Non-local collaborative denoising via weighted nuclear norm minimization for point cloud

In order to suppress noise in 3D point clouds while preserving geometric features, a non-local collaborative denoising method based on weighted nuclear norm minimization is proposed. Firstly, an iterative weighted PCA algorithm is used for preliminary normal estimation, followed by bilateral filtering and normal-based PCA for refinement. The eigenvectors of the covariance matrix constructed from the neighboring points can form the local coordinate system. Then the local point cloud is projected and transformed into a height-map patch. Subsequently, to reduce the difficulty of constructing similar structures, similar height maps are searched in the global point clouds, and assembled to form the low-rank height map patch group matrix, which is considered as a descriptor of non-local similar structures. Subsequently, the weighted nuclear norm minimization is applied for low-rank matrix recovery, thereby reducing the noise of local point clouds. Finally, the denoised local point clouds are combined to form the global point cloud, realizing non-local collaborative denoising. Based on updated positions, a projection optimization algorithm is used to recover sharp features. Experiment results indicate that the proposed method effectively reduces noise while preserving the original features of the point cloud.