The Mean of Multi-Object Trajectories

This paper introduces the concept of a mean for trajectories and multi-object trajectories (defined as sets or multisets of trajectories) along with algorithms for computing them. Specifically, we use the Fréchet mean, and metrics based on the optimal sub-pattern assignment (OSPA) construct, to extend the notion of average from vectors to trajectories and multiobject trajectories. Further, we develop efficient algorithms to compute these means using greedy search and Gibbs sampling. Using distributed multi–object tracking as an application, we demonstrate that the Fréchet mean approach to multi–object trajectory consensus significantly outperforms state-of-the-art distributed multi-object tracking methods.