Methods of density estimation for pedestrians moving in small groups without a spatial boundary

TL;DR

This paper examines the challenges of estimating pedestrian density in small, boundary-less groups, highlighting limitations of existing methods and proposing adaptations for Voronoi-based estimates in crossing flow scenarios.

Contribution

It identifies the inadequacies of traditional density estimation methods in boundary-less pedestrian groups and adapts Voronoi-based methods for small sample sizes in crossing flows.

Findings

Voronoi method requires adaptation for small samples

Traditional methods become ill-defined without spatial boundaries

Density measurements need contextual interpretation

Abstract

For a group of pedestrians without any spatial boundaries, the methods of density estimation is a wide area of research. Besides, there is a specific difficulty when the density along one given pedestrian trajectory is needed in order to plot an `individual-based' fundamental diagram. We illustrate why several methods become ill-defined in this case. We then turn to the widely used Voronoi-cell based density estimate. We show that for a typical situation of crossing flows of pedestrians, Voronoi method has to be adapted to the small sample size. We conclude with general remarks about the meaning of density measurements in such context.