A Nonparametric Approach for Assessing Precision in Georeferenced Point Clouds Best Fit Planes: Toward More Reliable Thresholds

Abstract

The fitting of a plane to data points is essential to the geosciences. However, it is recognized that the reliability of these best fit planes depends upon the point set distribution and geometry, evaluated in terms of the eigen-based parameters derived from the moment of inertia analysis. Despite its significance, few studies have addressed the uncertainties of the analysis, which can adversely affect the reproduction of results one of the cornerstones of scientific endeavor. Aiming to contribute toward the neglected issue of the moment of inertia precision, we have developed a bootstrap resampling scheme to empirically discover the distribution of uncertainties in the orientation of best fit planes. Dispersion of the bootstrapped normal vectors to the best fit plane is regarded as a measure of precision, evaluated with the maximum angular distance from the optimal solution. This rationale was tested using Monte Carlo-generated samples covering a comprehensive range of shape parameters to assess the dependence between eigen parameters and their inherent bias. Our results show that the oblateness of the point cloud is a robust parameter to assess the reliability of the best fit plane. Given this, the method was then applied to a publicly available lidar data set. We argue that georeferenced point clouds with an oblateness parameter greater than 3 and 1.5 may be placed at 95% confidence levels of 5° and 10°, respectively. We propose using these values as thresholds to obtain robust best fit planes, guaranteeing reproducible results for scientific research.