A generalized weighted total least squares-based, iterative solution to the estimation of 3D similarity transformation parameters. (31st March 2023)

• Record Type: Journal Article
• Authors: Wang, Yongbo; Yuan, Kun; Zheng, Nanshan; Bian, Zhengfu; Yang, Min
• Is Part Of: Measurement. Volume 210(2023)
• Publication Date: 2023-03-31
• Subjects: Total least squares -- Spatial similarity transformation -- Point cloud registration -- Quaternions; Weights and measures -- Periodicals; Measurement -- Periodicals; Measurement; Weights and measures; Periodicals; 530.8
• DOI: 10.1016/j.measurement.2023.112563
• Languages: English
• ISSNs: 0263-2241

Abstract

Highlights: Using EIV model in point cloud registration, random errors contained in the two neighboring LiDAR stations can both be considered, which is more in line with the reality. Unit quaternions are introduced to represent spatial rotation, which makes the expression of the spatial similarity transformation model become more concise. More importantly, no matter what the initial estimates are given for the experimental scheme designed in this paper, the correct results can always be obtained. The introduction of unit quaternions makes the solution be applicable to the case where the rotation angle between the two neighboring systems are big. The constraint that the modulo of the unit quaternions which represent 3D spatial rotation must be 1 is explicitly added into our algorithm. As a result, the scaling factor is no longer integrated with the rotation matrix, which makes it possible to estimate the scaling factor directly. Abstract: The essence of point cloud registration is to estimate the seven similarity transformation parameters of the Bursa-Wolf model which describes the relative position of the two neighboring LiDAR stations. So far, Gauss–Markov (GM) model has been widely used in point cloud registration, however, only the random errors contained in one LiDAR station are considered, which is seriously inconsistent with the reality. To simultaneously take the random errors contained in both of the two neighboring LiDAR stations into account in registration, the EIV model is constructed based on the introduction of unit quaternions to describe the spatial rotation in 3D similarity transformation, and an iterative solution to the estimation of the transformation parameters is systematically discussed. Detailed derivation of the formulas for the estimation of the seven transformation parameters are displayed step by step. Finally, three experiments are designed to verify the correctness and effectiveness of the solution.