This paper introduces the concept of a mean for trajectories and multi-object trajectories (defined as sets or multi-sets of trajectories) along with algorithms for computing them. Specifically, we use the Fr\'{e}chet mean, and metrics based on the optimal sub-pattern assignment (OSPA) construct, to extend the notion of average from vectors to trajectories and multi-object 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 Fr\'{e}chet mean approach to multi-object trajectory consensus significantly outperforms state-of-the-art distributed multi-object tracking methods.
@article{arxiv.2504.20391,
title = {The Mean of Multi-Object Trajectories},
author = {Tran Thien Dat Nguyen and Ba Tuong Vo and Ba-Ngu Vo and Hoa Van Nguyen and Changbeom Shim},
journal= {arXiv preprint arXiv:2504.20391},
year = {2026}
}