Topological Feature Search in Time-Varying Multifield Data

Abstract

A wide range of data that appear in scientific experiments and simulations are multivariate or multifield in nature, consisting of multiple scalar fields. Topological feature search of such data aims to reveal important properties useful to the domain scientists. It has been shown in recent works that a single scalar field is insufficient to capture many important topological features in the data, instead one needs to consider topological relationships between multiple scalar fields. In the current paper, we propose a novel method of finding similarity between two multifield data by comparing their respective fiber component distributions. Given a time-varying multifield data, the method computes a metric plot for each pair of histograms at consecutive time stamps to understand the topological changes in the data over time. We validate the method using real and synthetic data. The effectiveness of the proposed method is shown by its ability to capture important topological features that are not always possible to detect using the individual component scalar fields.

Scalar Field Comparison with Topological Descriptors: Properties and Applications for Scientific Visualization

“…Comparison of multi-fields. An approach proposed by Agarwal et al [ACN21] for comparing multi-fields suggested using fiber component distributions. First, the JCN is computed for the given multi-field.…”

“…In the study of time-varying and multi-field comparison (see Sect. 7), the L p distance between two fiber component distributions is proven to be a metric [ACN21]. The mathematical properties associated with the similarity measures for multi-resolution Reeb spaces remain unknown due to partially heuristic matchings between nodes and attributions, in a way similar to the situation in [HSKK01,ZBB04].…”