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    Area of Science:

    • Scientific visualization
    • Computational topology
    • Data analysis

    Background:

    • Topological simplification is crucial for analyzing and visualizing scalar data.
    • Existing methods are limited in the types of topological features they can preserve, especially saddle pairs in 3D data.
    • Optimization of topological simplification is computationally intensive and not practical for real-world datasets.

    Purpose of the Study:

    • To develop a practical and efficient approach for optimizing topological simplification of scalar data.
    • To extend existing persistence optimization frameworks for topological simplification.
    • To enable the preservation of significant topological features, including saddle pairs, and the cancellation of non-signal features.

    Main Methods:

    • Leveraging generic persistence optimization frameworks.
    • Developing tailored accelerations for topological simplification.
    • Producing an output field close to the input field by optimizing the cancellation of non-signal persistence pairs and the preservation of signal persistence pairs.
    • Extending the approach beyond extrema to include saddle pairs.

    Main Results:

    • Achieved substantial accelerations compared to existing frameworks, making optimization practical for real-life datasets.
    • Enabled direct visualization and analysis of topologically simplified data, such as isosurfaces with fewer components and handles.
    • Demonstrated practical improvements in extracting filament structures and removing filament loops from 3D data.
    • Showcased the ability to repair genus defects in surface processing.

    Conclusions:

    • The proposed approach offers a practical and efficient solution for topological simplification optimization.
    • It significantly enhances the analysis and visualization of scalar data by preserving essential topological features.
    • The method has broad applicability in scientific data analysis, including feature extraction and surface processing.