Point cloud denoising using non-local collaborative projections

Point cloud is important for object detection and recognition. The main challenge of point cloud denoising is to preserve the geometric structures. Several state-of-the-art point cloud denoising methods focus only on analyzing local geometric information, which is sensitive to noise and outliers. In this paper, we propose a novel point cloud denoising algorithm based on the characteristics of non-local self-similarity. First, we present an adaptive curvature threshold to select the edge points and tune their corresponding normals, which can preserve the sharp details. Then we propose a structure-aware descriptor called projective height vector to capture the local height variations by normal height projection and the most similar non-local projective height vectors are grouped into a height matrix to enhance the structure representation. Moreover, the proposed structure descriptor is invariant with rigid transformation. Finally, an improved weighted nuclear norm minimization is proposed to optimize the height matrix and reconstruct a high-quality point cloud. Rather than treating each singular value independently, each component in our proposed weight definition connects with the most important components to preserve the major structural information. Experiments on synthetic and scanned point cloud datasets demonstrate that our algorithm outperforms state-of-the-art methods in terms of reconstruction accuracy and structure preservation.