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Parallel Computation of Piecewise Linear Morse-Smale Segmentations.

Robin G C Maack, Jonas Lukasczyk, Julien Tierny

    IEEE Transactions on Visualization and Computer Graphics
    |April 8, 2023
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    This study introduces a parallel algorithm for Morse-Smale (MS) segmentations, significantly improving computation speed and accuracy. The method efficiently identifies region boundaries and separators, offering a faster approach for data analysis.

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    Area of Science:

    • Computational topology
    • Data analysis and visualization

    Background:

    • Morse-Smale (MS) segmentations are crucial for understanding complex data structures.
    • Existing methods can be computationally intensive, limiting their application.

    Purpose of the Study:

    • To develop a well-scaling parallel algorithm for computing MS segmentations.
    • To enhance the efficiency of identifying region separators and boundaries.

    Main Methods:

    • A parallel algorithm leveraging path compression on vertex-defined manifolds.
    • Multi-label marching tetrahedra for generating region boundaries and separators.
    • MS complex preview for rapid parameter exploration and visualization.

    Main Results:

    • Achieved speedups of over an order of magnitude compared to existing implementations.
    • Demonstrated efficient segmentation of border regions.
    • Provided a fast and simple solution for MS complex preview and visualization.

    Conclusions:

    • The proposed algorithm offers a significant performance improvement for MS segmentation.
    • Enables faster exploration of parameter spaces and immediate utilization of region geometries.
    • The implementation is provided, facilitating further research and application.