A New Closed Form Approach to the Absolute Orientation Problem

The absolute orientation problem has applications in numerous fields; including robotics, pose estimation, photogrammetry, and computer graphics. With the exception of the contributions by B. K. P. Horn, most absolute orientation research has focused on rotation matrixes. However, in many cases, representing rotations as quaternions has significant advantages over the more traditional forms. This paper presents a new, compact, purely quaternion-based, closed form solution to the absolute orientation problem and introduces unique features that distinguish it from previous research. In particular, we focus on its compactness, which enables the rapid acquisition of absolute orientation estimations and permits us to perform a closed-form perterbation error analysis.