Comparative Study of the Representative Algorithms for Fitting Spherical Target Based on Point Cloud

Abstract

Spherical target fitting (STF) is a challenging problem in terrestrial 3D laser scanning applications, and many algorithms have been developed for this task. This paper aims to address the issues, including how to find the proper algorithm for the specific requirements from the existing algorithms, what influencing factors should be considered when utilizing those algorithms, and how to improve them further, etc. We classify the existing STF algorithms into least squares (LS) and numerical optimization (NO) categories and select seven representative algorithms as major research objectives. Based on the dissection of their fundamental principles, we comprehensively verify the selected seven algorithms using simulated and field data, respectively. The experimental findings reveal that the linear least squares (LLS), orthogonal non-linear least squares (ONLS), and gradient descent (GD) have high computational efficiency; however, they are sensitive to noise and coverage. General total least squares (GTLS) has a certain degree of noise immunity but suffers from low efficiency and the constructed stochastic model. By introducing specific constraint rules, M-estimate sample consensus (MSAC) and feature-constrained random search (FCRS) may provide higher-precision fitting results, but indicate obvious instability and unreliability. Feature-constrained grid search (FCGS) can achieve good results in most cases in the usage of feature constraints and uniform sampling, but still presents drawbacks under the severely ill-conditioned situation. Additionally, comprehensive analysis indicates that the accuracy and robustness of the STF algorithms are influenced by noise and coverage, whereas computational efficiency is primarily affected by the number of measurement points.