Point Cloud Denoising Algorithm via Geometric Metrics on the Statistical Manifold

Abstract

A denoising algorithm was proposed for point cloud with high-density noise. The algorithm utilized geometric metrics on the statistical manifold and applied the idea of clustering K-means based on local statistical characteristics between noise and valid data. First, by calculating the expectation and covariance matrix of the data points, the point cloud with high-density noise was projected onto the Gaussian distribution family manifold, aiming to form the parameter point cloud. Afterwards, the geometry metrics were assigned to the manifold, and the K-means algorithm was applied to cluster the parameter point cloud, so as to classify the valid data and noise. Furthermore, in order to analyze the robustness of the means with different metrics, the approximate values of their influence functions were calculated, respectively. Finally, simulation analysis was conducted using the algorithm based on geometric metrics to verify the effectiveness in point cloud denoising.

Keywords

• point cloud denoising
• statistical manifold
• differential geometry
• influence function