What's Wrong with the Absolute Trajectory Error?

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.