Point cloud denoising using a generalized error metric

Effective removal of noises from raw point clouds while preserving geometric features is the key challenge for point cloud denoising. To address this problem, we propose a novel method that jointly optimizes the point positions and normals. To preserve geometric features, our formulation uses a generalized robust error metric to enforce piecewise smoothness of the normal vector field as well as consistency between point positions and normals. By varying the parameter of the error metric, we gradually increase its non-convexity to guide the optimization towards a desirable solution. By combining alternating minimization with a majorization-minimization strategy, we develop a numerical solver for the optimization which guarantees convergence. The effectiveness of our method is demonstrated by extensive comparisons with previous works.