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1. Formation of lanes and stripes in crossing pedestrian flows using an empirical human model

   https://doi.org/10.1051/epjconf/202533404011  

   Feldmann, Sina; Veprek, Kyra; Warren, William H (January 2025, EPJ Web of Conferences: Traffic and Granular Flow 2024)

   Nicolas, A; Bain, N; Douin, A; Ramos, O; Furno, A (Ed.)

   Crossing flows of pedestrians result in collective motions containing self-organized lanes or stripes. Over a wide range of crossing angles, stripe orientation is observed to be perpendicular to the mean walking direction. Here, we test the behavioral components needed to reproduce the lanes and stripes in human data using an empirical, vision-based pedestrian model (Visual SCruM). We examine combinations of (i) steering toward a goal, (ii) collision avoidance, and (iii) alignment (both with and without visual occlusion). The minimal model sufficient to reproduce perpendicular stripes was the combination of a common goal and collision avoidance, although the addition of alignment with occlusion better approximated human heading adjustments. However, the model overestimated the variation in heading and underestimated the variation in speed, suggesting that recalibration of the collision avoidance component is needed. 

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2. Simulating crossing pedestrian flows with a vision-based model of collision avoidance. 12th International Conference on Pedestrian and Evacuation Dynamics.

   Feldmann, S; Veprek, K; Warren, WH (September 2025, Czech Technical University in Prague, https://www.ped25.cz/program)

   Previous simulations of crossing flows using a vision-based collision-avoidance model reproduced lanes and stripes but showed larger heading adjustments during crossing than the human data. Here we investigate two possible explanations. First, we tested participants walking through a virtual crowd under two density conditions, refit the collision avoidance model, and re-simulated the crossing flows data. Our findings reveal little influence of moderate densities on human collision avoidance behavior. Second, we are testing mutual collision avoidance between two participants to determine whether a revised model better approximates the crossing flows data. 

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3. Analysis of emergent patterns in crossing flows of pedestrians reveals an invariant of ‘stripe’ formation in human data

   https://doi.org/10.1371/journal.pcbi.1010210  

   Mullick, Pratik; Fontaine, Sylvain; Appert-Rolland, Cécile; Olivier, Anne-Hélène; Warren, William H.; Pettré, Julien (June 2022, PLOS Computational Biology)

   Fu, Feng (Ed.)

   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. 

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4. A visual model of collective motion in human crowds

   Warren, W.H.; Dachner, G. (February 2020, Perception)

   null (Ed.)

   Collective motion in human crowds emerges from local interactions between individual pedestrians. Previously, we found that an individual in a crowd aligns their velocity vector with a weighted average of their neighbors’ velocities, where the weight decays with distance (Rio, Dachner, & Warren, PRSB, 2018; Warren, CDPS, 2018). Here, we explain this “alignment rule” based solely on visual information. When following behind a neighbor, the follower controls speed by canceling the neighbor’s optical expansion (Bai & Warren, VSS, 2018) and heading by canceling the neighbor’s angular velocity. When walking beside a neighbor, these relations reverse: Speed is controlled by canceling angular velocity and heading by canceling optical expansion. These two variables trade off as sinusoidal functions of eccentricity (Dachner & Warren, VSS, 2018). We use this visual model to simulate the trajectories of participants walking in virtual (12 neighbors) and real (20 neighbors) crowds. The model accounts for the data with root mean square errors (.04–.05 m/s, 1.5°–2.0°) the distance decay as a consequence of comparable to those of our previous velocity-alignment model. Moreover, the model explains Euclid’s law of perspective, without an explicit distance term. The visual model thus provides a better explanation of collective motion. 

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5. Singular Foliations for Knit Graph Design

   https://doi.org/10.1145/3641519.3657487  

   Mitra, Rahul; Jimenez_Berumen, Erick; Hofmann, Megan; Chien, Edward (July 2024, ACM)

   We build upon the stripes-based knit planning framework of [Mitra et al. 2023], and view the resultant stripe pattern through the lens of singular foliations. This perspective views the stripes, and thus the candidate course rows or wale columns, as integral curves of a vector field specified by the spinning form of [Knöppel et al. 2015]. We show how to tightly control the topological structure of this vector field with linear level set constraints, preventing helicing of any integral curve. Practically speaking, this obviates the stripe placement constraints of [Mitra et al. 2023] and allows for shifting and variation of the stripe frequency without introducing additional helices. En route, we make the first explicit algebraic characterization of spinning form level set structure within singular triangles, and replace the standard interpolant with an “effective” one that improves the robustness of knit graph generation. We also extend the model of [Mitra et al. 2023] to surfaces with genus, via a Morse-based cylindrical decomposition, and implement automatic singularity pairing on the resulting components. 

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