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.

The problem of tracking and visualizing cyclones is still an active area of climate research, since the nature of cyclones varies depending on geospatial location and temporal season, resulting in no clear mathematical definition. Thus, many cyclone tracking methods are tailored to specific datasets and therefore do not support general cyclone extraction across the globe. To address this challenge, we present a conceptual application for exploring cyclone evolution by organizing the extracted cyclone tracks into hierarchical groups. Our approach is based on extrema tracking, and the resulting tracks can be defined in a multi-scale structure by grouping the points based on a novel feature descriptor defined on the merge tree, so-called crown features. Consequently, multiple parameter settings can be visualized and explored in a level-of-detail approach, supporting experts to quickly gain insights on cyclonic formation and evolution. We describe a general cyclone exploration pipeline that consists of four modular building blocks: (1) an extrema tracking method, (2) multiple definitions of cyclones as groups of extrema, including crown features, (3) the correlation of cyclones based on the underlying tracking information, and (4) a hierarchical visualization of the resulting feature tracks and their spatial embedding, allowing exploration on a global and local scale. In order to be as flexible as possible, our pipeline allows for exchanging every module with different techniques, such as other tracking methods and cyclone definitions.

We describe a benchmark data generator for tracking methods for two- and three-dimensional time-dependent scalar fields. More and more topology-based tracking methods are presented in the visualization community, but the validation and evaluation of the tracking results are currently limited to qualitative visual approaches. We present a pipeline for creating different ground truth features that support evaluating tracking methods based on quantitative measures. In short, our approach randomly simulates a temporal point cloud with birth, death, split, merge, and continuation events, where the points are then used to derive a scalar field whose topological features correspond to the points. These scalar fields can be used as the input for different tracking methods, where the computed tracks can be compared against the ground truth feature evolution. This approach facilitates directly comparing the results of different tracking methods, independent of the initial feature characterization.