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，当仅存在少数异常值时，它往往无法反映随着内点轨迹误差或异常值数量变化而变化的精度。在本研究中，我们提出了一种替代性误差度量方法，用于评估重建相机轨迹的精度。我们提出的度量称为可辨别轨迹误差（DTE），其计算分为五个步骤：（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，以最小化对应相机方向之间的测地距离之和。（3）缩放估计轨迹，使相机到其几何中位数的距离中位数与真实轨迹相同。（4）计算、缩尾处理并归一化对应相机之间的距离。（5）对所得距离的均值与均方根（RMS）取平均，得到DTE。该度量是ATE的一个有吸引力的替代方案，因为它能够辨别随着内点轨迹误差或异常值数量变化而变化的轨迹精度。基于类似思想，我们还提出了一种新颖的旋转误差度量，称为可辨别旋转误差（DRE），其具有与DTE相似的优势。此外，我们提出了一种简单而有效的方法来标定相机到标记的旋转，这是计算我们提出的度量所必需的。我们的方法通过大量仿真实验得到了验证。