Branch Decomposition?Independent Edit Distances for Merge Trees

Edit distances between merge trees of scalar fields have many applications in scientific visualization, such as ensemble analysis, feature tracking or symmetry detection. In this paper, we propose branch mappings, a novel approach to the construction edit mappings for trees. Classic match nodes edges two onto each other, and therefore either rely on decompositions both use auxiliary node properties determine matching. contrast, employ instead similarity information, are independent predetermined decompositions. Especially topological features, which typically based properties, allows more intuitive distance measure is also less susceptible instabilities from small-scale perturbations. For with ????(n) nodes, describe an ????(n4) algorithm computing optimal faster than only other decomposition-independent method literature by linear factor. Furthermore, compare results our synthetic real-world examples demonstrate its practicality utility.