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Robust Detection of Singularities in Vector Fields Read chapter Read first chapter

2014 | OriginalPaper | Chapter

Measuring the Distance Between Merge Trees

Authors : Kenes Beketayev, Damir Yeliussizov, Dmitriy Morozov, Gunther H. Weber, Bernd Hamann

Published in: Topological Methods in Data Analysis and Visualization III

Publisher: Springer International Publishing

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Abstract

Merge trees represent the topology of scalar functions. To assess the topological 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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Metadata
Title
Measuring the Distance Between Merge Trees
Authors
Kenes Beketayev
Damir Yeliussizov
Dmitriy Morozov
Gunther H. Weber
Bernd Hamann
Copyright Year
2014
Book
Topological Methods in Data Analysis and Visualization III

Print ISBN: 978-3-319-04098-1

Electronic ISBN: 978-3-319-04099-8

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-319-04099-8_10

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