Dealing with a procedure for the automatic classification of laser point clouds based on surface curvature values, one of the most critical aspects is the correct interpretation of the estimated results. This care is required since the measurements are characterised by errors of different kind, and simplified analytical models are applied to estimate the differential terms used to locally compute the object surface curvature values. Following a non-parametric approach, the differential terms are the first- and second-order partial derivatives of a Taylor’s expansion used to determine the Gaussian K and the mean H local curvatures. Therefore, a statistical analysis is proposed in this paper. It is based at first on a chi-square test applied to verify the fulfilment of the second-order Taylor’s expan- sion. Successively, the variance–covariance propagation law is applied to the estimated differential terms, in order to calculate the covariance matrix of a two-row vector containing the Gaussian and the mean curvature estimates, and an F ratio test is then applied to verify their significance. 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. A robust parametric modelling is then applied to estimate the analytical function of each classified surface. This parametric modelling allows also the indirect segmen- tation of the geometrical units. Nevertheless, to directly perform the unit segmentation by detecting the discontinu- ity lines, an extension of the Taylor’s expansion to the third- and fourth-order terms is also suggested. Some numerical experiments on noisy synthetic laser data confirm the validity of the method proposed.
