Wasserstein Distances, Geodesics and Barycenters of Merge Trees

  title={Wasserstein Distances, Geodesics and Barycenters of Merge Trees},
  author={Mathieu Pont and Jules Vidal and Julie Delon and Julien Tierny},
  journal={IEEE transactions on visualization and computer graphics},
  • Mathieu Pont, Jules Vidal, +1 author J. Tierny
  • Published 16 July 2021
  • Medicine, Computer Science, Engineering
  • IEEE transactions on visualization and computer graphics
This paper presents a unified computational framework for the estimation of distances, geodesics and barycenters of merge trees. We extend recent work on the edit distance [104] and introduce a new metric, called the Wasserstein distance between merge trees, which is purposely designed to enable efficient computations of geodesics and barycenters. Specifically, our new distance is strictly equivalent to the L2-Wasserstein distance between extremum persistence diagrams, but it is restricted to a… Expand


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