Edit Distance between Merge Trees.

Abstract: A merge tree captures the topology of sub-level and super-level sets of a scalar function. Topological structures such as the merge tree provide an abstract and succinct representation of scientific data available as a static or time-varying scalar function. They facilitate effective visualization and interactive exploration of feature-rich data. Comparative tasks such as visual identification of correspondence between features in the data or locating key events require a feature-aware comparison measure between scalar functions. We present an approach based on tree edit distance to compare merge trees. The comparison measure satisfies metric properties, it can be computed efficiently, and the cost model for the edit operations is both intuitive and captures well-known properties of merge trees. I will introduce the distance measure, outline an algorithm for computing the measure, and describe how the edit distance supports feature-driven analysis and visualization of time-varying scalar functions from CFD and 3D cryo electron microscopy data. [https://vgl.csa.iisc.ac.in/pub/paper.php?pid=057]

computational geometryalgebraic topologycombinatoricsgeometric topologyprobability

Audience: advanced learners

Asia Pacific Seminar on Applied Topology and Geometry