ABSTRACT

Vector field data analysis is indispensable for many applications in science and engineering, ranging from climate study, physics, chemistry, automobile design, to medical practice. Most existing analysis techniques for vector field data are not scalable to the real-world data with ever-increasing sizes and complexity. More importantly, the inherent limited visual perception channel largely constrains the ability to understand the complex geometric and physical behaviors of vector fields as a whole or in detail. To address these challenges, this exploratory project investigates a graph-based vector field data reduction for the subsequent extraction of a multi-scale vector field data summary. The summary serves as a condensed, yet informative, representation of the original vector field, supporting data interpretation and interaction and shielding the user from the underlying complexity of the flow dynamics. The key to computing such a summary representation is the construction of a novel, enhanced graph representation that encodes both the global structural information and local characteristics of the vector field, as well as other derived information. The approach focuses on development and validation of critical issues in graph-based vector field data reduction , including; (1) identification of the key information of a vector field for the construction of the enhanced graph: (2) efficient storage of the graph; and (3) new graph algorithms for extracting features of interest from the obtained graph. To address these issues, theories and algorithms from dynamical system, algebraic topology, tensor calculus, information theory, and graph theory are extended and integrated in a novel framework. To validate the approach, the PI is working closely with domain scientists from mechanical engineering and aerodynamics to receive advice on the representation of the summary and its utility in specific applications.

The expected results in vector field summary represents will yield an important addition to the existing summarization techniques for various data forms. The analysis and abstraction are based on the enhanced graph and can enrich the conventional graph theory and graph algorithms. The ability to handle both steady and unsteady vector fields improves the theory and practice of dynamical systems in describing fluid dynamic phenomena, benefiting a wide variety of disciplines. Knowledge learned from the vector field summarization can be adapted to the study of summarized representation of more complex geometric data, such as tensor field data. In addition, the research on vector field summary represents one step towards a unified framework of knowledge discovery and integrity from heterogeneous data forms. The developed techniques are expected to be implemented as a software tool that will be applicable in a wider range of scientific and engineering domains. Furthermore, the new theory stemming from this work is expected to enrich the existing education on data analysis and visualization, enabling the development of new courses at both undergraduate and graduate levels in many academic disciplines. The project web site (http://www2.cs.uh.edu/~chengu/vf_summary/vf_summary.html) will provide access to project results, including developed software tools.

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