Related papers: A Finitely Stable Edit Distance for Merge Trees

This paper introduces a novel stability measure for edit distances between merge trees of piecewise linear scalar fields. We apply the new measure to various metrics introduced recently in the field of scalar field comparison in scientific…

In this work we define a novel edit distance for trees considered with some abstract weights on the edges. The metric is driven by the idea of considering trees as topological summaries in the context of persistence and topological data…

In this work we define a metric structure to compare functions defined on different merge trees. The metric introduced possesses some stability properties, which we illustrate within a standard topological data analysis (TDA) framework, and…

Distances on merge trees facilitate visual comparison of collections of scalar fields. Two desirable properties for these distances to exhibit are 1) the ability to discern between scalar fields which other, less complex topological…

In this paper, we present a novel heuristic algorithm for the stable but NP-complete deformation-based edit distance on merge trees. Our key contribution is the introduction of a user-controlled look-ahead parameter that allows to trade off…

Comparative analysis of scalar fields in scientific visualization often involves distance functions on topological abstractions. This paper focuses on the merge tree abstraction (representing the nesting of sub- or superlevel sets) and…

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…

This paper presents a unified computational framework for the estimation of distances, geodesics and barycenters of merge trees. We extend recent work on the edit distance [106] and introduce a new metric, called the Wasserstein distance…

In scientific visualization, scalar fields are often compared through edit distances between their merge trees. Typical tasks include ensemble analysis, feature tracking and symmetry or periodicity detection. Tree edit distances represent…

Adapting a definition given by Bjerkevik and Lesnick for multiparameter persistence modules, we introduce an $\ell^p$-type extension of the interleaving distance on merge trees. We show that our distance is a metric, and that it…

In this work we study the interleaving distance between merge trees from a combinatorial point of view. We use a particular type of matching between trees to obtain a novel formulation of the distance. With such formulation, we tackle the…

This paper introduces decorated merge trees (DMTs) as a novel invariant for persistent spaces. DMTs combine both $\pi_0$ and $H_n$ information into a single data structure that distinguishes filtrations that merge trees and persistent…

Metrics for merge trees that are simultaneously stable, informative, and efficiently computable have so far eluded researchers. We show in this work that it is possible to devise such a metric when restricting merge trees to ordered domains…

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…

We study the problem of how well a tree metric is able to preserve the sum of pairwise distances of an arbitrary metric. This problem is closely related to low-stretch metric embeddings and is interesting by its own flavor from the line of…

Merge trees are fundamental structures in topological data analysis. Interleaving distance is a widely accepted metric for comparing merge trees, with applications in visualization and scientific computing. While a greedy algorithm exists…

In this article, we propose tree edit distance with variables, which is an extension of the tree edit distance to handle trees with variables and has a potential application to measuring the similarity between mathematical formulas,…

The graph edit distance is used for comparing graphs in various domains. Due to its high computational complexity it is primarily approximated. Widely-used heuristics search for an optimal assignment of vertices based on the distance…

Geometric graphs appear in many real-world data sets, such as road networks, sensor networks, and molecules. We investigate the notion of distance between embedded graphs and present a metric to measure the distance between two geometric…

Merge trees are a type of graph-based topological summary that tracks the evolution of connected components in the sublevel sets of scalar functions. They enjoy widespread applications in data analysis and scientific visualization. In this…