ABSTRACT
As mentioned in Preface, 3D rotation has been historically an important theme of physics in relation to rigid body motion and quantum mechanics. In today’s computer age, however, “computational” aspects of 3D rotation are important issues of 3D measurement using cameras and 3D sensors for computer vision and computer graphics applications as well as control and simulation of robots. In practical situations, this problem arises in the process of estimating the motion between two 3D objects. A “motion” is a composition of translation and rotation. Given a 3D object in motion, the authors compute its translation and rotation from the locations before and after the motion. They show that it coincides with the covariance matrix of maximum likelihood estimation except for high order noise terms. This indicates that maximum likelihood estimation attains the theoretical accuracy bound except for high order noise terms.
