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Point cloud registration plays a central role in various applications, such as 3-D scene reconstruction, preservation of cultural heritage and deformation monitoring. The point cloud data are usually huge. Processing such huge data is very time-consuming, so a fast and accurate registration method is crucial. However, the existing registration methods still have high computation complexity or low accuracy. To address this issue, we develop a registration method for terrestrial point clouds. The method projects the point clouds onto the horizontal plane. Therefore, our method processes point cloud data in 2-D space, leading to high computation efficiency. Then, the 2-D feature lines are extracted from the projected point clouds. We calculate the intersection points of the 2-D feature lines, which are treated as the 2-D feature points. Due to the high accuracy of the 2-D feature lines, the 2-D feature points also have high accuracy. Thus, our method can get accurate registration results. Afterward, the feature triangles are constructed by using the 2-D feature points, and the geometric constraints are utilized to find the corresponding feature triangles for calculating the 2-D transformation. This strategy boosts the process of searching for the corresponding 2-D feature points. Subsequently, the <italic>Z</italic>-axis displacement is computed by the cylindrical neighborhoods. By combining the <italic>Z</italic>-axis displacement and 2-D transformation, the 3-D rigid transformation is obtained. Experimental evaluation conducted on two publicly available datasets well demonstrates that the proposed registration method can achieve good computational efficiency and high accuracy.