In this article, we propose a metric on the space of finite sets of trajectories for assessing multi-target tracking algorithms in a mathematically sound way. The main use of the metric is to compare estimates of trajectories from different algorithms with the ground truth of trajectories. The proposed metric includes intuitive costs associated to localization error for properly detected targets, missed and false targets and track switches at each time step. The metric computation is based on solving a multi-dimensional assignment problem. We also propose a lower bound for the metric, which is also a metric for sets of trajectories and is computable in polynomial time using linear programming. We also extend the proposed metrics on sets of trajectories to random finite sets of trajectories.

中文翻译：

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用于评估多目标跟踪算法的有限轨迹集空间度量

在本文中，我们提出了一个关于有限轨迹集空间的度量，用于以数学上合理的方式评估多目标跟踪算法。该度量的主要用途是将来自不同算法的轨迹估计与轨迹的基本事实进行比较。建议的度量包括与正确检测到的目标、遗漏和错误目标以及每个时间步的跟踪切换的定位错误相关的直观成本。度量计算基于解决多维分配问题。我们还提出了度量的下限，它也是轨迹集的度量，并且可以使用线性规划在多项式时间内进行计算。我们还将关于轨迹集的建议度量扩展到随机的有限轨迹集。