Optimization of the Use of Spherical Targets for Point Cloud Registration Using Monte Carlo Simulation

Registrations based on the manual placement of spherical targets are still being employed by many professionals in the industry. However, the placement of those targets usually relies solely on personal experience without scientific evidence supported by numerical analysis. This paper presents a comprehensive investigation, based on Monte Carlo simulation, into determining the optimal number and positions for efficient target placement in typical scenes consisting of a pair of facades. It demonstrates new check-up statistical rules and geometrical constraints that can effectively extract and analyze massive simulations of unregistered point clouds and their corresponding registrations. More than $6\times 10^{7}$ sets of the registrations were simulated, whereas more than 100 registrations with real data were used to verify the results of simulation. The results indicated that using five spherical targets is the best choice for the registration of a large typical registration site consisting of two vertical facades and a ground, when there is only a box set of spherical targets available. As a result, the users can avoid placing extra targets to achieve insignificant improvements in registration accuracy. The results also suggest that the higher registration accuracy can be obtained when the ratio between the facade-to-target distance and target-to-scanner distance is approximately 3:2. Therefore, the targets should be placed closer to the scanner rather than in the middle between the facades and the scanner, contradicting to the traditional thought. Besides, the results reveal that the accuracy can be increased by setting the largest projected triangular area of the targets to be large.