The edit distance for Reeb graphs of surfaces
Abstract
Reeb graphs are structural descriptors that capture shape properties of a topological space from the perspective of a chosen function. In this work we define a combinatorial metric for Reeb graphs of orientable surfaces in terms of the cost necessary to transform one graph into another by edit operations. The main contributions of this paper are the stability property and the optimality of this edit distance. More precisely, the stability result states that changes in the functions, measured by the maximum norm, imply not greater changes in the corresponding Reeb graphs, measured by the edit distance. The optimality result states that our edit distance discriminates Reeb graphs better than any other metric for Reeb graphs of surfaces satisfying the stability property.
Keywords
Cite
@article{arxiv.1411.1544,
title = {The edit distance for Reeb graphs of surfaces},
author = {Barbara Di Fabio and Claudia Landi},
journal= {arXiv preprint arXiv:1411.1544},
year = {2014}
}
Comments
An extended abstract of this work appeared in: E. Barcucci et al. (Eds.): DGCI 2014, LNCS 8668, pp. 202-213, 2014. c