论文标题
绝对轨迹错误有什么问题？
What's Wrong with the Absolute Trajectory Error?
论文作者
论文摘要
常用的绝对轨迹误差（ATE）的局限性之一是它对异常值高度敏感。结果，在仅存在一些离群值的情况下，它通常无法反映出随着嵌入式轨迹误差或异常值的数量而变化的准确性。在这项工作中，我们提出了一个替代错误度量，以评估重建的摄像头轨迹的准确性。我们的指标（称为可分辨轨迹误差（DTE））分为五个步骤：（1）移动地面真相和估计的轨迹，以使它们的两个几何中位数都位于原点。 （2）旋转估计的轨迹，以最大程度地减少相应摄像机方向之间的大地距离之和。 （3）扩展估计的轨迹，以使摄像机与几何中位数的中值与地面真相相同。 （4）计算相应摄像机之间的距离，调查并归一化。 （5）通过取出所得距离的平均值和均方根（RMS）来获得DTE。该度量是ATE的有吸引力的替代方法，因为它能够辨别出变化的轨迹精度，因为轨迹轨迹误差或异常值的数量各不相同。使用类似的想法，我们还提出了一个新颖的旋转误差度量，称为可辨认旋转误差（DRE），该误差（DRE）与DTE具有相似的优势。此外，我们提出了一种简单而有效的方法来校准摄像头到标记旋转，这是计算指标所需的。我们的方法通过广泛的模拟得到验证。
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.
