Keypoint detection plays a pivotal role in three-dimensional computer vision, with widespread applications in improving registration precision and efficiency. However, current keypoint detection methods often suffer from poor robustness and low discriminability. In this study, a novel keypoint detection approach based on the local variation of surface (LVS) is proposed. The LVS keypoint detection method comprises three main steps. Firstly, the surface variation index for each point is calculated using the local coordinate system. Subsequently, points with a surface variation index lower than the local average are identified as initial keypoints. Lastly, the final keypoints are determined by selecting the minimum value within the neighborhood from the initial keypoints. Additionally, a sampling consensus correspondence estimation algorithm based on geometric constraints (SAC-GC) for efficient and robust estimation of optimal transformations in correspondences is proposed. By combining LVS and SAC-GC, we propose a coarse-to-fine point cloud registration algorithm. Experimental results on four public datasets demonstrate that the LVS keypoint detection algorithm offers improved repeatability and robustness, particularly when dealing with noisy, occluded, or cluttered point clouds. The proposed coarse-to-fine point cloud registration algorithm also exhibits enhanced robustness and computational efficiency.