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    This study introduces Continuous Representation-based NonLocal (CRNL) method, enhancing nonlocal self-similarity (NSS) for both on-meshgrid and off-meshgrid data. CRNL offers improved effectiveness and efficiency in diverse data processing tasks.

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    Area of Science:

    • Computer Vision
    • Data Science
    • Signal Processing

    Background:

    • Nonlocal self-similarity (NSS) is a powerful prior for multi-dimensional data processing, primarily applied to meshgrid data like images and videos.
    • Existing NSS methods are limited to meshgrid data and cannot handle emerging off-meshgrid data, such as point clouds and weather data.

    Purpose of the Study:

    • To develop a novel method that extends NSS applicability to both on-meshgrid and off-meshgrid data.
    • To introduce a Continuous Representation-based NonLocal (CRNL) method that unifies self-similarity measures for diverse data types.
    • To improve the efficiency and effectiveness of NSS-based data processing.

    Main Methods:

    • Revisiting NSS from a continuous representation perspective.
    • Proposing the CRNL method with unified self-similarity measurement for on- and off-meshgrid data.
    • Employing coupled low-rank function factorization for compact and efficient representation of nonlocal continuous groups, capturing inter-group similarities.

    Main Results:

    • CRNL demonstrates versatility by successfully processing both on-meshgrid (image inpainting, denoising) and off-meshgrid (weather data prediction, point cloud recovery) data.
    • The method achieves superior performance compared to conventional NSS methods in terms of both effectiveness and efficiency.
    • Coupled low-rank factorization effectively exploits similarities within and across nonlocal groups, outperforming methods that neglect cross-group similarities.

    Conclusions:

    • The CRNL method effectively extends NSS principles to a broader range of data, including off-meshgrid formats.
    • CRNL offers a unified and efficient approach to nonlocal data processing, outperforming existing state-of-the-art methods.
    • The continuous representation perspective and coupled low-rank factorization are key innovations enabling CRNL's broad applicability and enhanced performance.