Collaborative Research: Compression of Geometry Datasets

合作研究：几何数据集的压缩

• 批准号: 0221642
• 负责人: Ronald DeVore
• 金额: $ 22.5万
• 依托单位: University South Carolina Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-05-01 至 2005-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0221642&HistoricalAwards=false
• 关键词: Collaborative; Research; Compression; Geometry; Datasets

DMS-0138458Peter SchroderDMS-0221642Ronald A. DevoreDMS-0221669Mathieu DesbrunThis is a collaborative project funded by the CARGO program underDMS-0138458, DMS-0221642, and DMS-0221669. This is the Age of Information. Whether it be in scientific computation or reverse engineering, in remote sensing or medicine, data sets of incredible resolution and exquisite detail are createddaily. These data sets often have geometric structure which contains important information about the data and its application. The usefulness of such geometric datasets rests on our ability to process them efficiently, whether it be for storage, transmission, visual display, correlation, or registration against data from other modalities. Compression is the common critical issue in allthese applications.Current data processing technology does not provide the efficient and geometrically faithful representations demanded by applications. In fact, a satisfactory data processing platform will not be created by incremental advances of current technology but rather through a fundamental investigation of how to represent large data sets with inherent geometry. To pursue the necessary advances a team of researchers and application developers representing expertise fromseveral disciplines including mathematics, computer science, and engineering has been assembled. As drivers of the research, specially targeted applications (DTED, reverse engineering, physical simulation) have been selected to guide the formulation of the most critical and meaningful problems, as well as testing approaches to solving them. The team is carrying out fundamental investigations on the representation and compression of data sets with geometry by building new mathematical theoryincluding deterministic models, appropriate application specific error metrics (e.g., Haussdorf distance ratherthan Lp norms), an information theory based on Kolmogorov entropy to determine the optimal compression, and the development of nonlinear methods for representing the data sets which are near optimal in the entropy sense.

DMS-0138458PETER SCHRODERDMS-0221642RONALD A. DEVOREDMS-0221669MATHIEU DESBRUNTHITHIS是由货运计划UnderDMS-0138458资助的协作项目 这是信息时代。 无论是在科学计算还是逆向工程中，在遥感或药物中，都会创建令人难以置信的分辨率和精致细节的数据集。 这些数据集通常具有几何结构，其中包含有关数据及其应用的重要信息。 这种几何数据集的有用性取决于我们有效地处理它们的能力，无论是用于存储，传输，视觉显示，相关性还是针对其他模式的数据进行注册。 压缩是Allthe应用程序中常见的关键问题。电流数据处理技术不能提供应用程序要求的有效且几何忠实的表示。实际上，通过当前技术的增量进步，而是通过对如何用固有几何形状表示大型数据集的基本调查来创建令人满意的数据处理平台。为了追求必要的进步，已经组建了一组研究人员和应用程序开发人员，这些研究人员和应用程序开发人员组成了包括数学，计算机科学和工程在内的专业知识。作为研究的驱动因素，已经选择了专门针对的应用程序（DTED，反向工程，物理模拟）来指导最关键和最有意义的问题的制定以及解决这些问题的测试方法。 该团队正在通过建立包括确定性模型的新数学理论，包括适当的应用特定误差指标（例如，Haussdorf距离而不是LP Norms），基于Kolmogorov的信息理论来确定确定的信息理论，从而对具有几何学的数据集进行了基本调查，包括确定性误差指标（例如，适当的应用程序）最佳压缩以及用于表示熵意义上几乎最佳数据集的非线性方法的开发。