TitleMeasuring the Distance between Merge Trees (In Book)
inTopological Methods in Data Analysis and Visualization III - Theory, Algorithms, and Applications
Author(s) Kenes Beketayev, Damir Yeliussizov, Dmitriy Morozov, Gunther H. Weber, Bernd Hamann
Editor(s) Peer-Timo Bremer, Valerio Pascucci, Ingrid Hotz, Ronald Peikert
Year 2014
SeriesMathematics 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).