In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

Lieyu Shi

will defend his proposal

Clustering-based Integral Curve Reduction and Feature Extraction for Flow Visualization

Abstract

Vector fields are commonly used in various engineering and scientific applications for the study of different dynamical systems. Among many visualization techniques, integral curves based approaches (e.g., streamlines and pathlines) play an important role for understanding and interpreting the physical behaviors of vector fields. Spatial occlusion and cluttering of integral curves generated from complex vector fields severely hinder the proper investigation of latent physical features resident in the flow. To solve this issue, clustering-based techniques are often adopted to simplify unimportant integral curves while preserving those with important features (e.g., vortex structures and separation regions). However, current clustering-based techniques (coupled with specific similarity measures for integral curves) cannot produce simplified representation within reasonable time to effectively convey the important features of the data, especially for particle trajectories stemming from particle-based fluid simulation that consists of tens of thousands of curves. Furthermore, there is no an empirical guidance nor a systematic evaluation for the selection of proper clustering techniques and similarity measures.

To address the above challenges, we first propose a simple geometric-based similarity measure with linear time complexity to extract the vortical structures from densely placed streamlines of vector fields. We demonstrate its effectiveness and efficiency by comparing it with the state-of-the-art method and by applying it to particle trajectory data sets. Second, to systematically evaluate the current clustering-based techniques for flow data, we perform a first comprehensive evaluation on more than 80 different combinations of the clustering techniques and similarity metrics. In particular, we perform both quantitative and qualitative evaluation on their clustering quality. We report the evaluation results via a ranking strategy and a number of comparative visualizations, from which we derived a first set of empirical guidance for selecting appropriate clustering techniques and similarity measures that will be instructive for the flow visualization community. Finally, we propose a separation estimate strategy based on the analysis and quantification of the different characteristics between neighboring line segments, which enables us to extract separation regions from sparse input of integral curves without reconstructing the entire vector fields. Such a separation estimate strategy can be integrated into the integral curve clustering framework to enable the clustering algorithm to identify more complete features in the integral curve data.

Date: Tuesday, April 9, 2019
Time: 1:00 - 2:30 PM
Place: PGH 550
Advisors: Dr. Guoning Chen

Faculty, students, and the general public are invited.