Efficient Non-Local Point Cloud Denoising Using Curvature Entropy and $\gamma$γ-Norm Minimization

Non-local similarity (NLS) has been successfully applied to point cloud denoising. However, existing non-local methods either involve high algorithmic complexity in capturing NLS or suffer from diminished accuracy in estimating low-rank matrices. To address these problems, we propose a Point Cloud Denoising framework using $\gamma$-norm minimization based on Curvature Entropy (PCD-$\gamma$CE) for efficiently removing noise. First, we develop a structure descriptor, which exploits Curvature Entropy (CE) to accurately capture shape variation details of Non-Local Similar Structure (NLSS), and employs Angle Subdivision (AS) of NLSS to control the complexity of initial normal matrix construction. Second, we introduce $\gamma$-norm to construct a low-rank denoising model for initial normal matrix, thereby providing a nearly unbiased estimation of rank function with better robustness to noise. Extensive experiments on synthetic and raw scanned point clouds show that our approach outperforms the popular denoising methods, with a 99.90% time reduction and gains in Mean Square Error (MSE) and Chamfer Distance (CD) compared with the Weighted Nuclear Norm Minimization (WNNM) method.