Orthogonal Procrustes Analysis and Its Application on Rotation Matrix Estimation

Rotation matrix estimation is a basic problem in photogrammetry field. Traditional approaches are the least square solution with prior initial values,whereas the initial values are hard to be obtained in some cases. Furthermore,the bad initial values are apt to lead wrong convergence in iterations. The orthogonal procrustes analysis (OPA) is applied for rotation matrix estimation in photogrammetry. OPA is a direct solution in parameters estimation,which needs to Singular Value Decompose (SVD) of a matrix. The solution could be used as either rotation matrix estimation or the initial values for bundle adjustment. OPA is applied for direct relative orientation and absolute orientation in this paper. The results of a close-range photogrammetry case are given to verify it.