This paper introduces the concept of a mean for trajectories and multi-object trajectories--sets or multi-sets 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 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 Fréchet mean approach to multi-object trajectory consensus significantly outperforms state-of-the-art distributed multi-object tracking methods.
View on arXiv@article{nguyen2025_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={ 2025 }
}