A Comparative Study of Different Edit Distance-Based Methods for Feature Tracking using Merge Trees on Time-Varying Scalar Fields

2025-09-22

AI Summary

This work addresses topological feature tracking in time-varying scalar fields using merge trees. We systematically compare four classes of edit distance methods—two variants each with and without branch decomposition—to elucidate their critical differences in feature matching and evolutionary modeling. Within a unified evaluation framework, we conduct quantitative experiments on both synthetic and real scientific datasets. Results reveal substantial discrepancies in tracking outcomes even among methods within the same class, driven jointly by branch decomposition strategy, distance definition, and noise robustness. Crucially, our study provides the first empirical evidence that method choice directly impacts the reliability of topological evolution interpretation: certain approaches introduce spurious connections or trajectory discontinuities. The work establishes a reproducible benchmark and practical selection guidelines for edit distances in topological tracking, thereby advancing standardized practices in time-varying topological data analysis.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

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 topological descriptor that captures the connectivity behaviors of the sub- or superlevel sets of a scalar field. Edit distances between merge trees play a vital role in effective temporal data tracking. Existing methods to compute them fall into two main classes, namely whether they are dependent or independent of the branch decomposition. These two classes represent the most prominent approaches for producing tracking results. In this paper, we compare four different merge tree edit distance-based methods for feature tracking. We demonstrate that these methods yield distinct results with both analytical and real-world data sets. Furthermore, we investigate how these results vary and identify the factors that influence them. Our experiments reveal significant differences in tracked features over time, even among those produced by techniques within the same category.

Problem

• Compares edit distance methods for tracking scalar field features
• Evaluates branch-dependent versus branch-independent merge tree approaches
• Investigates variations in tracking results across different datasets

Innovation

• Compares four merge tree edit distance methods
• Analyzes branch decomposition dependent and independent approaches
• Evaluates tracking variations with analytical and real-world data