  Hand-eye calibration is an important and extensively researched method for
calibrating rigidly coupled sensors, solely based on estimates of their motion.
Due to the geometric structure of this problem, at least two motion estimates
with non-parallel rotation axes are required for a unique solution. If the
majority of rotation axes are almost parallel, the resulting optimization
problem is ill-conditioned. In this paper, we propose an approach to
automatically weight the motion samples of such an ill-conditioned optimization
problem for improving the conditioning. The sample weights are chosen in
relation to the local density of all available rotation axes. Furthermore, we
present an approach for estimating the sensitivity and conditioning of the cost
function, separated into the translation and the rotation part. This
information can be employed as user feedback when recording the calibration
data to prevent ill-conditioning in advance. We evaluate and compare our
approach on artificially augmented data from the KITTI odometry dataset.
