Toward learning dynamic origin-destination matrices from crowd density heatmaps

Abstract

Knowing the origins and destinations of pedestrians’ paths is key to the initialization of crowd simulations. Unfortunately, they are difficult to measure in the real world. This is one major challenge for live predictions during events such as festivals, soccer games, protest marches, and many others. Sensor data can be used to feed real-world observations into simulations in real-time. As input data for this study, we use density heatmaps generated from real-world trajectory data obtained from stereo sensors. Density information is compact, of constant size, and in general easier to obtain than e.g., individual trajectories. Therefore, the information limitation improves the applicability to other scenarios. We include the absolute pedestrian trip counts from origins to destinations during a brief time interval in an OD matrix, including unknown destinations due to sensor errors. Our goal is to estimate these OD matrices from a series of density heatmaps for the same interval. For this, we compute the ground truth OD matrices and density heatmaps using real-world trajectory data from a train station. We employ linear regression as a statistical learning method for estimation. We observe that the linear share of the relationship between density and OD matrix is estimated successfully. Nevertheless, a portion of the data remains that cannot be explained. We attempt to overcome this difficulty with random forest as a nonlinear model. The results indicate that both a linear and a nonlinear model can estimate some features of the OD matrices. However, there is no clear winner in terms of the chosen metric, the R 2 score. Overall, our findings are a strong indicator that OD matrices can indeed be estimated from density heatmaps extracted automatically from sensors.