Eliminating Bias in Pedestrian Density Estimation: A Voronoi Cell Perspective

TL;DR

This paper introduces a modified Voronoi-cell based density estimation method for pedestrians that eliminates bias, is parameter-independent, and applicable to small and large groups, improving accuracy and physical relevance.

Contribution

A novel, bias-free Voronoi-based density estimation method tailored for small and large pedestrian groups, overcoming limitations of existing approaches.

Findings

The modified Voronoi method provides unbiased density estimates.

It is an instantaneous, parameter-independent approach.

The method is applicable to diverse pedestrian group sizes and situations.

Abstract

For pedestrians moving without spatial constraints, extensive research has been devoted to develop methods of density estimation. In this paper we present a new approach based on Voronoi cells, offering a means to estimate density for individuals in small, unbounded pedestrian groups. A thorough evaluation of existing methods, encompassing both Lagrangian and Eulerian approaches employed in similar contexts, reveals notable limitations. Specifically, these methods turn out to be ill-defined for realistic density estimation along a pedestrian's trajectory, exhibiting systematic biases and fluctuations that depend on the choice of parameters. There is thus a need for a parameter-independent method to eliminate this bias. We propose a modification of the widely used Voronoi-cell based density estimate to accommodate pedestrian groups, irrespective of their size. The advantages of this modified Voronoi method are that it is an instantaneous method that requires only knowledge of the pedestrians' positions at a give time, does not depend on the choice of parameter values, gives us a realistic estimate of density in an individual's neighborhood, and has appropriate physical meaning for both small and large human crowds in a wide variety of situations. We conclude with general remarks about the meaning of density measurements for small groups of pedestrians.