FILTERING OF SUBWAY TUNNELPOINT CLOUD BASEDON P-NORM MINIMUM FITTING METHOD

摘要

With the improvement of the accuracy and efficiency of laser scanning technology, high-resolution terrestrial laser scanning (TLS) technology which can obtain high precise points-cloud has been applied to high-precision deformation monitoring of subway tunnels, building structures and other fields. Many problems in geometry processing are stated as least-squares (2-norm minimum) optimizations. Least-squares problems are well studied and widely used but exhibit immanent drawbacks such as high sensitivity to outliers Theoretical backing for using least-squares methods is given by the Gauss-Markov theorem which basically states, that if the input data to the problem fulfills some statistical properties, e.g. zero mean, unique variance and zero covariance, the least-squares way is the best way to go. However, as praxis has shown, the input data does not always meet these requirements. Real world data poses severe challenges to the least-squares approach. One particular problem is outliers, which naturally occur in various ways in physical measurement processes. The threshold to remove the outliers is 2x or 3x mean square error in many literatures, which is not reasonable Experiments show that if the threshold is too large many inliers will be removed, in contrast, if the threshold is too small many outliers will not be removed. It is essential to choose an appropriate threshold. In this case, a method for removing outliers of the tunnel is presented, In view of the special section characteristic of the subway tunnel and its long shape This method firstly extracts tunnel cross sections and fitting the points on the slices to an ellipse using p-norm minimum algorithm, finally an adaptive threshold selection method based fitting residuals is introduced to identify and remove the outliers whose residuals are more than the threshold The method described in this paper has been tested and verified by the experiment using the data of a Shanghai subway tunnel. Results show that the p-norm minimum fitting algorithm is more robust than least-squares algorithm. The threshold can distinguish the outliers and inliers well. The proposed method is rather simple and can be easily implemented.