Comparative Analysis of Merge Trees Using Local Tree Edit Distance

Comparative analysis of scalar fields is an important problem with various applications including feature-directed visualization and feature tracking in time-varying data. Comparing topological structures that are abstract and succinct representations of the scalar fields lead to faster and meaningful comparison. While there are many distance or similarity measures to compare topological structures in a global context, there are no known measures for comparing topological structures locally. While the global measures have many applications, they do not directly lend themselves to fine-grained analysis across multiple scales. We define a local variant of the tree edit distance and apply it towards local comparative analysis of merge trees with support for finer analysis. We also present experimental results on time-varying scalar fields, 3D cryo-electron microscopy data, and other synthetic data sets to show the utility of this approach in applications like symmetry detection and feature tracking.

Automated summary

Comparative analysis of scalar fields is important for various applications such as feature-directed visualization and feature tracking in time-varying data. Comparing topological structures of scalar fields provides faster and more meaningful comparisons. While global measures exist for comparing topological structures, there is a lack of measures for local comparison. This study presents a local variant of the tree edit distance to enable fine-grained analysis of merge trees, with experimental results demonstrating its utility in different applications.