3D Point Cloud Color Denoising Using Convex Graph-Signal Smoothness Priors

Point cloud is a collection of 3D coordinates and associated color information, which are discrete samples of an object's 2D surfaces. Imperfection in the acquisition process means that point clouds are often corrupted with noise in both geometric and color spaces. Building on recent advances in graph signal processing, we design two algorithms for 3D point cloud color denoising. Specifically, we develop a smoothness notion for 3D color point clouds using graph Laplacian regularizer (GLR) or graph total variation (GTV) priors defined on the RGB space to promote piecewise smoothness (PWS) of RGB values. Using GLR or GTV as signal prior, we formulate the point cloud color denoising problem as a maximum a posteriori (MAP) estimation problem. For the GLR prior, the MAP formulation leads to an unconstrained quadratic programming (QP) problem, which can be efficiently computed using conjugate gradient (CG). For the GTV prior, the MAP formulation results in an ℓ1-ℓ2 cost function; we minimize it using alternating direction method of multipliers (ADMM) and proximal gradient descent, where a good step size is chosen via Lipschitz continuity analysis. Extensive experiments show satisfactory denoising performance using our proposed algorithms.