Observation distribution modelling and closed-from precision estimation of scanned 2D geometric features for network design

Abstract

Geometric features such as cylinders and planes are important objects of interest in terrestrial laser scanner surveys of complex scenes. The quality of the objects modelled from the laser scanner data is a function of many variables and geometric network design plays a key role in maximizing precision. The expected precision can be predicted at the planning stage from simulations of the environment to be scanned. However, this practice can incur a high computational load, even if performed in 2D rather than in 3D. In this paper, a closed-form solution to estimate geometric object precision is proposed as an efficient first order network design tool. It models the laser scanner measurement process with an observation distribution function that is introduced into the least-squares normal equations. Parameter precision is evaluated directly by solving a few (three to six) integrals and inverting the normal equations matrix. The method is presented for two cases of a circle lying in the horizontal plane and a 2D line scanned from a single location. Both a simplified circle model and a more general circle model are explored. The method is then extended using the summation of normals method to allow precision estimation from the combination of multiple scans from different locations. Results from many real datasets, 95 circles and 30 lines, show that the distributions of the range observations and derived Cartesian coordinates follow model predictions. Moreover, results demonstrate that the method can predict circle parameter standard deviations within 4%–6% of the experimental values. The agreement is at the 10% level for a very specific case due to inherent high parameter correlation. The agreement of line parameter standard deviations is much greater, approximately 0.1%. The results show the method can be a valuable tool to predict feature quality with minimal computational requirements. The method is beneficial to not only laser scanner network design but could also be to instantaneous 2D map construction performed for SLAM-based surveys.

Keywords

• Terrestrial laser scanning
• Network design
• Observation distribution
• Normal equations