Diagnostic-robust Statistical Analysis for Local Surface Fitting in 3d Point Cloud Data

This paper investigates the problem of local surface reconstruction and best fitting for planar surfaces from unorganized 3D point cloud data. Least Squares (LS), its equivalent Principal Component Analysis (PCA) and RANSAC are the three most popular techniques for fitting planar surfaces to 3D data. LS and PCA are sensitive to outliers and do not give reliable and robust parameter estimation. The RANSAC algorithm is robust but it is not completely free from the effect of outliers and is slow for large datasets. In this paper, we propose a diagnostic-robust statistical algorithm that uses both diagnostics and robust approaches in combination for fitting planar surfaces in the presence of outliers. Recently introduced high breakdown and fast Minimum Covariance Determinant (MCD) based location and scatter estimates are used for robust distance to identify outliers and a MCD based robust PCA approach is used as an outlier resistant technique for plane fitting. The benefits of the new diagnostic-robust algorithm are demonstrated with artificial and real laser scanning point cloud datasets. Results show that the proposed method is significantly better and more efficient than the other three methods for planar surface fitting. This method also has great potential for robust local normal estimation and for other surface shape fitting applications. * Corresponding author.