Topology-based Methods for Analysis and Visualization of Noisy Data

基于拓扑的噪声数据分析和可视化方法

• 批准号: 0702817
• 负责人: Bernd Hamann
• 金额: --
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-09-01 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0702817&HistoricalAwards=false
• 关键词: Topology; based; Methods; Analysis; Visualization

Topology-based Methods for Analysis and Visualization of Noisy DataPrincipal Investigator: Bernd Hamann, University of California, DavisAbstractThe size of scientific data sets that are generated by evolving supercomputers, large sensor networks, and high-resolution imaging devices is increasing rapidly, at an exponential rate. This project addresses the need for more effective data analysis methods. It develops technologies concerned with the analysis and representation of very large scientific data sets, emphasizing concepts that capture qualitative characteristics. In light of the limitations of purely visualization-based approaches applied to "raw" scientific data sets directly, this project aims at devising new concepts for visualizing very large and complex data sets. The methods being developed first extract meaningful qualitative information from a given data set, which is then used to present the higher-level information content of the data set in a significantly more compact form, thus stressing relevant qualitative behavior.The project builds on concepts from classical topology and geometry, which have contributed substantially to the development of the relatively new fields of computational topology and computational geometry. These two fields hold great potential for substantially advancing the visualization technology for understanding extremely large, complicated data sets. This projects adapts (and generalizes) computational topology and computational geometry algorithms that are well-established for smooth mathematical functions to real-world, finite-sample data sets, i.e., functions sampled at a finite number of points (that could possibly be connected by a mesh). Real-world data sets are noisy, which further complicates the application of topological methods that were developed originally for smooth functions. This project investigates the generalization of techniques based on Morse and Morse-Smale theory (studying critical-point behavior and drawing qualitative conclusions about functions) to discretized scalar fields that change over time and also contain noise.

基于拓扑的方法，用于分析和可视化噪声数据的研究者：加利福尼亚大学伯恩德·哈曼（Bernd Hamann速度。该项目解决了对更有效的数据分析方法的需求。它开发了与非常大的科学数据集的分析和表示有关的技术，强调捕获定性特征的概念。鉴于直接应用于“原始”科学数据集的纯粹基于可视化的方法的局限性，该项目旨在设计新的概念来可视化非常大而复杂的数据集。开发的方法首先从给定的数据集中提取有意义的定性信息，然后将其用来以更紧凑的形式出现数据集的高级信息内容，从而强调相关的定性行为。该项目基于概念。古典拓扑和几何形状，为相对较新的计算拓扑和计算几何学领域的发展做出了重大贡献。这两个领域具有很大的潜力，可以实质上推进可视化技术，以理解极其大，复杂的数据集。该项目适应（并概括）计算拓扑和计算几何算法，这些算法符合现实世界，有限样本数据集，即以有限数量采样的函数（可以通过有限的点来连接）网格）。现实世界中的数据集很嘈杂，这进一步使最初用于平滑功能开发的拓扑方法的应用变得复杂。该项目研究了基于Morse和Morse-Male理论（研究临界点行为并得出有关功能的定性结论）的技术的概括，以随着时间的流逝而变化并包含噪声。