  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 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.
