Extended WTLS iterative algorithm of 3D similarity transformation based on Gibbs vector

Zeng, Huaien; He, Hongwei; Le-geng, Chen; Chang, Guobin; He, Hangen

doi:10.1007/s40328-021-00363-3

Cited by 3 publications

(1 citation statement)

References 42 publications

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“…In some situations, e.g., registration of terrestrial laser scanning point clouds, it is not easy to obtain a good initial values due to the arbitrary size of rotation angles. Iterative algorithms can provide the accuracy estimation of transformation parameters and computed coordinates of non-control points, while the analytical algorithms cannot (Zeng et al 2020(Zeng et al , 2022.…”

Section: Introductionmentioning

confidence: 99%

Analytical dual quaternion algorithm of the weighted three-dimensional coordinate transformation

Zeng

Wang

et al. 2022

Earth Planets Space

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Considering that a unit dual quaternion can describe elegantly the rigid transformation including rotation and translation, the point-wise weighted 3D coordinate transformation using a unit dual quaternion is formulated. The constructed transformation model by a unit dual quaternion does not need differential process to eliminate the three translation parameters, while traditional models do. Based on the Lagrangian extremum law, the analytical dual quaternion algorithm (ADQA) of the point-wise weighted 3D coordinate transformation is proved existed and derived in detail. Four numerical cases, including geodetic datum transformation, the registration of LIDAR point clouds, and two simulated cases, are studied. This study shows that ADQA is valid as well as the modified procrustes algorithm (MPA) and the orthonormal matrix algorithm (OMA). ADQA is suitable for the 3D coordinate transformation with point-wise weight and no matter rotation angles are small or big. In addition, the results also indicate that if the distribution of common points degrades from 3D or 2D space to 1D space, the solvable correct transformation parameters decrease. In other words, all common points should not be located on a line. From the perspective of improving the transformation accuracy, high accurate control points (with small errors in the coordinates) should be chosen, and it is preferred to decrease the rotation angles as much as possible. Graphical Abstract

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Section: Introductionmentioning

confidence: 99%

Analytical dual quaternion algorithm of the weighted three-dimensional coordinate transformation

Zeng

Wang

et al. 2022

Earth Planets Space

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Iteratively weighted least squares solution for universal 3D similarity transformation

Zhang

Zhao

Liu

2023

Meas. Sci. Technol.

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The 3D similarity coordinate transformation is widely used to estimate the transformation parameters for measurement datum transformation. Accurate and reliable transformation parameters are crucial for accurate and reliable data integration. However, the accuracy of the transformation parameters can be significantly affected or even severely distorted when the observed coordinates are contaminated by gross errors. To address this problem, an advanced iteratively weighted least squares (IWLS) solution based on the weighted least squares (WLS) is proposed. This solution utilizes the singular value decomposition (SVD) method to obtain the rotation matrix and introduces a novel weight estimation approach based on Gaussian function. This approach enables the weight to be normalized and optimized iteratively. To verify the accuracy and reliability of the proposed algorithm, the root mean square errors (RMSEs) from both true and pseudo-observed values are analyzed by simulation experiments. Furthermore, the results of simulated and empirical experiments show that the proposed algorithm can effectively reduce the influence of gross errors to obtain reliable measurement datum transformation parameters. It should be noted that the new algorithm can easily be extended to the 2D/3D affine and rigid transformation cases, such as image matching, point cloud registration, and absolute orientation of photogrammetry.

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Dual-quaternion-based iterative algorithm of the three dimensional coordinate transformation

Zeng,

Wang,

et al. 2024

Earth Planets Space

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Nowadays a unit quaternion is widely employed to represent the three-dimensional (3D) rotation matrix and then applied to the 3D similarity coordinate transformation. A unit dual quaternion can describe not only the 3D rotation matrix but also the translation vector meanwhile. Thus it is of great potentiality to the 3D coordinate transformation. The paper constructs the 3D similarity coordinate transformation model based on the unit dual quaternion in the sense of errors-in-variables (EIV). By means of linearization by Taylor's formula, Lagrangian extremum principle with constraints, and iterative numerical technique, the Dual Quaternion Algorithm (DQA) of 3D coordinate transformation in weighted total least squares (WTLS) is proposed. The algorithm is capable to not only compute the transformation parameters but also estimate the full precision information of computed parameters. Two numerical experiments involving an actual geodetic datum transformation case and a simulated case from surface fitting are demonstrated. The results indicate that DQA is not sensitive to the initial values of parameters, and obtains the consistent values of transformation parameters with the quaternion algorithm (QA), regardless of the size of the rotation angles and no matter whether the relative errors of coordinates (pseudo-observations) are small or large. Moreover, the DQA is advantageous to the QA. The key advantage is the improvement of estimated precisions of transformation parameters, i.e. the average decrease percent of standard deviations is 18.28%, and biggest decrease percent is 99.36% for the scaled quaternion and translations in the geodetic datum transformation case. Another advantage is the DQA implements the computation and precision estimation of traditional seven transformation parameters (which still are frequent used yet) from dual quaternion, and even could perform the computation and precision estimation of the scaled quaternion. Graphical Abstract

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Extended WTLS iterative algorithm of 3D similarity transformation based on Gibbs vector

Cited by 3 publications

References 42 publications

Analytical dual quaternion algorithm of the weighted three-dimensional coordinate transformation

Analytical dual quaternion algorithm of the weighted three-dimensional coordinate transformation

Iteratively weighted least squares solution for universal 3D similarity transformation

Dual-quaternion-based iterative algorithm of the three dimensional coordinate transformation

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