INRIA Rennes - Bretagne Atlantique, Campus de Beaulieu, Rennes, France.
Université Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, France.
PLoS Comput Biol. 2022 Jun 9;18(6):e1010210. doi: 10.1371/journal.pcbi.1010210. eCollection 2022 Jun.
When two streams of pedestrians cross at an angle, striped patterns spontaneously emerge as a result of local pedestrian interactions. This clear case of self-organized pattern formation remains to be elucidated. In counterflows, with a crossing angle of 180°, alternating lanes of traffic are commonly observed moving in opposite directions, whereas in crossing flows at an angle of 90°, diagonal stripes have been reported. Naka (1977) hypothesized that stripe orientation is perpendicular to the bisector of the crossing angle. However, studies of crossing flows at acute and obtuse angles remain underdeveloped. We tested the bisector hypothesis in experiments on small groups (18-19 participants each) crossing at seven angles (30° intervals), and analyzed the geometric properties of stripes. We present two novel computational methods for analyzing striped patterns in pedestrian data: (i) an edge-cutting algorithm, which detects the dynamic formation of stripes and allows us to measure local properties of individual stripes; and (ii) a pattern-matching technique, based on the Gabor function, which allows us to estimate global properties (orientation and wavelength) of the striped pattern at a time T. We find an invariant property: stripes in the two groups are parallel and perpendicular to the bisector at all crossing angles. In contrast, other properties depend on the crossing angle: stripe spacing (wavelength), stripe size (number of pedestrians per stripe), and crossing time all decrease as the crossing angle increases from 30° to 180°, whereas the number of stripes increases with crossing angle. We also observe that the width of individual stripes is dynamically squeezed as the two groups cross each other. The findings thus support the bisector hypothesis at a wide range of crossing angles, although the theoretical reasons for this invariant remain unclear. The present results provide empirical constraints on theoretical studies and computational models of crossing flows.
当两股行人流以一定角度交叉时，由于局部行人相互作用，会自发出现条纹图案。这种明显的自组织模式形成仍有待阐明。在对向流中，交叉角度为 180°，常见的是观察到两条相反方向行驶的车道，而在 90°交叉流中，已经报道了对角线条纹。Naka（1977）假设条纹方向垂直于交叉角的平分线。然而，对锐角和钝角交叉流的研究仍不发达。我们在小团体（每组 18-19 名参与者）在七个角度（30°间隔）交叉的实验中测试了平分线假说，并分析了条纹的几何性质。我们提出了两种用于分析行人数据中条纹图案的新计算方法：（i）边缘切割算法，它可以检测条纹的动态形成，并允许我们测量单个条纹的局部属性；（ii）基于 Gabor 函数的模式匹配技术，它可以让我们在 T 时刻估计条纹图案的全局属性（方向和波长）。我们发现了一个不变的属性：在所有交叉角度下，两组中的条纹都是平行和垂直于平分线的。相比之下，其他属性取决于交叉角度：条纹间距（波长）、条纹大小（每条纹的行人数量）和交叉时间都随着交叉角度从 30°增加到 180°而减小，而条纹数量则随着交叉角度增加而增加。我们还观察到，当两组行人相互交叉时，单个条纹的宽度会动态压缩。因此，尽管平分线不变性的理论原因尚不清楚，但这些发现支持了在广泛的交叉角度下的平分线假说。本研究结果为交叉流的理论研究和计算模型提供了经验约束。
