To solve the problems of low matching accuracy and slow convergence speed in point cloud registration, a point cloud registration algorithm based on two-dimensional (2D) image features and singular value decomposition (SVD) is proposed. First, a three-dimensional (3D) point cloud was transformed into a 2D bearing angle (BA) image and the BA image was registered using the internal-distance shape context (IDSC) algorithm. Then, using the one-to-one mapping relationship between the 3D point cloud and the 2D pixel, the rigid body transformation of the 3D point cloud was calculated to achieve the rough registration of the two point clouds. Finally, the iterative closest point (ICP) algorithm based on SVD was used to accurately register the two point clouds. In the experiment, the proposed registration algorithm was validated using public point cloud, skull point cloud, and cultural relics point cloud data. Results show that the proposed algorithm is a fast and high-precision point cloud registration algorithm.