The visual coupling between neighbours explains local interactions underlying human 'flocking'.

Patterns of collective motion in bird flocks, fish schools and human crowds are believed to emerge from local interactions between individuals. Most 'flocking' models attribute these local interactions to hypothetical rules or metaphorical forces and assume an omniscient third-person view of the positions and velocities of all individuals in space. We develop a visual model of collective motion in human crowds based on the visual coupling that governs pedestrian interactions from a first-person embedded viewpoint. Specifically, humans control their walking speed and direction by cancelling the average angular velocity and optical expansion/contraction of their neighbours, weighted by visibility (1 - occlusion). We test the model by simulating data from experiments with virtual crowds and real human 'swarms'. The visual model outperforms our previous omniscient model and explains basic properties of interaction: 'repulsion' forces reduce to cancelling optical expansion, 'attraction' forces to cancelling optical contraction and 'alignment' to cancelling the combination of expansion/contraction and angular velocity. Moreover, the neighbourhood of interaction follows from Euclid's Law of perspective and the geometry of occlusion. We conclude that the local interactions underlying human flocking are a natural consequence of the laws of optics. Similar perceptual principles may apply to collective motion in other species.

Human Crowds as Social Networks: Collective Dynamics of Consensus and Polarization.

A ubiquitous type of collective behavior and decision-making is the coordinated motion of bird flocks, fish schools, and human crowds. Collective decisions to move in the same direction, turn right or left, or split into subgroups arise in a self-organized fashion from local interactions between individuals without central plans or designated leaders. Strikingly similar phenomena of consensus (collective motion), clustering (subgroup formation), and bipolarization (splitting into extreme groups) are also observed in opinion formation. As we developed models of crowd dynamics and analyzed crowd networks, we found ourselves going down the same path as models of opinion dynamics in social networks. In this article, we draw out the parallels between human crowds and social networks. We show that models of crowd dynamics and opinion dynamics have a similar mathematical form and generate analogous phenomena in multiagent simulations. We suggest that they can be unified by a common collective dynamics, which may be extended to other psychological collectives. Models of collective dynamics thus offer a means to account for collective behavior and collective decisions without appealing to a priori mental structures.

Is the neighborhood of interaction in human crowds metric, topological, or visual?

Global patterns of collective motion in bird flocks, fish schools, and human crowds are thought to emerge from local interactions within a neighborhood of interaction, the zone in which an individual is influenced by their neighbors. Both metric and topological neighborhoods have been reported in animal groups, but this question has not been addressed for human crowds. The answer has important implications for modeling crowd behavior and predicting crowd disasters such as jams, crushes, and stampedes. In a metric neighborhood, an individual is influenced by all neighbors within a fixed radius, whereas in a topological neighborhood, an individual is influenced by a fixed number of nearest neighbors, regardless of their physical distance. A recently proposed alternative is a visual neighborhood, in which an individual is influenced by the optical motions of all visible neighbors. We test these hypotheses experimentally by asking participants to walk in real and virtual crowds and manipulating the crowd's density. Our results rule out a topological neighborhood, are approximated by a metric neighborhood, but are best explained by a visual neighborhood that has elements of both. We conclude that the neighborhood of interaction in human crowds follows naturally from the laws of optics and suggest that previously observed "topological" and "metric" interactions might be a consequence of the visual neighborhood.

Robust weighted averaging accounts for recruitment into collective motion in human crowds.

Agent-based models of 'flocking' and 'schooling' have shown that a weighted average of neighbor velocities, with weights that decay gradually with distance, yields emergent collective motion. Weighted averaging thus offers a potential mechanism of self-organization that recruits an increasing, but self-limiting, number of individuals into collective motion. Previously, we identified and modeled such a 'soft metric' neighborhood of interaction in human crowds that decays exponentially to zero at a distance of 4-5m. Here we investigate the limits of weighted averaging in humans and find that it is surprisingly robust: pedestrians align with the mean heading direction in their neighborhood, despite high levels of noise and diverging motions in the crowd, as predicted by the model. In three Virtual Reality experiments, participants were immersed in a crowd of virtual humans in a mobile head-mounted display and were instructed to walk with the crowd. By perturbing the heading (walking direction) of virtual neighbors and measuring the participant's trajectory, we probed the limits of weighted averaging. (1) In the 'Noisy Neighbors' experiment, the neighbor headings were randomized (range 0-90°) about the crowd's mean direction (±10° or ±20°, left or right); (2) in the 'Splitting Crowd' experiment, the crowd split into two groups (heading difference = 10-40°) and the proportion of the crowd in one group was varied (50-84%); (3) in the 'Coherent Subgroup' experiment, a perturbed subgroup varied in its coherence (heading SD = 0-2°) about a mean direction (±10° or ±20°) within a noisy crowd (heading range = 180°), and the proportion of the crowd in the subgroup was varied. In each scenario, the results were predicted by the weighted averaging model, and attraction strength (turning rate) increased with the participant's deviation from the mean heading direction, not with group coherence. However, the results indicate that humans ignore highly discrepant headings (45-90°). These findings reveal that weighted averaging in humans is highly robust and generates a common heading direction that acts as a positive feedback to recruit more individuals into collective motion, in a self-reinforcing cascade. Therefore, this 'soft' metric neighborhood serves as a mechanism of self-organization in human crowds.

Perception of another person's maximum reach-with-jump height from walking kinematics.

Humans can perceive affordances (possibilities for action) for themselves and others, including the maximum overhead height reachable by jumping (reach-with-jump height, RWJ). While observers can accurately perceive maximum RWJ for another person without previously seeing the person jump, estimates improve after viewing the person walk, suggesting there is structure in walking kinematics that is informative about the ability to produce vertical force for jumping. We used principal component analysis (PCA) to identify patterns in human walking kinematics that specify another person's maximum RWJ ability, and to determine whether athletes are more sensitive than non-athletes to these patterns. Kinematic data during treadmill walking were collected and submitted to PCA to obtain loading values for the kinematic time series variables on the first principal component. Kinematic data were also used to create point-light (PL) displays, in which the movement kinematics of PL walkers were manipulated using the obtained PCA loading values to determine how changes in body-segment movements impacted perception of maximum RWJ height. While manipulating individual segmental loadings in the PL displays did not substantially affect RWJ estimates, PL displays created by replacing the PCA loadings of a high-jumper with those of a low-jumper, and vice versa, resulted in corresponding reversals of participants' RWJ estimates, suggesting that the global structure of walking kinematics carries information about another's maximum RWJ height. Athletes exhibited greater sensitivity than controls to the kinematic manipulations, indicating that they are better attuned to useful kinematic information as a result of their sport experience.