航空动力学、大气物理和气象分析等领域。对平面矢量场进行可视化的方法有很多种,常见的有点图标法、流线法、线积分卷积法和拓扑分析法等。论文主要研究常见的可视化方法,分析它们的性能,并通过实际的例子,对具体的可视化结果图像进行比较。通过该研究,能够给人们在选择可视化方法时提供依据。     

一种非结构矢量场的线卷积积分方法

传统的结构化LIC方法不适用于非结构矢量场数据处理的主要原因有两个,一是矢量幅度的表现力不强,二是因分辨率等因素无法有效地应用于采样点位置随机的矢量场．为解决上述问题,可以采用如下方法：在DDA曲线的生成过程中,采用基于数值的计算方法替代结构化LIC中基于网格的计算方法,从而有效地保证了处理结果的分辨率;在DDA曲线的卷积积分（LIC）处理过程中,采用区域标记的策略替代快速LIC方法中的线标记策略,一方面,因为被标记的采样点不再作为以后各轮DAA曲线生成的起始点,从而可以有效地减少计算量;另一方面,区域标记方法能够使LIC处理的结果稀疏化,表现为矢量场中幅度大的区域矢量线密集,而幅度小的区域矢量线稀疏,从而有效地提高矢量场幅度、结构的表现力．     

二维LIC矢量场可视化算法的研究及改进

线积分卷积(LIC)是一种针对矢量场的可视化方法.针对二维空间上的LIC算法进行了研究并提出了改进.首先,针对某些二维矢量场在用户关注区域矢量大小比较接近的问题,采用非线性的颜色映射法进行处理,最终的可视化结果可以突出用户感兴趣区域的矢量场特征.其次,从原始LIC算法的串行计算任务中提取出4个可以并行计算的子模块,并依托NVIDIA的CUDA架构实现了颜色增强LIC法的硬件加速.结果表明,加速后算法的加速比随着输入矢量场分辨率的增加而增加.因此,该算法适用于高分辨率二维矢量场的交互式可视化,且没有特别高的硬件要求,通用性较好.总之,新的算法较原始算法在视觉效果和性能上都有所改进.     

Inertial Steady 2D Vector Field Topology

Vector field topology is a powerful and matured tool for the study of the asymptotic behavior of tracer particles in steady flows. Yet, it does not capture the behavior of finite‐sized particles, because they develop inertia and do not move tangential to the flow. In this paper, we use the fact that the trajectories of inertial particles can be described as tangent curves of a higher dimensional vector field. Using this, we conduct a full classification of the first‐order critical points of this higher dimensional flow, and devise a method to their efficient extraction. Further, we interactively visualize the asymptotic behavior of finite‐sized particles by a glyph visualization that encodes the outcome of any initial condition of the governing ODE, i.e., for a varying initial position and/or initial velocity. With this, we present a first approach to extend traditional vector field topology to the inertial case.     

Wavelet-Based 3D Compression Scheme for Interactive Visualization of Very Large Volume Data

Interactive visualization of very large volume data has been recognized as a task requiring great effort in a variety of science and engineering fields. In particular, such data usually places considerable demands on run-time memory space. In this paper, we present an effective 3D compression scheme for interactive visualization of very large volume data, that exploits the power of wavelet theory. In designing our method, we have compromised between two important factors: high compression ratio and fast run-time random access ability. Our experimental results on the Visual Human data sets show that our method achieves fairly good compression ratios. In addition, it minimizes the overhead caused during run-time reconstruction of voxel values. This 3D compression scheme will be useful in developing many interactive visualization systems for huge volume data, especially when they are based on personal computers or workstations with limited memory.     

矢量量化高光谱数据压缩性能评估

性能评估是高光谱数据有损压缩研究的一个关键问题。本文在分析三种典型的基于矢量量化压缩方案的基础上,以K-means聚类准确率的仿真统计比较了三种方案的性能优劣;提出一种失真标准抽取的性能评估框架,在缺乏背景资料的情况下,该框架可以对压缩方案性能给出直观评价,方便了压缩方案的选择及应用。