Researchers track Reeb-space sheets to visualize time-varying bivariate fields

Time-varying bivariate fields appear across scientific applications, but topological analysis of them has lagged behind univariate methods like merge trees. Reeb spaces extend topology to multivariate data by modeling fiber connectivity as a collection of interconnected sheets, making those sheets natural features for tracking. However, correlating sheets across timesteps is difficult due to structural complexity, sensitivity to noise, and the lack of meaningful similarity measures. Now, Mohit Sharma and colleagues propose a framework that tracks Reeb-space sheets by using complementary similarity measures defined in both the spatial domain and the range space, enabling robust correspondences between consecutive timesteps.

The method was evaluated on a synthetic torus dataset and two time-varying molecular electronic structure datasets. Results show that sheet tracking reliably exposes persistent structures while highlighting intervals of significant temporal change. This demonstrates that Reeb-space sheets can serve as trackable topological structures, providing a foundation for interactive visual analysis of time-varying bivariate data. The work opens the door to better understanding of dynamic scientific phenomena, from chemical reactions to physical simulations, by turning abstract topological features into concrete, traceable objects.