@inproceedings{Bauer2014MeasuringDB,
title={Measuring Distance between Reeb Graphs},
author={U. Bauer and Xiaoyin Ge and Y. Wang},
booktitle={Symposium on Computational Geometry},
year={2014}
}

We propose a metric for Reeb graphs, called the functional distortion distance. Under this distance, the Reeb graph is stable against small changes of input functions. At the same time, it remains discriminative at differentiating input functions. In particular, the main result is that the functional distortion distance between two Reeb graphs is bounded from below by the bottleneck distance between both the ordinary and extended persistence diagrams for appropriate dimensions.
As an… CONTINUE READING