Automatic modeling of laser point clouds by statistical analysis of surface curvature values

Laser scanning measurements are characterized by errors of different kind and simplified analytical models are normally applied to estimate the differential terms used to locally compute the object surface curvature values. The paper synthesizes the statistical analyses of the non parametric model applied, and of the Gaussian K and mean H local curvatures values, as already proposed by the authors in recent papers. The statistical analyses are based at first on a Chi-Square test applied to verify the second order Taylor’s expansion model fulfilment. Afterwards, the variance-covariance propagation law is applied to the estimated differential terms to calculate the covariance matrix of a vector containing the Gaussian and the mean curvature estimates and an F ratio test is applied to verify their significance. By analyzing the test results for K and H, and their sign, a reliable classification of the whole point cloud into its geometrical basic types is carried out. To perform the units segmentation, by analytically detecting discontinuity lines, an analysis of the extended Taylor’s model to the third and fourth order terms is mentioned. Some numerical experiments on real noisy laser data relating to a complex surface of a church apse confirm the validity of the method proposed.