A time-weighted metric for sets of trajectories to assess multi-object tracking algorithms

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.

Generalized optimal sub-pattern assignment metric

This paper presents the generalized optimal sub-pattern assignment (GOSPA) metric on the space of finite sets of targets. Compared to the well-established optimal sub-pattern assignment (OSPA) metric, GOSPA is unnormalized as a function of the cardinality and it penalizes cardinality errors differently, which enables us to express it as an optimisation over assignments instead of permutations. An important consequence of this is that GOSPA allows us to penalize localization errors for detected targets and the errors due to missed and false targets, as indicated by traditional multiple target tracking (MTT) performance measures, in a sound manner. In addition, we extend the GOSPA metric to the space of random finite sets, which is important to evaluate MTT algorithms via simulations in a rigorous way.

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.