Nonlocal Low-Rank Point Cloud Denoising for 3-D Measurement Surfaces

3-D imaging devices (e.g., depth cameras and optical and laser scanners) are frequently used to measure outdoor/indoor scenes. The measurement data represented by 3-D point clouds are, however, usually noisy and should be denoised to facilitate subsequent applications. Existing point cloud denoising methods typically perform: 1) point position updating directly or 2) point normal filtering followed by point position updating, and seldom consider the correlation between position updating and normal filtering, leading to less desirable denoised results. This article proposes a nonlocal low-rank point cloud denoising framework (NL-PCD) to handle 3-D measurement surfaces with different-scale and -type noise. We first design a rotation-invariant feature descriptor, called height and normal patch (HNP), to encode the position and normal information of each point, and search nonlocal yet geometrically similar HNPs in the whole point cloud. Similar HNPs are then grouped and packed into a noisy matrix which exhibits high rank due to the existence of the noise. Finally, we remove the noise from the noisy matrix through low-rank matrix recovery by making use of nonlocal similarities among HNPs. In such a way, we can optimize both point positions and normals (i.e., dual geometry domains) in a joint framework to fully exploit the correlation between the two domains for point cloud denoising. Experimental results on synthetic and real-world data demonstrate that our NL-PCD outperforms both traditional and deep learning-based denoising methods in terms of noise removal and feature preservation.