EigenTrajectory: Low-Rank Descriptors for Multi-Modal Trajectory Forecasting

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 Bézier 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 ($\mathbb{E}\mathbb{T}$), a trajectory prediction approach that uses a novel trajectory descriptor to form a compact space, known here as $\mathbb{E}\mathbb{T}$ 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 $\mathbb{E}\mathbb{T}$ 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 $\mathbb{E}\mathbb{T}$ space. Lastly, we propose a trajectory anchor-based refinement method to cover all possible futures in the proposed $\mathbb{E}\mathbb{T}$ 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.