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.

中文翻译：

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使用广义误差度量进行点云去噪

有效去除原始点云中的噪声，同时保留几何特征是点云去噪的关键挑战。为了解决这个问题，我们提出了一种联合优化点位置和法线的新方法。为了保留几何特征，我们的公式使用广义鲁棒误差度量来强制法向量场的分段平滑性以及点位置和法线之间的一致性。通过改变误差度量的参数，我们逐渐增加其非凸性，以引导优化走向理想的解决方案。通过将交替最小化与主化-最小化策略相结合，我们开发了一种用于保证收敛的优化的数值求解器。我们的方法的有效性通过与以前的作品的广泛比较得到了证明。