Diagnostic-robust statistical analysis for Local Surface Fitting in 3D Point Cloud Data
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Objectives: Surface reconstruction and fitting for geometric primitives and three Dimensional (3D) modeling is a fundamental task in the field of photogrammetry and reverse engineering. However it is impractical to get point cloud data without outliers/noise being present. The noise in the data acquisition process induces rough and uneven surfaces, and reduces the precision/accuracy of the acquired model. This paper investigates the problem of local surface reconstruction and best fitting from unorganized outlier contaminated 3D point cloud data. Methods: Least Squares (LS) method, Principal Component Analysis (PCA) and RANSAC are the three most popular techniques for fitting planar surfaces to 2D and 3D data. All three methods are affected by outliers and do not give reliable and robust parameter estimation. In the statistics literature, robust techniques and outlier diagnostics are two complementary approaches but any one alone is not sufficient for outlier detection and robust parameter estimation. We propose a diagnostic-robust statistical algorithm that uses both approaches in combination for fitting planar surfaces in the presence of outliers.Robust distance is used as a multivariate diagnostic technique for outlier detection and robust PCA is used as an outlier resistant technique for plane fitting. The robust distance is the robustification of the well-known Mohalanobis distance by using the recently introduced high breakdown Minimum Covariance Determinant (MCD) location and scatter estimates. The classical PCA measures data variability through the variance and the corresponding directions are the latent vectors which are sensitive to outlying observations. In contrast, the robust PCA which combines the 'projection pursuit' approach with a robust scatter matrix based on the MCD of the covariance matrix, is robust with outlying observations in the dataset. In addition, robust PCA produces graphical displays of orthogonal distance and score distance as the by-products which can detects outliers and aids better robust fitting by using robust PCA for a second time in the final plane fitting stage. In summary, the proposed method removes the outliers first and then fits the local surface in a robust way.Results and conclusions: We present a new diagnostic-robust statistical technique for local surface fitting in 3D point cloud data. Finally, the benefits of the new diagnostic-robust algorithm are demonstrated through an artificial dataset and several terrestrial mobile mapping laser scanning point cloud datasets. Comparative results show that the classical LS and PCA methods are very sensitive to outliers and failed to reliably fit planes. The RANSAC algorithm is not completely free from the effect of outliers and requires more processing time for large datasets. The proposed method smooths away noise and is significantly better and efficient than the other three methods for local planar surface fitting even in the presence of roughness. This method is applicable for 3D straight line fitting as well and has great potential for local normal estimation and different types of surface fitting.
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