Collaborative Research: Compression of Geometry Datasets

California Institute Of Technology, Pasadena CA

Investigators

Abstract

DMS-0138458 Peter Schroder DMS-0221642 Ronald A. Devore DMS-0221669 Mathieu Desbrun This is a collaborative project funded by the CARGO program under DMS-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 created daily. 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 all these 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 from several 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 theory including deterministic models, appropriate application specific error metrics (e.g., Haussdorf distance rather than 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.