Related papers: Geometry-Aware Merge Tree Comparisons for Time-Var…
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…
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…
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…
Physical phenomena in science and engineering are frequently modeled using scalar fields. In scalar field topology, graph-based topological descriptors such as merge trees, contour trees, and Reeb graphs are commonly used to characterize…
Comparative analysis of scalar fields is an important problem with various applications including feature-directed visualization and feature tracking in time-varying data. Comparing topological structures that are abstract and succinct…
Feature tracking in time-varying scalar fields is a fundamental task in scientific computing. Topological descriptors, which summarize important features of data, have proved to be viable tools to facilitate this task. The merge tree is a…
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…
Temporal sequences of terrains arise in various application areas. To analyze them efficiently, one generally needs a suitable abstraction of the data as well as a method to compare and match them over time. In this paper we consider merge…
The interleaving distance is a key tool for comparing merge trees, which provide topological summaries of scalar functions. In this work, we define an average merge tree for a pair of merge trees using the interleaving distance. Since such…
Merge trees, contour trees, and Reeb graphs are graph-based topological descriptors that capture topological changes of (sub)level sets of scalar fields. Comparing scalar fields using their topological descriptors has many applications in…
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 flexible and probabilistic framework for tracking topological features in time-varying scalar fields using merge trees and partial optimal transport. Merge trees are topological descriptors that record the…
Merge trees are a common topological descriptor for data with a hierarchical component, such as terrains and scalar fields. The interleaving distance, in turn, is a common distance for comparing merge trees. However, the interleaving…
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…
Merge trees are a type of topological descriptors that record the connectivity among the sublevel sets of scalar fields. They are among the most widely used topological tools in visualization. In this paper, we are interested in sketching a…
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…
Merge trees are a powerful tool from topological data analysis that is frequently used to analyze scalar fields. The similarity between two merge trees can be captured by an interleaving: a pair of maps between the trees that jointly…
In this work, we propose trait-based merge trees a generalization of merge trees to feature level sets, targeting the analysis of tensor field or general multi-variate data. For this, we employ the notion of traits defined in attribute…
In topological data analysis and visualization, topological descriptors such as persistence diagrams, merge trees, contour trees, Reeb graphs, and Morse-Smale complexes play an essential role in capturing the shape of scalar field data. We…
This paper presents a generalization of the Wasserstein distance for both persistence diagrams and merge trees [20], [66] that takes advantage of the regions of their topological features in the input domain. Specifically, we redefine the…