One of the main 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 and winsorize 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 winsorized 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）的主要局限之一在于其对离群值高度敏感。因此，当仅存在少数离群值时，该指标往往无法反映随着内点轨迹误差或离群值数量变化而变化的精度。本文提出了一种用于评估重建相机轨迹精度的替代误差指标。该指标名为可辨轨迹误差（DTE），通过五个步骤计算：（1）平移真值和估计轨迹，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总和最小化；（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值相同；（4）计算并缩尾处理对应相机之间的距离；（5）取缩尾后距离的均值与均方根（RMS）的平均值作为DTE。该指标是ATE富有吸引力的替代方案，因为它能有效区分随内点轨迹误差或离群值数量变化而变化的轨迹精度。基于类似思路，我们还提出了一种新颖的旋转误差指标——可辨旋转误差（DRE），其具有与DTE相似的优点。此外，我们提出了一种简单有效的相机-标记物旋转标定方法，该方法是计算上述指标所需的前提。通过大量仿真实验验证了所提方法的有效性。