Probabilistic Gradient-Based Extrema Tracking

TL;DR

This paper introduces a probabilistic method for tracking extrema in temporal scalar fields, improving robustness over traditional one-to-one correspondence approaches by capturing multiple potential matches.

Contribution

It proposes a novel probabilistic gradient-based extrema tracking method that considers multiple possible correspondences, addressing limitations of existing topological data analysis techniques.

Findings

Enhanced robustness in extrema tracking.

Successful application in two case studies.

Better handling of low-gradient and boundary regions.

Abstract

Feature tracking is a common task in visualization applications, where methods based on topological data analysis (TDA) have successfully been applied in the past for feature definition as well as tracking. In this work, we focus on tracking extrema of temporal scalar fields. A family of TDA approaches address this task by establishing one-to-one correspondences between extrema based on discrete gradient vector fields. More specifically, two extrema of subsequent time steps are matched if they fall into their respective ascending and descending manifolds. However, due to this one-to-one assignment, these approaches are prone to fail where, e.g., extrema are located in regions with low gradient magnitude, or are located close to boundaries of the manifolds. Therefore, we propose a probabilistic matching that captures a larger set of possible correspondences via neighborhood sampling, or by computing the overlap of the manifolds. We illustrate the usefulness of the approach with two application cases.