Light detection and ranging (LiDAR) data systems mounted on a moving or stationary platform provide 3D point cloud data for various purposes. In applications where the interested area or object needs to be measured twice or more with a shift, precise registration of the obtained point clouds is crucial for generating a healthy model with the combination of the overlapped point clouds. Automatic registration of the point clouds in the common coordinate system using the iterative closest point (ICP) algorithm or its variants is one of the frequently applied methods in the literature, and a number of studies focus on improving the registration process algorithms for achieving better results. This study proposed and tested a different approach for automatic keypoint detecting and matching in coarse registration of the point clouds before fine registration using the ICP algorithm. In the suggested algorithm, the keypoints were matched considering their geometrical relations expressed by means of the angles and distances among them. Hence, contributing the quality improvement of the 3D model obtained through the fine registration process, which is carried out using the ICP method, was our aim. The performance of the new algorithm was assessed using the root mean square error (RMSE) of the 3D transformation in the rough alignment stage as well as a-prior and a-posterior RMSE values of the ICP algorithm. The new algorithm was also compared with the point feature histogram (PFH) descriptor and matching algorithm, accompanying two commonly used detectors. In result of the comparisons, the superiorities and disadvantages of the suggested algorithm were discussed. The measurements for the datasets employed in the experiments were carried out using scanned data of a 6 cm x 6 cm x 10 cm Aristotle sculpture in the laboratory environment, and a building facade in the outdoor as well as using the publically available Stanford bunny sculpture data. In each case study, the proposed algorithm provided satisfying performance with superior accuracy and less iteration number in the ICP process compared to the other coarse registration methods. From the point clouds where coarse registration has been made with the proposed method, the fine registration accuracies in terms of RMSE values with ICP iterations are calculated as similar to 0.29 cm for Aristotle and Stanford bunny sculptures, similar to 2.0 cm for the building facade, respectively.