Edit distances for comparing merge trees

A merge tree captures the topology of sub-level and super-level sets in a scalar field. Estimating the similarity or dissimilarity between merge trees is an important problem with applications to visualization of time-varying and multi-field data. We present a tree edit distance based approach with a general subtree gap model to compare merge trees. The cost model is based on topological persistence. Experimental results on time-varying data show the utility of the method towards a feature-driven analysis of scalar fields.