Point Cloud Denoising via Feature Graph Laplacian Regularization.

Point cloud is a collection of 3D coordinates that are discrete geometric samples of an object's 2D surfaces. Imperfection in the acquisition process means that point clouds are often corrupted with noise. Building on recent advances in graph signal processing, we design local algorithms for 3D point cloud denoising. Specifically, we design a signal-dependent feature graph Laplacian regularizer (SDFGLR) that assumes surface normals computed from point coordinates are piecewise smooth with respect to a signal-dependent graph Laplacian matrix. Using SDFGLR as a signal prior, we formulate an optimization problem with a general 'p-norm fidelity term that can explicitly remove only two types of additive noise: small but non-sparse noise like Gaussian (using '2 fidelity term) and large but sparser noise like Laplacian (using '1 fidelity term). To establish a linear relationship between normals and 3D point coordinates, we first perform bipartite graph approximation to divide the point cloud into two disjoint node sets (red and blue). We then optimize the red and blue nodes' coordinates alternately. For '2-norm fidelity term, we iteratively solve an unconstrained quadratic programming (QP) problem, efficiently computed using conjugate gradient with a bounded condition number to ensure numerical stability. For '1-norm fidelity term, we iteratively minimize an '1-'2 cost function using accelerated proximal gradient (APG), where a good step size is chosen via Lipschitz continuity analysis. Finally, we propose simple mean and median filters for flat patches of a given point cloud to estimate the noise variance given the noise type, which in turn is used to compute a weight parameter trading off the fidelity term and signal prior in the problem formulation. Extensive experiments show state-of-the-art denoising performance among local methods using our proposed algorithms.