Measuring the Distance between Merge Trees

title="Measuring the Distance between Merge Trees",
booktitle="Topological Methods in Data Analysis and Visualization III - Theory, Algorithms, and Applications",
author="Kenes Beketayev AND Damir Yeliussizov AND Dmitriy Morozov AND Gunther H. Weber AND Bernd Hamann ",
editor=" Peer-Timo Bremer AND Valerio Pascucci AND Ingrid Hotz AND Ronald Peikert ",
series="Mathematics and Visualization",
abstract="Merge trees represent the topology of scalar functions. To assess the topo- logical similarity of functions, one can compare their merge trees. To do so, one needs a notion of a distance between merge trees, which we define. We provide examples of using our merge tree distance and compare this new measure to other ways used to characterize topological similarity (bottleneck distance for persistence diagrams) and numerical difference (L∞-norm of the difference between functions).",
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