Methods for measuring pedestrian density, flow, speed and direction with minimal scatter

Abstract

The progress of image processing during recent years allows the measurement of pedestrian characteristics on a "microscopic" scale with low costs. However, density and flow are concepts of fluid mechanics defined for the limit of infinitely many particles. Standard methods of measuring these quantities locally (e.g. counting heads within a rectangle) suffer from large data scatter. The remedy of averaging over large spaces or long times reduces the possible resolution and inhibits the gain obtained by the new technologies.In this contribution we introduce a concept for measuring microscopic characteristics on the basis of pedestrian trajectories. Assigning a personal space to every pedestrian via a Voronoi diagram reduces the density scatter. Similarly, calculating direction and speed from position differences between times with identical phases of movement gives low-scatter sequences for speed and direction. Closing we discuss the methods to obtain reliable values for derived quantities and new possibilities of in depth analysis of experiments. The resolution obtained indicates the limits of stationary state theory.

Universal flow-density relation of single-file bicycle, pedestrian and car motion

“…The individual flow-density relation of bicycle traffic obtained from the Voronoi-based and headway-based methods do not show large discrepancies but the results of the headway-based method are more scattered. This has previously been observed for pedestrian dynamics [19,20].…”

“…Microscopically, an individual density can either be defined based on a Voronoi tesselation [19] or the headway. The headway d H (i) is defined as the distance between the centers of mass of an agent i and its predecessor, whereas the Voronoi space d V (i), for one-dimensional motion, is the distance between the midpoints of the headway and the headway of its follower i − 1.…”

Modeling, Evaluation, and Scale on Artificial Pedestrians

“…In general, empirical density measurements show a high variability and lack of consistency. To mitigate this, other methods have been proposed based on space partition using Voronoi diagrams [Steffen and Seyfried 2010;Nikolic et al 2015;Nikolic et al 2016].…”

Individual Microscopic Results of Bottleneck Experiments

“…Various experiments have been conducted in order to verify crowd behavior models and to enable fundamental research of pedestrians phenomena [6,9,7,8].…”