A Lagrangian Particle Dynamics Approach for Crowd Flow Segmentation and Stability Analysis

Abstract

This paper proposes a framework in which Lagrangian particle dynamics is used for the segmentation of high density crowd flows and detection of flow instabilities. For this purpose, a flow field generated by a moving crowd is treated as an aperiodic dynamical system. A grid of particles is overlaid on the flow field, and is advected using a numerical integration scheme. The evolution of particles through the flow is tracked using a flow map, whose spatial gradients are subsequently used to setup a Cauchy Green deformation tensor for quantifying the amount by which the neighboring particles have diverged over the length of the integration. The maximum eigenvalue of the tensor is used to construct a finite time Lyapunov exponent (FTLE) field, which reveals the Lagrangian coherent structures (LCS) present in the underlying flow. The LCS divide flow into regions of qualitatively different dynamics and are used to locate boundaries of the flow segments in a normalized cuts framework. Any change in the number of flow segments over time is regarded as an instability, which is detected by establishing correspondences between flow segments over time. The experiments are conducted on a challenging set of videos taken from Google Video and a National Geographic documentary.