A metric on the space of finite sets of trajectories for evaluation of multi-target tracking algorithms

In this paper, we propose a metric on the space of finite sets of trajectories for assessing multi-target tracking algorithms in a mathematically sound way. The metric can be used, e.g., to compare estimates from algorithms with the ground truth. It includes intuitive costs associated to localization, missed and false targets and track switches. The metric computation is based on multi-dimensional assignments, which is an NP hard problem. Therefore, 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 (LP). The LP metric can be implemented using alternating direction method of multipliers such that the complexity scales linearly with the length of the trajectories.