Edit Distance between Merge Trees

TL;DR

This paper introduces a metric-based tree edit distance method for comparing merge trees, enabling effective feature-driven analysis of scalar fields in various scientific data applications.

Contribution

It presents a novel, efficient, and intuitive approach to compute the similarity between merge trees using a metric-preserving edit distance with a well-designed cost model.

Findings

The method satisfies metric properties and is computationally efficient.

Experimental results demonstrate its utility across diverse datasets.

The approach supports feature-driven visualization and analysis.

Abstract

Topological structures such as the merge tree provide an abstract and succinct representation of scalar fields. They facilitate effective visualization and interactive exploration of feature-rich data. A merge tree captures the topology of sub-level and super-level sets in a scalar field. Estimating the similarity between merge trees is an important problem with applications to feature-directed visualization of time-varying data. We present an approach based on tree edit distance to compare merge trees. The comparison measure satisfies metric properties, it can be computed efficiently, and the cost model for the edit operations is both intuitive and captures well-known properties of merge trees. Experimental results on time-varying scalar fields, 3D cryo electron microscopy data, shape data, and various synthetic datasets show the utility of the edit distance towards a feature-driven analysis of scalar fields.