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    This study introduces volumetric functions for point cloud attribute compression, improving upon existing methods. Higher-order volumetric functions offer better compression efficiency than first-order approaches in the MPEG Point Cloud Compression standard.

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    Area of Science:

    • Computer Vision
    • Data Compression
    • Signal Processing

    Background:

    • Point cloud compression traditionally focuses on discrete point positions and attributes.
    • Existing methods may not fully capture the continuous nature of spatial data.
    • The MPEG Point Cloud Compression standard is emerging, utilizing region-adaptive hierarchical transforms.

    Purpose of the Study:

    • To introduce a novel point cloud attribute compression method using volumetric functions.
    • To demonstrate the superiority of higher-order volumetric functions over first-order methods.
    • To generalize and improve upon existing region-adaptive hierarchical transforms.

    Main Methods:

    • Representing point cloud attributes using continuous volumetric functions.
    • Employing a B-spline wavelet basis for coding volumetric functions.
    • Generalizing the region-adaptive hierarchical transform to higher orders.

    Main Results:

    • Volumetric functions effectively represent point cloud attributes.
    • Higher-order volumetric functions show improved attribute compression performance.
    • The proposed method surpasses first-order volumetric functions used in the MPEG standard.

    Conclusions:

    • Volumetric functions provide an effective alternative for point cloud attribute compression.
    • Higher-order B-spline wavelet-based volumetric functions offer significant compression gains.
    • This approach represents a notable advancement over current MPEG standards for point cloud data.