CAREER: Generating Hierarchical Vector-Valued Data Summaries for Scalable Flow Data Processing, Analysis and Visualization

矢量场是描述各种动力学系统行为的普遍工具，这些动力学系统支配着许多重要的物理现象，尤其是流体。它们的分析对于从血液循环等医学数据分析到海啸模拟以及科学和工程中的许多其他问题的许多应用都是不可或缺的。然而，定义在高维空间中的超大规模矢量场数据的处理和解释已经成为许多关键科学研究任务的瓶颈。更具体地说，尤其是当可视化受到现代显示器的有限分辨率和尺寸的限制，并且通过可视化传达的信息量受到人类视觉感知通道的有限带宽的限制时，对在大小上固有的复杂和可怕的矢量场数据的分析尤其具有挑战性。如果没有一个全面的、总结的矢量场流动数据的表示，这一问题就无法解决，这在流动可视化社区中还没有得到很好的研究。拟议中的研究将填补这一空白。这项研究的理论贡献将影响计算拓扑学、流体力学和数学的方法，其应用将使包括气候研究、物理、化学、机械和土木工程以及心血管疾病诊断在内的多个学科受益。这项工作的结果将被纳入本科生和研究生水平的矢量场数据处理和可视化领域的新课程，这将使广泛学科的学生受益。矢量场是为任何空间点分配描述物体位移的矢量值的函数。为了开发一种有效的矢量场摘要表示，该项目将首先研究不同流动特征和描述符之间的关系，旨在减少摘要提取过程中的冗余。其次，将开发一种新的链接图混合表示，其目标是将从不同角度和不同尺度表征的各种流信息无缝地集成到与维度无关的表示中。第三，基于这种中间表示，将开发一个新的、可伸缩的矢量场分析框架，从中可以定义矢量场数据的分层摘要。将采用信息理论框架来评估摘要陈述中的信息损失。这一总结将使科学发现和教育的一些应用程序成为可能，包括流数据的可扩展和知识辅助探索、矢量场比较和矢量场合成游戏。在本项目期间获得的知识将用于研究更复杂数据的汇总表示法，例如张量场数据。更重要的是，这项研究代表着朝着从异类数据源中发现知识和完整性的统一框架迈出了一步。开发的理论和算法将发表在同行评议的期刊和会议上。项目网页(http://www2.cs.uh.edu/~chengu/Hier_VVDSummary/Hier_VVDSummary.html)将提供关键成果的简要说明以及指向相应出版物和生成的数据集的链接或指针。开发的软件、库、插件和开放源代码将在项目网页和Github上发布。

Vector fields are a ubiquitous tool to describe the behaviors of various dynamical systems that dominate many important physical phenomena, especially fluids. Their analysis is indispensable for many applications ranging from medical data analysis such as blood circulation to tsunami simulations and many other problems in science and engineering. However, processing and interpreting very large scale vector field data defined in a high dimensional space has become the bottleneck of many critical scientific research tasks. More specifically, the analysis of vector field data, that is inherently complex and formidable in size, is particularly challenging especially when visualization is limited by the finite resolution and dimensions of modern displays, and the amount of information conveyed via the visualization is constrained by the limited bandwidth of the human visual perception channel. This problem cannot be solved without a comprehensive, summary representation of vector field flow data, which has not been well studied in the flow visualization community. The proposed research will fill this gap. Theoretical contributions of this research will impact methods in computational topology, fluid mechanics, and mathematics, while its applications will benefit a wide variety of disciplines including climate study, physics, chemistry, mechanical and civil engineering, and cardiovascular disease diagnosis. The results of this work will be incorporated into new courses in the area of vector field data processing and visualization at both the undergraduate and graduate levels that will benefit students of a broad range of disciplines.A vector field is a function that assigns any spatial point a vector value describing the displacement of objects. To develop an effective summary representation for vector fields, the proposed project will first study the relations between different flow characteristics and descriptors, aiming to reduce the redundancy in the extraction of the summary. Second, a novel link-graph hybrid representation will be developed with the goal of seamlessly integrating various flow information, characterized from different perspectives and in various scales, into a dimension-independent representation. Third, based on this intermediate representation, a new and scalable vector field analysis framework will be developed, from which a hierarchical summary for vector field data can be defined. The information theoretical framework will be adapted to evaluate the information loss in the summary representation. This summary will enable a number of applications for scientific discovery and education including the scalable and knowledge-assisted exploration of flow data, vector field comparison, and vector field synthesis gaming. The knowledge obtained during this project will be adapted to study the summary representation of more complex data, such as tensor field data. More importantly, this research represents one step towards a unified framework of knowledge discovery and integrity from heterogeneous data sources. The developed theory and algorithms will be published in peer-reviewed journal and conferences. The project webpage (http://www2.cs.uh.edu/~chengu/Hier_VVDSummary/Hier_VVDSummary.html) will provide brief description of the key outcome and links or pointers to the corresponding publications and generated datasets. The developed software, libraries, plug-ins, and open source code will be released on the on the project webpage and Github.