Categorizing Merge Tree Edit Distances by Stability using Minimal Vertex Perturbation

📝 Original Info

• Title: Categorizing Merge Tree Edit Distances by Stability using Minimal Vertex Perturbation
• ArXiv ID: 2508.02352
• Date: 2025-08-04
• Authors: Florian Wetzels, Christoph Garth

📝 Abstract

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 visualization. While previous stability measures are unable to capture the fine-grained hierarchy of the considered distances, we obtain a classification of stability that fits the efficiency of current implementations and quality of practical results. Our results induce several open questions regarding the lacking theoretical analysis of such practical distances.

💡 Deep Analysis

This research explores the key findings and methodology presented in the paper: Categorizing Merge Tree Edit Distances by Stability using Minimal Vertex Perturbation.

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 visualization. While previous stability measures are unable to capture the fine-grained hierarchy of the considered distances, we obtain a classification of stability that fits the efficiency of current implementations and quality of practical results. Our results induce several open questions regarding the lacking theoretical analysis of such practical distances.

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