A statistically proven automatic curvature based classification procedure of laser points

Abstract

One of the critical aspects of the curvature based classification of spatial objects from laser point clouds is the correct interpretation of the results. This is due to the fact that measurements are characterized by errors and that simplified analytical models are applied to estimate the differential terms used to compute the object surface curvature values. In particular, the differential terms are the first and second order partial derivatives of a Taylor’s expansion used to determine, by the so-called “Weingarten map” matrix, the Gaussian and the mean curvatures. Due to the measurement errors and to the simplified model adopted, a statistical procedure is proposed in this paper. It is based at first on the analysis of variance (ANOVA) carried out to verify the fulfilment of the second order Taylor’s expansion applied to locally compute the curvature differential terms. Successively, the variance covariance propagation law is applied to the estimated differential terms in order to calculate the variance covariance matrix of a two rows vector containing the Gaussian and the mean curvature estimates. An F ratio test is then applied to verify the significance of the Gaussian and of the mean curvature values. By analysing the test acceptance or rejection for K and H, and their sign, a reliable classification of the whole point cloud into its geometrical basic types is carried out. Some numerical experiments on synthetic and real laser data finally emphasize the capabilities of the method proposed.