• Corpus ID: 238634284

Reeb Graph Metrics from the Ground Up

@article{Bollen2021ReebGM,
  title={Reeb Graph Metrics from the Ground Up},
  author={Brian Bollen and Erin W. Chambers and Joshua A. Levine and E. Munch},
  journal={ArXiv},
  year={2021},
  volume={abs/2110.05631}
}
The Reeb graph has been utilized in various applications including the analysis of scalar fields. Recently, research has been focused on using topological signatures such as the Reeb graph to compare multiple scalar fields by defining distance metrics on the topological signatures themselves. Here we survey five existing metrics that have been defined on Reeb graphs: the bottleneck distance, the interleaving distance, functional distortion distance, the Reeb graph edit distance, and the… 
1 Citations
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TLDR
It is shown that the bottleneck distance is in fact good enough {\em locally}, in the sense that it is able to discriminate a Reeb graph from any other Reeb graphs in a small enough neighborhood, as efficiently as the other metrics do.
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TLDR
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TLDR
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TLDR
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TLDR
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TLDR
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TLDR
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TLDR
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TLDR
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