A Novel Robust Point Cloud Fitting Algorithm Based on Nonlinear Gauss–Helmert Model

Point cloud fitting plays an important role in various applications of laser scanning technology. Currently, the most dominant algorithms are the linear least-squares (LS) method and the random sample consensus (RANSAC) algorithm, in which the random noises of the point cloud coordinates and the influence of the corresponding stochastic model cannot be fully considered. In this study, the mathematical model of point cloud fitting is uniformly described using the nonlinear Gauss–Helmert (NGH) model, in which the nonlinear relationship between the measurements and parameters, as well as the effects of all random errors, can be considered. In addition, the covariance matrix of point cloud coordinates obtained from the precision of the original measurements is employed to construct the corresponding stochastic model. By further introducing an equivalent weight scheme of robust estimation, a novel point cloud fitting method is proposed based on the robust NGH (RNGH) model. Unlike the previous studies, the RNGH-based algorithm can effectively resist the negative effects of outliers with full consideration of all random errors in various linear and nonlinear fitting problems. To verify the performance of the proposed RNGH, comparative experiments of point cloud fitting are employed in both simulated and real-world scenarios, respectively. The results demonstrate that the proposed point cloud fitting algorithm has significant advantages over LS and RANSAC in terms of accuracy and robustness.