A metric for sets of trajectories that is practical and mathematically consistent
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Metrics on the space of sets of trajectories are important for scientists in the field of computer vision, machine learning, robotics and general artificial intelligence. Yet existing notions of closeness are either mathematically inconsistent or of limited practical use. In this paper we outline the limitations in the existing mathematically-consistent metrics, which are based on Schuhmacher et al. 2008, and the inconsistencies in the heuristic notions of closeness used in practice, whose main ideas are common to the CLEAR MOT measures widely used in computer vision. In two steps we then propose a new intuitive metric between sets of trajectories and address these problems. First we explain a natural solution that leads to a metric that is hard to compute. Then we modify this formulation to obtain a metric that is easy to compute and keeps all the good properties of the previous metric. In particular, our notion of closeness is the first that has the following three properties: it can be quickly computed, it incorporates confusion of trajectories' identity in an optimal way and it is a metric in the mathematical sense.
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