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    Area of Science:

    • Medical visualization
    • Computer graphics
    • Computational geometry

    Background:

    • Visualizing complex medical organs and biological structures is hindered by intricate geometry and occlusions.
    • Existing global mapping techniques simplify geometry but fail to preserve crucial geometric context.
    • This limitation makes current methods unsuitable for mission-critical biomedical applications.

    Purpose of the Study:

    • To present a novel shape-preserving local mapping technique for biomedical visualization.
    • To introduce the LMap algorithm for conformal parameterization and deformation of local regions of interest (ROIs).
    • To address the limitations of global mapping techniques in preserving geometric context.

    Main Methods:

    • Developed the LMap algorithm based on extrinsic Ricci flow.
    • Utilized dynamic Ricci flow to ensure local map existence for arbitrary surfaces.
    • Applied the technique to resolve occlusions locally while maintaining overall geometric context.

    Main Results:

    • Demonstrated a shape-preserving local mapping technique that effectively visualizes complex surfaces.
    • Successfully preserved geometric context during occlusion resolution.
    • Validated the LMap algorithm's efficacy in multimodal brain, virtual colonoscopy, and molecular surface visualization.

    Conclusions:

    • The LMap algorithm offers a robust solution for occlusion problems in biomedical visualization.
    • Shape-preserving local mappings enhance the visualization of complex structures without losing geometric context.
    • This method advances the field of mission-critical biomedical visualization.