Topology-based Methods for Analysis and Visualization of Noisy Data

University Of California-Davis, Davis CA

Investigators

Abstract

Topology-based Methods for Analysis and Visualization of Noisy Data Principal Investigator: Bernd Hamann, University of California, Davis Abstract The 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.