Title: Fast Rigid 3D Registration Solution: A Simple Method Free of SVD and Eigen-Decomposition,
Abstract: A novel solution is obtained to solve the rigid 3D registration problem,
motivated by previous eigen-decomposition approaches. Different from existing
solvers, the proposed algorithm does not require sophisticated matrix
operations e.g. singular value decomposition 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 need of quaternion. The
simple framework provides very easy approach of integer-implementation on
embedded platforms. 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 $60\%
\sim 80\%$ less computation time than representatives. It has also been applied
to real-world applications for faster relative robotic navigation.