Point cloud fitting method based on the robust nonlinear Gauss-Helmert model

Currently, most of the existing point cloud fitting methods are based on linear Gauss-Markov (GM) or Errors-in-Variables (EIV) models, which cannot be strictly applied to nonlinear surface fitting problems. In this paper, the mathematical model of point cloud fitting is abstracted as a more general nonlinear Gauss-Helmert (GH) model. To deal with the case when there exist outliers in the dataset, we further introduce an equivalent weight scheme and propose a point cloud fitting method based on Robust Nonlinear Gauss-Helmert (RGH) model. In this method, the covariance matrices of point coordinates derived from the errors of the original observations are treated as the prior random model, and the weight function is constructed using standardized residuals and median to carry out the robust iterative calculation. The experimental results demonstrate the significant advantages of the proposed method in terms of the accuracy and robustness of point cloud fitting. Specifically, under the conditions with outliers, the root mean square errors of parameters for the simulated sphere data obtained by RGH model are only 25.77%~30.67% of those from RANSAC method, and the standard deviations of parameters for the real data are only 4.63%~5.01% of those from RANSAC method, respectively.