Capturing high-dimensional social interactions and feasible futures is essential for predicting trajectories. To address this complex nature, several attempts have been devoted to reducing the dimensionality of the output variables via parametric curve fitting such as the B\'ezier curve and B-spline function. However, these functions, which originate in computer graphics fields, are not suitable to account for socially acceptable human dynamics. In this paper, we present EigenTrajectory ($\mathbb{ET}$), a trajectory prediction approach that uses a novel trajectory descriptor to form a compact space, known here as $\mathbb{ET}$ space, in place of Euclidean space, for representing pedestrian movements. We first reduce the complexity of the trajectory descriptor via a low-rank approximation. We transform the pedestrians' history paths into our $\mathbb{ET}$ space represented by spatio-temporal principle components, and feed them into off-the-shelf trajectory forecasting models. The inputs and outputs of the models as well as social interactions are all gathered and aggregated in the corresponding $\mathbb{ET}$ space. Lastly, we propose a trajectory anchor-based refinement method to cover all possible futures in the proposed $\mathbb{ET}$ space. Extensive experiments demonstrate that our EigenTrajectory predictor can significantly improve both the prediction accuracy and reliability of existing trajectory forecasting models on public benchmarks, indicating that the proposed descriptor is suited to represent pedestrian behaviors. Code is publicly available at https://github.com/inhwanbae/EigenTrajectory .

翻译：摘要：捕捉高维社交互动与可行未来轨迹是轨迹预测的核心挑战。为应对这一复杂特性，研究者通过参数曲线拟合（如贝塞尔曲线与B样条函数）降低输出变量维度，然而这些源自计算机图形学的函数难以解释符合社会规范的人类运动规律。本文提出EigenTrajectory（$\mathbb{ET}$）轨迹预测方法，采用新型轨迹描述子构建紧凑空间（称为$\mathbb{ET}$空间）替代欧氏空间以表征行人运动。首先通过低秩近似降低轨迹描述子的复杂度，将行人历史路径变换至由时空主成分表征的$\mathbb{ET}$空间，并输入现成的轨迹预测模型。模型输入输出及社交互动均在对应$\mathbb{ET}$空间中进行聚合与融合。最后提出基于轨迹锚点的精炼方法，覆盖所提$\mathbb{ET}$空间中的全部可能未来。大量实验表明，EigenTrajectory预测器能显著提升现有轨迹预测模型在公开基准上的准确性与可靠性，证明所提描述子适用于表征行人运动行为。代码开源地址：https://github.com/inhwanbae/EigenTrajectory。