conference paper
Measuring distance between Reeb graphs
published
yes
Ulrich
Bauer
author 2ADD483A-F248-11E8-B48F-1D18A9856A870000-0002-9683-0724
Xiaoyin
Ge
author
Yusu
Wang
author
HeEd
department
SoCG: Symposium on Computational Geometry
Topological Complex Systems
project
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. Copyright is held by the owner/author(s).
ACM2014Kyoto, Japan
eng
Proceedings of the Annual Symposium on Computational Geometry10.1145/2582112.2582169
464 - 473
Bauer, Ulrich, et al. “Measuring Distance between Reeb Graphs.” <i>Proceedings of the Annual Symposium on Computational Geometry</i>, ACM, 2014, pp. 464–73, doi:<a href="https://doi.org/10.1145/2582112.2582169">10.1145/2582112.2582169</a>.
U. Bauer, X. Ge, Y. Wang, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 464–473.
Bauer, Ulrich, Xiaoyin Ge, and Yusu Wang. “Measuring Distance between Reeb Graphs.” In <i>Proceedings of the Annual Symposium on Computational Geometry</i>, 464–73. ACM, 2014. <a href="https://doi.org/10.1145/2582112.2582169">https://doi.org/10.1145/2582112.2582169</a>.
Bauer U, Ge X, Wang Y. 2014. Measuring distance between Reeb graphs. Proceedings of the Annual Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, 464–473.
Bauer, U., Ge, X., & Wang, Y. (2014). Measuring distance between Reeb graphs. In <i>Proceedings of the Annual Symposium on Computational Geometry</i> (pp. 464–473). Kyoto, Japan: ACM. <a href="https://doi.org/10.1145/2582112.2582169">https://doi.org/10.1145/2582112.2582169</a>
U. Bauer, X. Ge, and Y. Wang, “Measuring distance between Reeb graphs,” in <i>Proceedings of the Annual Symposium on Computational Geometry</i>, Kyoto, Japan, 2014, pp. 464–473.
Bauer U, Ge X, Wang Y. Measuring distance between Reeb graphs. In: <i>Proceedings of the Annual Symposium on Computational Geometry</i>. ACM; 2014:464-473. doi:<a href="https://doi.org/10.1145/2582112.2582169">10.1145/2582112.2582169</a>
21562018-12-11T11:56:02Z2021-01-12T06:55:39Z