Point cloud registration is essential for processing terrestrial laser scanning 16 (TLS) point cloud datasets. The registration precision directly in uences 17 and determines the practical usefulness of TLS surveys. However, in terms 18 of target based registration, analytical point cloud registration error models 19 employed by scanner manufactures are only suitable to evaluate target regis20 tration error, rather than point cloud registration error. This paper proposes 21 an new analytical approach called the registration error (RE) model to di22 rectly evaluate point cloud registration error. We verify the proposed model 23 by comparing RE and root mean square error (RMSE) for all points in 24 three point clouds that are approximately equivalent.

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Standard deviation of points is regarded as an effective precision indicator and has been used widely for over 100 years. However, to date, no standard deviation for line objects exists, despite lines being the most fundamental geometric objects in geographic information science. This paper proposes a new theory: the measurement of random line precision using standard deviation. The new theory involves: (1) standard deviation presented graphically, in a band-shape: termed the standard deviation band; (2) the rigorous derivation of analytical equations for the standard deviation band; (3) the probability that a line falls within the standard deviation band. The main contributions of this research include: (1) the derivation of an analytical equation of the standard deviation band; (2) a method to estimate the probability of a line falling within a standard deviation band. These contributions form a foundation for the proposition of further control measures for spatial data quality.

The precision of target-based registration is related to the geometry distribution of targets, while the current method of setting the targets mainly depends on experience, and the impact is only evaluated qualitatively by the findings from empirical experiments and through simulations. In this paper, we propose a new quantitative evaluation model, which is comprised of the rotation dilution of precision ( r D O P , assessing the impact of targets’ geometry distribution on the rotation parameters) and the translation dilution of precision ( t D O P , assessing the impact of targets’ geometry distribution on the translation parameters). Here, the definitions and derivation of relevant formulas of the r D O P and t D O P are given, the experience conclusions are theoretically proven by the model of r D O P and t D O P , and an accurate method for determining the optimal placement location of targets and the scanner is proposed by calculating the minimum value of r D O P and t D O P . Furthermore, we can refer to the model ( r D O P and t D O P ) as a unified model of the geometric distribution evaluation model, which includes the D O P model in GPS.

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.