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Point cloud is a collection of 3D coordinates that are discrete geometricsamples of an object's 2D surfaces. Imperfection in the acquisition processmeans that point clouds are often corrupted with noise. Building on recentadvances in graph signal processing, we design local algorithms for 3D pointcloud denoising. Specifically, we design a reweighted graph Laplacianregularizer (RGLR) for surface normals and demonstrate its merits in rotationinvariance, promotion of piecewise smoothness, and ease of optimization. UsingRGLR as a signal prior, we formulate an optimization problem with a generallp-norm fidelity term that can explicitly model two types of independent noise:small but non-sparse noise (using l2 fidelity term) and large but sparser noise(using l1 fidelity term).  To establish a linear relationship between normals and 3D point coordinates,we first perform bipartite graph approximation to divide the point cloud intotwo disjoint node sets (red and blue). We then optimize the red and blue nodes'coordinates alternately. For l2-norm fidelity term, we iteratively solve anunconstrained quadratic programming (QP) problem, efficiently computed usingconjugate gradient with a bounded condition number to ensure numericalstability. For l1-norm fidelity term, we iteratively minimize an l1-l2 costfunction sing accelerated proximal gradient (APG), where a good step size ischosen via Lipschitz continuity analysis. Finally, we propose simple mean andmedian filters for flat patches of a given point cloud to estimate the noisevariance given the noise type, which in turn is used to compute a weightparameter trading off the fidelity term and signal prior in the problemformulation. Extensive experiments show state-of-the-art denoising performanceamong local methods using our proposed algorithms.

3D Point Cloud Denoising via Bipartite Graph Approximation and Reweighted Graph Laplacian