Revisiting Nonlocal Self-Similarity from Continuous Representation

Nonlocal self-similarity (NSS) is an important prior that has been successfully applied in multi-dimensional data processing tasks, e.g., image and video recovery. However, existing NSS-based methods are solely suitable for meshgrid data such as images and videos, but are not suitable for emerging off-meshgrid data, e.g., point cloud and climate data. In this work, we revisit the NSS from the continuous representation perspective and propose a novel Continuous Representation-based NonLocal method (termed as CRNL), which has two innovative features as compared with classical nonlocal methods. First, based on the continuous representation, our CRNL unifies the measure of self-similarity for on-meshgrid and off-meshgrid data and thus is naturally suitable for both of them. Second, the nonlocal continuous groups can be more compactly and efficiently represented by the coupled low-rank function factorization, which simultaneously exploits the similarity within each group and across different groups, while classical nonlocal methods neglect the similarity across groups. This elaborately designed coupled mechanism allows our method to enjoy favorable performance over conventional NSS methods in terms of both effectiveness and efficiency. Extensive multi-dimensional data processing experiments on-meshgrid (e.g., image inpainting and image denoising) and off-meshgrid (e.g., climate data prediction and point cloud recovery) validate the versatility, effectiveness, and efficiency of our CRNL as compared with state-of-the-art methods.