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.

Various algorithms derived from the errors-invariables (EIV) model are always commonly used for estimating transformation parameters in three-dimensional (3-D) point cloud registration, which is attributed to the flexible and robust nature of its mathematical framework. Despite the effectiveness of conventional methods in handling a range of transformation problems, limitations may arise when dealing with scenarios that involve large rotation angles and arbitrary scale ratios. Moreover, the presence of complex external environmental variables can introduce outliers in datasets, which significantly affect registration outcomes. To tackle these challenges, we propose to abstract the transformation model of point cloud registration as a generalized EIV model, utilizing quaternions to represent spatial rotation parameters. Subsequently, we introduce a sensitivity analysis-based data snooping algorithm to identify outliers. Unlike previous studies, our method employs a new algorithm utilizing quaternions to improve computational efficiency, removing the requirement for exact initial parameter values at the beginning of iterations. Additionally, the proposed algorithm utilizes sensitivity analysis to build test statistics, with the goal of improving outlier detection and enhancing resistance to their negative effects. Our method has demonstrated superior efficiency and precision compared to traditional methods in both simulations and real experiments.

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.

The Smart City concept requires new, fast methods for collection of 3-D data representing features of urban landscape. Laser scanning technology (LiDAR - Light Detection and Ranging) enables such approach producing dense 3-D point clouds of millions of points, which, however, contain noise. Therefore, we developed a new approach allowing for a semi-automatic elimination of data noise resulting from motion of objects within the scanned scene such as persons. We used a connected-component labelling method to filter out the noise points from terrestrial laser scanning point clouds. Our approach was based on a step-by-step object classification with a proper parameterisation. In the first step, all points located close to the predicted terrain were selected. In the second step, the points representing the terrain and floor were classified using the surface filter tool implemented in the RiScan Pro software by RIEGL. The rest of points were classified using point cloud clustering via the connected-component labelling method implemented in the CloudCompare software. In the final step, the operator manually decides whether the point cluster represents the noise. The method was applied to the Cathedral of Saint Elizabeth, a sacral object located in the historical centre of the city of Košice in Slovakia during normal operating hours. We managed to capture approximately 80% of the data noise in total. The method provides a better flexibility in surveying overcrowded city locations using the laser scanning technology.

In downtown areas, the complex building layouts and the occlusion caused by dense crowds often lead to insufficient corresponding point features for point cloud registration. Additionally, although the Gauss-Markov (GM) model has been widely used in this context, it doesn’t fully account for sampling errors associated with the registration primitives. This study systematically explores the challenge of high-precision point cloud registration between two adjacent LiDAR stations. Two solutions are proposed: one based on the GM model and the other on the EIV model. Both approaches use linear features as registration primitives, employ dual quaternions to describe spatial transformation, and iteratively compute registration parameters using a least squares method. Two experiments — one with simulated data and the other with real LiDAR point clouds — are conducted to test the accuracy and effectiveness of the proposed solutions. In the first experiment, when error-free simulated data is used, both solutions yield identical results, indicating that both are capable of achieving the desired accuracy. However, when random errors are introduced into the simulated data, the solutions diverge, with the EIV model-based approach outperforming the GM model in terms of root mean square error (RMSE). In the second experiment, the registration parameters are estimated separately using the GM and EIV models, and the differences between the two approaches are analyzed, with potential explanations provided for these discrepancies.