On Measuring Pedestrian Density and Flow Fields in Dense as well as Sparse Crowds

In the framework of macroscopic human crowd models, pedestrian dynamics are described via local density and flow fields. In theory at least, these density and flow fields are often required to have a certain degree of regularity such as being smooth. In this paper, we describe a new method for the calculation of spatio-temporally smooth, locally defined density and flow fields from pedestrian trajectories. This method is based on kernel density estimation with variable bandwidth and—for a large range of scale—yields spatially averaged values close to the density or flow defined in the standard way. In order to evaluate our approach and compare with other techniques such as the fixed-bandwidth estimator or the Voronoi estimator, we use a data set of intersecting pedestrian flows extracted from a human crowd experiment that we conducted at Technische Universität Berlin. Finally, we argue that the proposed model may be interpreted as to not only describe the transport of pedestrian mass via particle flow but also as the result of variations in the pedestrians’ personal space in crowded situations. We suggest that this approach may be useful for the description and/or visualization of clogging phenomena, or crowd disasters which may be thought of as events where a sudden compression of personal space occurs.