Rigid 3D Registration: A Simple Method Free of SVD and Eigen-Decomposition

Abstract

The 3-D registration is extensively required in many industrial applications involving 3-D perception and reconstruction. However, conventional methods consisting of singular value decomposition (SVD) or eigendecomposition are all hard to be implemented and are difficult to be ported using simple digital circuit prototypes. A novel solution is obtained to solve the rigid 3-D registration problem, motivated by previous eigendecomposition approaches. Different from existing solvers, the proposed algorithm does not require sophisticated matrix operations, e.g., SVD or eigenvalue decomposition. Instead, the optimal eigenvector of the point cross-covariance matrix can be computed within several iterations. It is also proven that the optimal rotation matrix can be directly computed for cases without the need for a quaternion. The simple framework provides a very easy approach, even without floating-number processing. Simulations on noise-corrupted point clouds have verified the robustness and computation speed of the proposed method. The final results indicate that the proposed algorithm is accurate, robust, and owns over 60%-80% less computation time than representatives. It has also been applied to real-world applications for faster robotic visual perception.