This method calculates the density based on Voronoi diagrams, which are a special kind of decomposition of a metric space determined by distances to a specified discrete set of objects in the space. At any time the positions of the pedestrians can be represented as a set of points, from which the Voronoi diagram can be generated.
The density distribution of the space can be defined as
The Voronoi density for the measurement area is defined as:
For a given trajectory , the velocity is calculated by use of the displacement of pedestrian in a small time interval around :
The spatial mean velocity is the average of the instantaneous velocities for all pedestrians who have an intersection with the measurement area at the time :