Understanding the movement of crowds is important to the management of public places and urban safety. Existing researches mostly focused on tracking pedestrians in video clips from a single camera or across multiple cameras (Multi-Object Tracking) by identifying individuals with similar appearance or spatial-temporal movement features. However, how crowds navigate through invisible area between cameras in crowded environments have been overlooked. Moreover, identifying individuals across camera in a crowded environment could be challenging due to cluttered pedestrian appearance and highly uncertain movements. In this paper, we focus on recovering crowd trajectories in the invisible area of sparse camera networks within crowded public environments. We achieve better spatial-temporal feature matching by estimating the most likely travel time between segmented tracklet observations of individuals with elaborate consideration of pedestrian interactions, which reduces the dependence on unreliable appearance features. Subsequently, we recover trajectories for matched tracklets in the invisible area with a high fidelity crowd simulation model. Extensive experiments on two real-world trajectory datasets show that our proposed method is superior to existing spatial-temporal based MOT methods and improves the appearance-based MOT models in terms of association accuracy and trajectory fidelity.

Navigation through crowded human environments is challenging for social robots. While reinforcement learning has been adopted for its capacity to capture complex interactions, the training process often relies on simulators to replicate realistic crowd behaviors, ensuring cost-efficiency. Existing crowd simulation methods typically rely on either handcrafted rules, which may lead to overly aggressive navigation, or learning from human trajectory demonstrations, which can be challenging to generalize effectively. In this paper, we introduce a data-driven crowd simulation method called SocialGAIL, which leverages Generative Adversarial Imitation Learning (GAIL) to emulate real pedestrian navigation in crowded environments. SocialGAIL utilizes an attention-based graph neural network to encode observations and employs a generator-discriminator architecture to closely mimic pedestrian behavior. We propose a set of metrics to evaluate the faithfulness of crowd simulation. Experimental results demonstrate that SocialGAIL outperforms baseline methods in terms of goal-reaching, intermediate state faithfulness, trajectory faithfulness, and adherence to global trajectory patterns. The code of our approach is available at https://github.com/William-island/SocialGAIL.