A Rigorous Feature Extraction Algorithm for Spherical Target Identification in Terrestrial Laser Scanning

Precise and rapid extraction of spherical target features from laser point clouds is critical for achieving high-precision registration of multiple point clouds. Existing methods often use linear models to represent spherical target characteristics, which have several drawbacks. This paper proposes a rigorous estimation algorithm for spherical target features based on least squares configurations, in which the point-cloud data error is used as a random parameter, while the spherical center coordinates and radius are used as nonrandom parameters, emphasizing correlation between spherical parameters. The implementation details of this algorithm are illustrated by deriving calculation formulas for three variance–covariance matrices: variance–covariance matrices of the new observations, variance–covariance matrices of the new observation noise, and variance–covariance matrices of random parameters and the new observation noise. Experiments show that the estimation accuracy of sphere centers using our method is improved by at least 5.7% compared to classical algorithms, such as least squares, total least squares, and robust weighted total least squares.