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.

翻译：手眼标定是一种重要且被广泛研究的方法，用于标定刚性耦合的传感器，该方法仅基于传感器运动的估计值。由于该问题的几何结构，至少需要两个旋转轴非平行的运动估计才能获得唯一解。若大多数旋转轴近乎平行，则相应的优化问题会呈现病态。本文提出了一种方法，通过自动加权此类病态优化问题中的运动样本以改善其条件数。样本权重的选取与所有可用旋转轴的局部密度相关。此外，我们提出了一种方法，用于估计代价函数（分为平移部分和旋转部分）的敏感度与条件数。该信息可作为记录标定数据时的用户反馈，从而预先防止病态问题的出现。我们在KITTI里程计数据集的人工增强数据上对所提方法进行了评估与比较。