Computing a Stable Distance on Merge Trees

Abstract

Fig. 1. Starting with a baseline scalar field and merge tree, a small perturbation may change the topology of a merge tree. The top graph plots the bottleneck, merge tree matching, and L ∞ distance between the baseline and 36 perturbed scalar fields which all exhibit a horizontal instability. The merge tree matching distance is shown here to lie between the bottleneck distance and the L ∞ distance even when faced with these instabilities.