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系统行为的普遍工具，这些动力系统支配着许多重要的物理现象，特别是流体。从血液循环等医疗数据分析到海啸模拟以及科学和工程中的许多其他问题，它们的分析对于许多应用都是必不可少的。然而，在高维空间中定义的超大尺度向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，矢量场数据的分析，本质上是复杂和强大的，尤其具有挑战性，特别是当可视化受限于现代显示器的有限分辨率和尺寸时，通过可视化传达的信息量受限于人类视觉感知通道的有限带宽。如果没有矢量场流数据的全面、概括的表示，这个问题就无法解决，而这在流可视化界还没有得到很好的研究。拟议的研究将填补这一空白。本研究的理论贡献将影响计算拓扑、流体力学和数学的方法，而其应用将有益于广泛的学科，包括气候研究、物理、化学、机械和土木工程、心血管疾病诊断。这项工作的结果将被纳入在矢量场数据处理和可视化领域的新课程在本科和研究生的水平，这将有利于学生广泛的学科。向量场是一个函数，它赋予任何空间点一个描述物体位移的向量值。为了开发向量场的有效摘要表示，该项目将首先研究不同流特性与描述符之间的关系，旨在减少摘要提取中的冗余。其次，将开发一种新颖的链接图混合表示，其目标是将不同角度和不同尺度的各种流量信息无缝集成到一个与维度无关的表示中。第三，基于这种中间表示，将开发一个新的可扩展的向量场分析框架，从中可以定义向量场数据的分层摘要。将信息理论框架应用于总结表示中的信息损失评估。该总结将为科学发现和教育提供大量应用，包括流量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。在这个项目中获得的知识将用于研究更复杂数据的汇总表示，例如张量场数据。更重要的是，本研究向异构数据源的知识发现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审的期刊和会议上。项目网页（http://www2.cs.uh.edu/~chengu/Hier_VVDSummary/Hier_VVDSummary.html）将简要说明主要成果，并提供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.