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    This summary is machine-generated.

    This study introduces a novel local tree edit distance for comparing topological structures in scalar fields. This method enables finer-grained analysis and applications like feature tracking in complex datasets.

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    Area of Science:

    • Scientific visualization
    • Computational topology
    • Data analysis

    Background:

    • Comparative analysis of scalar fields is crucial for applications like feature tracking.
    • Topological structures offer efficient representations for scalar field comparison.
    • Existing global measures lack fine-grained, multi-scale analytical capabilities.

    Purpose of the Study:

    • To develop a local measure for comparing topological structures.
    • To enable detailed, multi-scale analysis of scalar fields.
    • To enhance applications such as feature tracking and symmetry detection.

    Main Methods:

    • Definition of a local variant of the tree edit distance.
    • Application of the local tree edit distance to merge trees.
    • Experimental validation on diverse datasets.

    Main Results:

    • The proposed local measure facilitates detailed comparative analysis of topological structures.
    • Demonstrated utility in analyzing time-varying scalar fields and 3D cryo-electron microscopy data.
    • Successful application in symmetry detection and feature tracking.

    Conclusions:

    • The local tree edit distance provides a powerful tool for fine-grained topological analysis.
    • This approach significantly advances the comparison of scalar field structures across different scales.
    • The method offers practical benefits for scientific visualization and data analysis applications.