Wasserstein Distances, Geodesics and Barycenters of Merge Trees

Explore a unified computational framework for estimating distances, geodesics, and barycenters of merge trees in this hour-long talk. Learn about the extension of recent work on edit distance and the introduction of a new metric called the Wasserstein distance between merge trees. Discover how this distance is designed for efficient computations of geodesics and barycenters, and its equivalence to the L2-Wasserstein distance between extremum persistence diagrams. Understand the task-based algorithm that can be applied to distance, geodesic, barycenter, or cluster computation, and its potential for acceleration through shared-memory parallelism. Examine extensive experiments on public ensembles and SciVis contest benchmarks, demonstrating the efficiency and qualitative abilities of this approach in generating representative barycenter merge trees. Explore practical applications in visualization, including feature tracking, temporal reduction, and ensemble clustering. Gain insights into the lightweight C++ implementation provided for reproducing results and further research.