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 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.

翻译：本文介绍了轨迹与多目标轨迹（定义为轨迹的集合或多重集合）的均值概念及其计算算法。具体而言，我们利用Fréchet均值以及基于最优子模式分配（OSPA）构造的度量，将平均的概念从向量推广至轨迹与多目标轨迹。此外，我们开发了基于贪婪搜索和吉布斯采样的高效算法来计算这些均值。以分布式多目标跟踪为应用场景，我们证明了多目标轨迹共识的Fréchet均值方法显著优于当前最先进的分布式多目标跟踪方法。