|Title||Measuring the Distance between Merge Trees
(In Book) |
|in||Topological Methods in Data Analysis and Visualization III - Theory, Algorithms, and Applications|
Kenes Beketayev, Damir Yeliussizov, Dmitriy Morozov, Gunther H. Weber, Bernd Hamann |
Peer-Timo Bremer, Valerio Pascucci, Ingrid Hotz, Ronald Peikert |
|Series||Mathematics and Visualization|
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).