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Using Foliation Leaves to Extract Reeb Graphs on Surfaces.

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    This study introduces a novel method for extracting Reeb graphs using foliation leaves, enhancing surface representation. This approach ensures stable and concise topological encoding, improving shape analysis and surface symmetry representation.

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    Area of Science:

    • Computer Graphics
    • Computational Geometry
    • Topology

    Background:

    • Reeb graph extraction is crucial for surface topology analysis.
    • Existing methods using isolines suffer from instability and lack conciseness.
    • Stable and accurate Reeb graph extraction remains a challenge.

    Purpose of the Study:

    • To develop a robust method for Reeb graph extraction using foliation leaves.
    • To enhance the stability and conciseness of Reeb graphs for surface representation.
    • To improve shape analysis by leveraging improved Reeb graph properties.

    Main Methods:

    • Generating measured harmonic foliations by defining loops for initialization.
    • Diffusing foliation leaves from initialized loops across the surface.
    • Utilizing determined loops to represent surface components for robust relationship detection.

    Main Results:

    • Extraction of stable and concise Reeb graphs.
    • Demonstrated fixed neighboring relationships between leaves once loops are determined.
    • Developed novel measures for loop determination and improved foliation generation.

    Conclusions:

    • The proposed foliation-based method offers a stable and concise approach to Reeb graph extraction.
    • Manual loop prescription allows for user-defined Reeb graph structures.
    • The method enhances Reeb graph potential for representing surface symmetries and ignoring topological noise, promoting shape analysis.