Computing and Visualizing Time-Varying Merge Trees for High-Dimensional Data

Patrick Oesterling, Christian Heine, Gunther Weber, Dmitriy Morozov, Gerik Scheuermann.
Topological Methods in Data Analysis and Visualization IV: Theory, Algorithms, and Applications, pages 87–101, 2017.
DOI: 10.1007/978-3-319-44684-4_5
We introduce a new method that identifies and tracks features in arbitrary dimensions using the merge tree—a structure for identifying topological features based on thresholding in scalar fields. This method analyzes the evolution of features of the function by tracking changes in the merge tree and relates features by matching subtrees between consecutive time steps. Using the time-varying merge tree, we present a structural visualization of the changing function that illustrates both features and their temporal evolution. We demonstrate the utility of our approach by applying it to temporal cluster analysis of high-dimensional point clouds.