  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.
