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With the fast development of AI-related techniques, the applications of trajectory prediction are no longer limited to easier scenes and trajectories. More and more heterogeneous trajectories with different representation forms, such as 2D or 3D coordinates, 2D or 3D bounding boxes, and even high-dimensional human skeletons, need to be analyzed and forecasted. Among these heterogeneous trajectories, interactions between different elements within a frame of trajectory, which we call the "Dimension-Wise Interactions", would be more complex and challenging. However, most previous approaches focus mainly on a specific form of trajectories, which means these methods could not be used to forecast heterogeneous trajectories, not to mention the dimension-wise interaction. Besides, previous methods mostly treat trajectory prediction as a normal time sequence generation task, indicating that these methods may require more work to directly analyze agents' behaviors and social interactions at different temporal scales. In this paper, we bring a new "view" for trajectory prediction to model and forecast trajectories hierarchically according to different frequency portions from the spectral domain to learn to forecast trajectories by considering their frequency responses. Moreover, we try to expand the current trajectory prediction task by introducing the dimension M from "another view", thus extending its application scenarios to heterogeneous trajectories vertically. Finally, we adopt the bilinear structure to fuse two factors, including the frequency response and the dimension-wise interaction, to forecast heterogeneous trajectories via spectrums hierarchically in a generic way. Experiments show that the proposed model outperforms most state-of-the-art methods on ETH-UCY benchmark, Stanford Drone Dataset and nuScenes with heterogeneous trajectories, including 2D coordinates, 2D and 3D bounding boxes. ! * Equal contribution. Codes are available at https://github.com/cocoon2wong/E-Vertical.

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Visual images usually contain the informative context of the environment, thereby helping to predict agents' behaviors. However, they hardly impose the dynamic effects on agents' actual behaviors due to the respectively fixed semantics. To solve this problem, we propose a deterministic model named BGM to construct a guidance map to represent the dynamic semantics, which circumvents to use visual images for each agent to reflect the difference of activities in different periods. We first record all agents' activities in the scene within a period close to the current to construct a guidance map and then feed it to a Context CNN to obtain their context features. We adopt a Historical Trajectory Encoder to extract the trajectory features and then combine them with the context feature as the input of the social energy based trajectory decoder, thus obtaining the prediction that meets the social rules. Experiments demonstrate that BGM achieves state-of-the-art prediction accuracy on the two widely used ETH and UCY datasets and handles more complex scenarios.