A Closed-Form Solution to Planar Feature-Based Registration of LiDAR Point Clouds

Stitching method based on dual quaternion for cylindrical mirrors

In this study, a stitching method based on dual quaternion is proposed. The application of a dual quaternion in sub-aperture stitching interferometry is analyzed in detail, and a calculation method for sub-aperture stitching based on a dual quaternion is deduced. The experimental results demonstrate the accuracy of the stitching method proposed in this study (residuals of overlapping area approximately 0.22 nm RMS). Finally, the residual differences of 0.79 nm RMS between the figure errors are acquired with a stitching by parts algorithm based on the dual quaternion and long trace profiler (FSP at HEPS). The high-accuracy and high-efficiency stitching method proposed in this study will expand its application in the metrology and manufacture of long cylindrical mirrors.

Fast Registration of Terrestrial LiDAR Point Clouds Based on Gaussian-Weighting Projected Image Matching

Terrestrial point cloud registration plays an important role in 3D reconstruction, heritage restoration and topographic mapping, etc. Unfortunately, current research studies heavily rely on matching the 3D features of overlapped areas between point clouds, which is error-prone and time-consuming. To this end, we propose an automatic point cloud registration method based on Gaussian-weighting projected image matching, which can quickly and robustly register multi-station terrestrial point clouds. Firstly, the point cloud is regularized into a 2D grid, and the point density of each cell in the grid is normalized by our Gaussian-weighting function. A grayscale image is subsequently generated by shifting and scaling the x-y coordinates of the grid to the image coordinates. Secondly, the scale-invariant features (SIFT) algorithm is used to perform image matching, and a line segment endpoint verification method is proposed to filter out negative matches. Thirdly, the transformation matrix between point clouds from two adjacent stations is calculated based on reliable image matching. Finally, a global least-square optimization is conducted to align multi-station point clouds and then obtain a complete model. To test the performance of our framework, we carry out the experiment on six datasets. Compared to previous work, our method achieves the state-of-the-art performance on both efficiency and accuracy. In terms of efficiency, our method is comparable to an existing projection-based methods and 4 times faster on the indoor datasets and 10 times faster on the outdoor datasets than 4PCS-based methods. In terms of accuracy, our framework is ~2 times better than the existing projection-based method and 6 times better than 4PCS-based methods.

Hexagonal Grid-Based Framework for Mobile Robot Navigation

The paper addresses the problem of mobile robots’ navigation using a hexagonal lattice. We carried out experiments in which we used a vehicle equipped with a set of sensors. Based on the data, a traversable map was created. The experimental results proved that hexagonal maps of an environment can be easily built based on sensor readings. The path planning method has many advantages: the situation in which obstacles surround the position of the robot or the target is easily detected, and we can influence the properties of the path, e.g., the distance from obstacles or the type of surface can be taken into account. A path can be smoothed more easily than with a rectangular grid.

A Closed-Form Solution to Linear Feature-Based Registration of LiDAR Point Clouds

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.