2021/11/04 by M. Pegoraro, Pegoraro, Matteo · 1 citation
Computer Science · Engineering · #Topological and Geometric Data Analysis #3D Shape Modeling and Analysis #Computer Graphics and Visualization Techniques
paper · pdf · doi:10.48550/arxiv.2111.02738
In this paper we define a novel edit distance for merge trees, which we argue to be suitable for a good range of applications. Relying also on some technical results contained in other works, we investigate its stability properties, which end up being analogous to the ones of the 1-Wasserstein distance between persistence diagrams. In the appendix, we extensively compare our metric in relationship with other metrics appearing in the literature, with both theoretic and practical considerations and a simulation.