Research on self-adaptive grid point cloud down-sampling method based on plane fitting and Mahalanobis distance Gaussian weighting

Abstract

In this manuscript, a self-adaptive grid point cloud down-sampling method based on plane fitting was proposed, which could effectively reduce redundant data while better preserving the geometric features of the original model and maintaining high accuracy. This method first constructs initial voxel grids and divides the grids into large density and small density ones according to the point cloud density. After that, for small density grids, the boundary points are extracted first, and the rest areas are uniformly sampled, while for large density grids, a method based on Mahalanobis distance Gaussian weighting is proposed and adopted to estimate the normal vector of points, and feature points are determined and retained by calculating the information entropy. Then, three models in the public dataset, the Cat model, Bed_0355 model and Fandisk model, were employed as test subjects to compare the proposed method with two commonly used down-sampling methods: uniform sampling and voxel grid sampling methods. The results indicated that this new method was able to better retain the geometric features of the original models, especially high curvature and sharp parts, with smaller errors and fewer holes. Finally, this method was applied to the down-sampling of 3D scanning point clouds of two typical metal machine parts, threaded joint and sheet metal part, and the measured results demonstrated that this method not only effectively preserved the model features, but also guaranteed accuracy of key geometric dimensions after high reduction ratio down-sampling, such as the relative errors of thread tooth angles and hole inner diameters being less than 1 %.