Point cloud denoising method with low-rank recovery and point optimization

Point cloud is a vital representation form for laser scanning reconstruction and reverse engineering. However, it is impossible to obtain a noise-free point cloud during the reconstruction process, considering the complex curve of an object surface, environmental disturbance, calibration error of a scanning system, etc. Therefore, the point cloud denoising seems to be necessary to enhance the precision of the reconstruction result. Existing point cloud denoising approaches mainly concentrate on discussing the local position or filtering the point normal, and directly refining the position of the points, resulting in the sensitiveness to the noise. To address the mentioned problem, a nonlocal point cloud denoising method with low-rank recovery (LMR) and point optimization method is proposed in this paper. A local feature descriptor NDA that contains the local geometric information (normal, distance, and angles) of a point in the local frame is formulated in this work. And all these features are projected onto a 2D grid, and a feature vector NDA patch vector is constructed. Then, our method seeks the most similar NDA patch vectors in the global point cloud set and packs them into an NDA matrix. Thereafter, an adaptive weighted LMR model is presented to recover the low-rank matrix (denoised point cloud) from the NDA matrix with high rank. Finally, a point optimization method based on multi-constraints is promoted to refine the recovered point cloud. The experiments validate the effectiveness of our method in both simulation and practical application scenarios.