As artificial intelligence spreads out to numerous fields, the application of AI to sports analytics is also in the spotlight. However, one of the major challenges is the difficulty of automated acquisition of continuous movement data during sports matches. In particular, it is a conundrum to reliably track a tiny ball on a wide soccer pitch with obstacles such as occlusion and imitations. Tackling the problem, this paper proposes an inference framework of ball trajectory from player trajectories as a cost-efficient alternative to ball tracking. We combine Set Transformers to get permutation-invariant and equivariant representations of the multi-agent contexts with a hierarchical architecture that intermediately predicts the player ball possession to support the final trajectory inference. Also, we introduce the reality loss term and postprocessing to secure the estimated trajectories to be physically realistic. The experimental results show that our model provides natural and accurate trajectories as well as admissible player ball possession at the same time. Lastly, we suggest several practical applications of our framework including missing trajectory imputation, semi-automated pass annotation, automated zoom-in for match broadcasting, and calculating possession-wise running performance metrics.

翻译：随着人工智能向众多领域扩展，其在体育分析中的应用也备受关注。然而，主要挑战之一是难以在体育比赛中自动获取连续运动数据。特别是在宽阔的足球场上，可靠追踪易受遮挡和仿射干扰的小球尤为困难。针对这一问题，本文提出了一种基于球员轨迹推断球轨迹的框架，作为球追踪的成本高效替代方案。我们结合集合变换器获取多智能体情境的置换不变与等变表示，并通过层级架构中间预测球员持球状态以支持最终轨迹推断。同时引入现实损失项与后处理步骤，确保估计轨迹的物理真实性。实验结果表明，我们的模型能同时生成自然且准确的轨迹及合理的球员持球状态。最后，我们提出该框架的若干实际应用，包括缺失轨迹插补、半自动传球标注、比赛转播自动变焦及计算持球相关运动表现指标。