Collaborative Research: Compression of Geometry Datasets

DMS-0138458彼得·施罗德DMS-0221642罗纳德·A. DevoreDMS-0221669 Mathieu Desbrun这是一个合作项目，由CARGO计划根据DMS-0138458、DMS-0221642和DMS-0221669资助。 这是信息时代。 无论是科学计算还是逆向工程，无论是遥感还是医学，每天都在创造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，相关性还是与其他模态的数据配准。 压缩是所有这些应用中共同的关键问题，现有的数据处理技术不能提供应用所要求的高效和几何上忠实的表示。事实上，一个令人满意的数据处理平台将不会创建当前技术的渐进式进步，而是通过一个基本的调查，如何表示与固有的几何大数据集。为了追求必要的进步，一个由研究人员和应用程序开发人员组成的团队，代表了包括数学，计算机科学和工程在内的几个学科的专业知识。作为研究的驱动力，特别有针对性的应用程序（DTED，逆向工程，物理模拟）已被选中，以指导制定最关键和最有意义的问题，以及测试方法来解决这些问题。 该团队正在通过建立新的数学理论，包括确定性模型，适当的应用程序特定的错误度量（例如，Haussdorf距离（而不是Lp范数），一种基于Kolmogorov熵的信息理论来确定最优压缩，以及发展非线性方法来表示熵意义上接近最优的数据集。

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.