Least-squares fitting of two 3-d point sets

IEEE Trans Pattern Anal Mach Intell. 1987 May;9(5):698-700. doi: 10.1109/tpami.1987.4767965.


Two point sets {pi} and {p'i}; i = 1, 2,..., N are related by p'i = Rpi + T + Ni, where R is a rotation matrix, T a translation vector, and Ni a noise vector. Given {pi} and {p'i}, we present an algorithm for finding the least-squares solution of R and T, which is based on the singular value decomposition (SVD) of a 3 × 3 matrix. This new algorithm is compared to two earlier algorithms with respect to computer time requirements.