One of the limitations of the commonly used Absolute Trajectory Error (ATE) is that it is highly sensitive to outliers. As a result, in the presence of just a few outliers, it often fails to reflect the varying accuracy as the inlier trajectory error or the number of outliers varies. In this work, we propose an alternative error metric for evaluating the accuracy of the reconstructed camera trajectory. Our metric, named Discernible Trajectory Error (DTE), is computed in five steps: (1) Shift the ground-truth and estimated trajectories such that both of their geometric medians are located at the origin. (2) Rotate the estimated trajectory such that it minimizes the sum of geodesic distances between the corresponding camera orientations. (3) Scale the estimated trajectory such that the median distance of the cameras to their geometric median is the same as that of the ground truth. (4) Compute, winsorize and normalize the distances between the corresponding cameras. (5) Obtain the DTE by taking the average of the mean and the root-mean-square (RMS) of the resulting distances. This metric is an attractive alternative to the ATE, in that it is capable of discerning the varying trajectory accuracy as the inlier trajectory error or the number of outliers varies. Using the similar idea, we also propose a novel rotation error metric, named Discernible Rotation Error (DRE), which has similar advantages to the DTE. Furthermore, we propose a simple yet effective method for calibrating the camera-to-marker rotation, which is needed for the computation of our metrics. Our methods are verified through extensive simulations.

翻译：常用绝对轨迹误差（ATE）的一个局限性在于其对异常值高度敏感。因此，当仅存在少量异常值时，ATE 往往无法反映因内点轨迹误差或异常值数量变化而改变的精度。本文提出一种用于评估重建相机轨迹精度的替代误差度量，名为可辨别轨迹误差（DTE），其计算包含五个步骤：（1）平移真实轨迹与估计轨迹，使两者的几何中位数均位于原点；（2）旋转估计轨迹，使对应相机方向之间的测地距离之和最小化；（3）缩放估计轨迹，使相机到其几何中位数的中位数距离与真实轨迹一致；（4）计算、温索化并归一化对应相机之间的距离；（5）取所得距离的均值与均方根（RMS）的平均值作为 DTE。该度量作为 ATE 的替代方案具有吸引力，能够在内点轨迹误差或异常值数量变化时辨别轨迹精度的变化。基于类似思路，我们还提出一种名为可辨别旋转误差（DRE）的新型旋转误差度量，其具备与 DTE 相似的优点。此外，我们提出一种简单有效的相机-标记物旋转标定方法，该标定是计算上述度量的必要前提。通过大量仿真实验验证了方法的有效性。