  This paper proposes a metric for sets of trajectories to evaluate
multi-object tracking algorithms that includes time-weighted costs for
localisation errors of properly detected targets, for false targets, missed
targets and track switches. The proposed metric extends the metric in [1] by
including weights to the costs associated to different time steps. The
time-weighted costs increase the flexibility of the metric [1] to fit more
applications and user preferences. We first introduce a metric based on
multi-dimensional assignments, and then its linear programming relaxation,
which is computable in polynomial time and is also a metric. The metrics can
also be extended to metrics on random finite sets of trajectories to evaluate
and rank algorithms across different scenarios, each with a ground truth set of
trajectories.
