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

向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。他们的分析是不可或缺的许多应用，从医疗数据分析，如血液循环，海啸模拟和许多其他问题的科学和工程。然而，在高维空间中处理和解释超大规模矢量场数据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，这是固有的复杂性和强大的大小，是特别具有挑战性的，特别是当可视化是有限的分辨率和现代显示器的尺寸限制，并通过可视化传达的信息量受到限制的有限带宽的人类视觉感知通道。如果没有矢量场流数据的全面、概括表示，这个问题就无法解决，而矢量场流数据在流场可视化领域还没有得到很好的研究。这项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，而其应用将有利于各种学科，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。这项工作的结果将被纳入新的课程在矢量场数据处理和可视化领域的本科生和研究生的水平，这将有利于学生的广泛的学科。矢量场是一个函数，分配给任何空间点的矢量值描述的位移对象。为发展有效的矢量场摘要表达法，建议的项目会首先研究不同的水流特性与描述符之间的关系，以减少提取摘要时的冗馀。其次，一种新的链接图混合表示将开发与无缝集成的各种流信息，从不同的角度和不同的尺度，到一个维度独立的表示的目标。第三，基于这种中间表示，一个新的和可扩展的矢量场分析框架将被开发，从该框架中可以定义矢量场数据的层次摘要。信息理论框架将适用于评估摘要表示中的信息损失。本摘要将使许多应用程序的科学发现和教育，包括可扩展的和知识辅助的探索流数据，矢量场比较，矢量场合成游戏。 在这个项目中获得的知识将适用于研究更复杂的数据，如张量场数据的摘要表示。更重要的是，这项研究代表了一个统一的框架，从异构数据源的知识发现和完整性的一步。 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/hichengu/Hier_VVDSummary/Hier_VVDSummary.html）将提供关键成果的简要说明以及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.