3D motion decomposition and linear estimation in the presence of spatial uncertainties

Motion estimation in the presence of spatial uncertainties is essentially nonlinear. A 3D motion estimation problem has a Degree of Freedom (DoF) = 6. The scalar problem can be easily decomposed to two independent DoF = 3 subproblems, where the rotation matrix and the translation vector can be assessed respectively. However in the case of introducing anisotropic measurement uncertainties this convenience has never been reported. In this paper we propose a motion decomposition theorem which gives the same answer. We also propose a linear algorithm for optimal motion estimation under 3D-3D point correspondences. Experimental results for both real and synthetic data are presented.