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This paper introduces a framework for tracking Reeb space sheets in time-varying bivariate fields, addressing the challenges of establishing temporal correspondences due to the complexity of Reeb spaces. By employing complementary similarity measures in both the spatial and range domains, the method effectively identifies and tracks persistent structures across different timesteps. Evaluations on synthetic and molecular datasets reveal that this approach not only captures significant temporal changes but also enhances the visual analysis of complex bivariate data.
Tracking Reeb space sheets reveals persistent structures in time-varying bivariate fields, unlocking new insights into dynamic data relationships.
Time-varying bivariate fields arise in many scientific applications, where the relationship between two scalar quantities evolves over time. While topological methods such as merge trees provide an effective framework for identifying and tracking features in univariate data, analogous approaches for bivariate fields remain comparatively underexplored. Reeb spaces extend topological analysis to multivariate data by representing fiber connectivity through a collection of interconnected sheets, making these sheets natural candidates for describing bivariate structures. However, establishing temporal correspondences between sheets is challenging due to the structural complexity of Reeb spaces, sensitivity to noise, and the difficulty of defining meaningful similarity measures across timesteps. We present a framework for tracking Reeb space sheets in time-varying bivariate fields. The method establishes correspondences between sheets in consecutive timesteps using complementary similarity measures defined in the spatial domain and the range space. We evaluate the method on a synthetic torus dataset and two time-varying molecular electronic structure datasets. The results show that Reeb space sheet tracking reveals persistent structures and highlights interesting intervals of temporal change. Overall, the results demonstrate that Reeb space sheets can serve as trackable topological structures and provide a foundation for the visual analysis of time-varying bivariate data.
