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To solve point cloud registration, a novel solution to planar feature-based registration of point clouds was proposed in this study according to dual quaternion description based on the constraint of planar feature. The normal vector of the homologous feature plane should be kept parallel according to the registration, and the points on the plane should satisfy the planar equation. Moreover, the modified Levenberg-Marquardt method was adopted to complete the registration model, so as to avoid inappropriate initial values from causing non-convergence of the iteration. Lastly, the robustness and accuracy exhibited by the method were verified using simulated and measured data. [ABSTRACT FROM AUTHOR]

Objectives: The high-precision registration of point cloud data is the key to ensure the integrity of 3D data on the surface of spatial objects. To address the problem that there are differences in position, attitude and scale of cloud data from neighboring stations, a method is proposed to solve the registration model of point cloud described by the dual quaternion under the constraints of point-planar feature. Methods: First, the rotation matrix and translation vector of the spatially similar transformation are represented by the dual quaternion, based on which the scale factor is taken into account and the vertical and parallel spatial topological relationships exist between the vectors constructed by the points in the plane and the points out of the plane respectively and the normal vectors of the plane, and this is used as the constraint of the spatially similar transformation to construct the parity model based on the least squares criterion. Then the Levenberg-Marquardt method is introduced to solve the level-difference model to avoid the possible non-convergence of the iterations in the level-difference treatment due to the inappropriateness of the initial values or due to the fact that the real symmetric matrix constructed by the Jacobi matrix is close to singularity. Result: Two sets of experiments are compared and analyzed with the existing methods, and the experimental results show that the proposed method can effectively achieve point cloud registration. Conclusions: Therefore, the method that takes into account the scale factor under the point-planar feature constraint and uses the dual quaternion to realize the spatial similarity transformation has a strong practical value. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Point cloud registration refers to a critical step in point cloud preprocessing, which aims to uniformly represent the objects expressed by the two point sets. To solve spatial discrepancies in the collected artificial building point clouds, this study develops a point cloud registration method by employing dual quaternion description based on the point-linear feature constraint. First, the spatial transformation parameters are expressed by the dual quaternion, and the rotation matrix and translation vector are expressed simultaneously to avoid the error of separate calculations from accumulating. Subsequently, the registration model is built by complying with the constraints of coordinate equivalence after the registration of the same-name points, parallelism of direction vectors after registration of the same-name lines and the spatial geometric relationship between points and lines. On that basis, the scale factor is considered to register point clouds at different scales. Second, an optimized Levenberg–Marquardt method is adopted to solve the registration model for avoiding the iterative non-convergence attributed to inappropriate initial values in the solution. Lastly, the robustness and reliability exhibited by the proposed method are verified by performing two experiments with the simulated and measured data. As indicated from the experimentally achieved results, the joint constraint of point-linear features can achieve higher accuracy than the constraint of point or line features independently, and the combined point-linear features can register point clouds in high quality when point cloud data are scaled and partially missing. This study presents an effective registration method for manually registered auxiliary targets when they are difficult to deploy. [ABSTRACT FROM AUTHOR]

Due to the high complexity of geo-spatial entities and the limited field of view of LiDAR equipment, pairwise registration is a necessary step for integrating point clouds from neighbouring LiDAR stations. Considering that accurate extraction of point features is often difficult without the use of man-made reflectors, and the initial approximate values for the unknown transformation parameters must be estimated in advance to ensure the correct operation of those iterative methods, a closed-form solution to linear feature-based registration of point clouds is proposed in this study. Plücker coordinates are used to represent the linear features in three-dimensional space, whereas dual quaternions are employed to represent the spatial transformation. Based on the theory of least squares, an error norm (objective function) is first constructed by assuming that each pair of corresponding linear features is equivalent after registration. Then, by applying the extreme value analysis to the objective function, detailed derivations of the closed-form solution to the proposed linear feature-based registration method are given step by step. Finally, experimental tests are conducted on a real dataset. The derived experimental result demonstrates the feasibility of the proposed solution: By using eigenvalue decomposition to replace the linearization of the objective function, the proposed solution does not require any initial estimates of the unknown transformation parameters, which assures the stability of the registration method. [ABSTRACT FROM AUTHOR]

Since pairwise registration is a necessary step for the seamless fusion of point clouds from neighboring stations, a closed-form solution to planar feature-based registration of LiDAR (Light Detection and Ranging) point clouds is proposed in this paper. Based on the Plücker coordinate-based representation of linear features in three-dimensional space, a quad tuple-based representation of planar features is introduced, which makes it possible to directly determine the difference between any two planar features. Dual quaternions are employed to represent spatial transformation and operations between dual quaternions and the quad tuple-based representation of planar features are given, with which an error norm is constructed. Based on L2-norm-minimization, detailed derivations of the proposed solution are explained step by step. Two experiments were designed in which simulated data and real data were both used to verify the correctness and the feasibility of the proposed solution. With the simulated data, the calculated registration results were consistent with the pre-established parameters, which verifies the correctness of the presented solution. With the real data, the calculated registration results were consistent with the results calculated by iterative methods. Conclusions can be drawn from the two experiments: (1) The proposed solution does not require any initial estimates of the unknown parameters in advance, which assures the stability and robustness of the solution; (2) Using dual quaternions to represent spatial transformation greatly reduces the additional constraints in the estimation process. [ABSTRACT FROM AUTHOR]