ITR: Procedures for the Rigorous Comparison of Vector and Tensor Fields

ITR：矢量场和张量场的严格比较程序

• 批准号: 0082898
• 负责人: Lambertus Hesselink
• 金额: $ 49万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-09-01 至 2003-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0082898&HistoricalAwards=false
• 关键词: ITR; Procedures; Rigorous; Comparison; Vector; ITR; Procedures; Rigorous; Comparison; Vector

During the last decade, researchers in our Scientific Visualization Group at Stanfor Universityhave been developing general data analysis techniques for vector and tensor fieldsbased on rigorous mathematical approaches. The work has systematically explored directvisualizations and feature extractions of both vector and tensor fields in two and threedimensions using computers. Recently, we have been developing the next stage of ourvisualization efforts: automated atad comparisons.Traditional techniques for vector field comparison fall into three basic categories: image,data, and feature based comparison. In most instances, comparisons are made visually,not automatically. In addition, there are fundamental limitations with these existing comparisontechniques. Image base comparisons suffer from difficulty in representing datasetsbeyond two-dimensional vector fields, data based comparisons suffer from grid alignmentproblems, and feature base comparisons, while providing excellent location of specific features,may not show all the global information in the field.Our new approach to this problem is essentially a feature-based comparison technique,with the important stipulation that our features attempt to represent the topological structureof the field. This ensures that we do not overlook any important structures in thefield. Our paradigm is to analytically study vector and tensor fields to extract topologicallycritical information, transfer this knowledge into effective computer programs, and then tovisualize the fields using the results of our analysis.We have successfully implemented our ideas for two-dimensional vector fields and forthree-dimensional vector fields. We now intend to study tensor fields associated with whitematter brain functions.Our fundamental technique for the comparison of vector and tensord ata would beapplicable to almost every field of science and engineering, ranging from the magnetic field ofthe sun to airflow over a wing. In addition, time varying fields can be studied by comparinga field at a fixed time with its state at later times. Our approach is unique in the field ofscientific visualization because it is based on rigorous mathematical analysis, and it is theonly approach available to quantitatively study NMR tensor brain data. Our methodologyin the analysis of tensor and vector datasets allows better design of air vehicles, betterunderstanding of electromagnetic problems, and provides substantial time savings whendealing with large experimental datasets. Quantitative understanding of white matter brainfunctions has the potential to open up a whole new area of medical research.

在过去的十年中，我们在Stanfor University的科学可视化小组的研究人员一直在开发基于严格的数学方法的矢量和张量字段的一般数据分析技术。这项工作已系统地探索了使用计算机的两个和三次二动的矢量和张量磁场的直接介绍和特征提取。最近，我们一直在开发我们的视觉化工作的下一阶段：自动化的ATAD比较。用于矢量字段比较的传统技术分为三个基本类别：图像，数据和基于功能的比较。在大多数情况下，比较是在视觉上进行的，而不是自动进行的。此外，这些现有的比较具有根本的局限性。图像基础比较在表示数据集二维矢量领域，基于数据的比较遭受网格对齐问题的苦难和功能基础比较而困难，同时可以提供特定特征的出色位置，可能并未显示该领域中的所有全球信息。这些问题本质上是一种基于特征的技术，是一种基于特征的技术，代表了我们重要的既定端口来代表我们的特征尝试，以供我们的功能尝试。这样可以确保我们不会忽略田野中的任何重要结构。我们的范式是分析研究向量和张量场，以提取拓扑临界信息，将这些知识转移到有效的计算机程序中，然后使用分析结果进行视野化。我们成功地实施了我们对二维矢量字段和Forthree-wree-voremenre-vector-biquesitional-vector-biquensional-vector vector Fields的想法。现在，我们打算研究与白ematter脑功能相关的张量场。我们的基本技术比较向量和tensord ata的基本技术，几乎可以击倒科学和工程的每个领域，从太阳的磁场到空气流到机翼的气流不等。此外，可以通过在固定时间与以后的状态进行比较，可以研究时间变化的字段。我们的方法在科学可视化领域是独一无二的，因为它基于严格的数学分析，并且是可用于定量研究NMR张量脑数据的方法。我们对张量和矢量数据集的分析的方法可以更好地设计空气车辆，更好地理解电磁问题，并通过大型实验数据集提供大量时间节省。对白质脑功能的定量理解有可能打开全新的医学研究领域。