Name
Abstract | ||
|---|---|---|
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 application of our results, we analyze a natural simplification scheme for Reeb graphs, and show that persistent features in Reeb graph remains persistent under simplification. Understanding the stability of important features of the Reeb graph under simplification is an interesting problem on its own right, and critical to the practical usage of Reeb graphs. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1145/2582112.2582169 | Proceedings of the thirtieth annual symposium on Computational geometry |
Keywords | DocType | Volume |
measuring distance,natural simplification scheme,reeb graph,reeb graphs,extended persistence diagram,differentiating input function,input function,functional distortion distance,bottleneck distance,important feature,persistent feature,appropriate dimension | Conference | abs/1307.2839 |
Citations | PageRank | References |
27 | 0.92 | 26 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ulrich Bauer | 1 | 102 | 10.84 |
| Ge, Xiaoyin | 2 | 63 | 3.10 |
| Yusu Wang | 3 | 860 | 57.40 |