VWC-LSPF: Voxelized weighted centroid least squares plane fitting based on point cloud data

Abstract

Plane fitting in point cloud data processing plays a crucial role in various domains, particularly in smart cities and autonomous driving applications. Efficient plane fitting methods enable the accurate extraction and representation of geometric features in complex environments, providing essential support for urban infrastructure management, traffic flow analysis, and environmental monitoring. However, current plane fitting methods tend to underperform in the presence of noise and sparse data. These techniques often struggle to process point cloud data effectively in high-noise environments, leading to decreased fitting accuracy and impacting the reliability of downstream applications. In this paper, a novel plane fitting algorithm based on voxelization, weighted centroid computation, and least squares has been proposed for the above problem, termed Voxelized Weighted Centroid Least Squares Plane Fitting (VWC-LSPF). Initially, we voxelize the point cloud data using an Axis-Aligned Bounding Box (AABB), which divides point clouds into uniformly sized voxel grids. Subsequently, the initial centroids of all points within each voxel are calculated and normalized to determine the distance between each point and its centroid. A modified Sigmoid function, which is based on the normalized distances, is then employed to update the centroid weights iteratively until the weights converge, thereby mitigating the influence of noise and distant points and enhancing the robustness of the fitting process. Finally, all the weighted centroids are aggregated and fitted using the least squares method to minimize the sum of squared distances between the centroids and the fitted plane. The effectiveness of the proposed VWC-LSPF algorithm is validated through experiments based on LiDAR scanning of steel plate surfaces, each containing an average of 1.6 million points. Comparative analysis with traditional methods such as Least Squares, RANSAC, LMEDS, and MSAC, as well as current state-of-the-art denoising methods and implicit surface methods, shows that VWC-LSPF performs well in terms of accuracy, robustness, and computational efficiency under various noise conditions. The experimental results show that our algorithm maintains the root mean square error (RMSE) below 0.2 and maintains the coefficient of determination ($R^2$) value over 0.92, which verifies the exceptional robustness in complex environments. VWC-LSPF provides an improved least squares fitting solution, particularly adapted for scenarios with significant noise and outliers.