  We propose a least-squares formulation to the noisy hand-eye calibration
problem using dual-quaternions, and introduce efficient algorithms to find the
exact optimal solution, based on analytic properties of the problem, avoiding
non-linear optimization. We further present simple analytic approximate
solutions which provide remarkably good estimations compared to the exact
solution. In addition, we show how to generalize our solution to account for a
given extrinsic prior in the cost function. To the best of our knowledge our
algorithm is the most efficient approach to optimally solve the hand-eye
calibration problem.
