Publications

Accurate measurements of pedestrian dynamics, in form of individual trajectories, are paramount to investigate the complex motion of walking individuals and to produce reliable crowd simulation models for ordinary and evacuation conditions. This paper reviews one pedestrian trajectory collection technique, recently employed by the same authors for acquiring crowd dynamics data in real-life conditions. Operating unsupervised, the technique has enabled unprecedented, 24/7, months-long, pedestrian measurement campaigns that provided millions of individual trajectories, allowing novel statistical insights. The tracking technique leverages overhead depth-sensors, such as Microsoft Kinects, arranged in grids, and ad hoc pedestrian localization algorithms. Here we review its relevant technological aspects in view of statistical crowd dynamics analyses.

Overhead depth map measurements capture sufficient amount of information to enable human experts to track pedestrians accurately. However, fully automating this process using image analysis algorithms can be challenging. Even though hand-crafted image analysis algorithms are successful in many common cases, they fail frequently when there are complex interactions of multiple objects in the image. Many of the assumptions underpinning the hand-crafted solutions do not hold in these cases and the multitude of exceptions are hard to model precisely. Deep Learning (DL) algorithms, on the other hand, do not require hand crafted solutions and are the current state-of-the-art in object localization in images. However, they require exceeding amount of annotations to produce successful models. In the case of object localization these annotations are difficult and time consuming to produce. In this work we present an approach for developing pedestrian localization models using DL algorithms with efficient weak supervision from an expert. We circumvent the need for annotation of large corpus of data by annotating only small amount of patches and relying on synthetic data augmentation as a vehicle for injecting expert knowledge in the model training. This approach of weak supervision through expert selection of representative patches, suitable transformations and synthetic data augmentations enables us to successfully develop DL models for pedestrian localization efficiently.

Understanding and modeling the dynamics of pedestrian crowds can help with designing and increasing the safety of civil facilities. A key feature of a crowd is its intrinsic stochasticity, appearing even under very diluted conditions, due to the variability in individual behaviors. Individual stochasticity becomes even more important under densely crowded conditions, since it can be nonlinearly magnified and may lead to potentially dangerous collective behaviors. To understand quantitatively crowd stochasticity, we study the real-life dynamics of a large ensemble of pedestrians walking undisturbed, and we perform a statistical analysis of the fully resolved pedestrian trajectories obtained by a yearlong high-resolution measurement campaign. Our measurements have been carried out in a corridor of the Eindhoven University of Technology via a combination of Microsoft Kinect 3D range sensor and automatic head-tracking algorithms. The temporal homogeneity of our large database of trajectories allows us to robustly define and separate average walking behaviors from fluctuations parallel and orthogonal with respect to the average walking path. Fluctuations include rare events when individuals suddenly change their minds and invert their walking directions. Such tendency to invert direction has been poorly studied so far, even if it may have important implications on the functioning and safety of facilities. We propose a model for the dynamics of undisturbed pedestrians, based on stochastic differential equations, that provides a good agreement with our field observations, including the occurrence of rare events.

Real-life, out-of-laboratory, measurements of pedestrian walking dynamics allow extensive and fully-resolved statistical analyses. However, data acquisition in real-life is subjected to the randomness and heterogeneity that characterizes crowd flows over time. In a typical real-life location, disparate flow conditions follow one another in random order: for instance, a low density pedestrian co-flow dynamics may suddenly turn into a high density counter-flow scenario and then back again. Isolating occurrences of similar flow conditions within the acquired data is a paramount first step in the analyses in order to avoid spurious statistics and to enable qualitative comparisons. In this paper we extend our previous investigation on the asymmetric pedestrian dynamics on a staircase landing, where we collected a large statistical database of measurements from ad hoc continuous recordings. This contribution has a two-fold aim: first, method-wise, we discuss an analysis workflow to consider large-scale experimental measurements, suggesting two querying approaches to automatically extract occurrences of similar flow scenarios out of datasets. These pursue aggregation of similar scenarios on either a frame or a trajectory basis. Second, we employ these two different perspectives to further explore asymmetries in the pedestrian dynamics in our measurement site. We report cross-comparisons of statistics of pedestrian positions, velocities and accelerations vs. flow conditions as well as vs. querying approach.

We investigate via extensive experimental data the dynamics of pedestrians walking in a corridor-shaped landing in a building at Eindhoven University of Technology. With year-long automatic measurements employing a Microsoft Kinect™ 3D-range sensor and ad hoc tracking techniques, we acquired few hundreds of thousands pedestrian trajectories in real-life conditions. Here, we discuss the asymmetric features of the dynamics in the two walking directions with respect to the flights of stairs (i.e. ascending or descending). We provide a detailed analysis of position and speed fields for the cases of pedestrians walking alone undisturbed and for couple of pedestrians in counter-flow. Then, we show average walking velocities exploring all the observed combinations in terms of numbers of pedestrians and walking directions.

We analyse the experimental data gathered at the Eindhoven train station and extent the mathematical model previously developed for describing single (undisturbed) pedestrian dynamics [Cor16]. Our goal is to develop a mathematical model which describes the dynamics shown by pedestrians more realistic, with the goals of describing them beyond their average motion. For this we first analyse the variety of flow conditions at the Eindhoven train station and develop a framework for selecting homogeneous flow conditions and extent the undisturbed pedestrian model. We show that we can describe the dynamics of undisturbed pedestrians at the train station including running individuals. In crowds, interactions play a prominent role and we start by analysing the avoidance behaviour of individuals. We show that,after avoidance, individual pedestrians continue walking along their new trajectory and that we can reproduce this behaviour by the means of averages. Lastly we study the effects of higher densities and conclude that the model needs further extensions to describe the dynamics at higher densities.

Employing partially overlapping overhead kinectTMS sensors and automatic pedestrian tracking algorithms we recorded the crowd traffic in a rectilinear section of the main walkway of Eindhoven train station on a 24/7 basis. Beside giving access to the train platforms (it passes underneath the railways), the walkway plays an important connection role in the city. Several crowding scenarios occur during the day, including high- and low-density dynamics in uni- and bi-directional regimes. In this paper we discuss our recording technique and we illustrate preliminary data analyses. Via fundamental diagrams-like representations we report pedestrian velocities and fluxes vs. pedestrian density. Considering the density range 0 - 1.1ped/m2, we find that at densities lower than 0.8ped/m2 pedestrians in unidirectional flows walk faster than in bidirectional regimes. On the opposite, velocities and fluxes for even bidirectional flows are higher above 0.8ped/m2.

In this thesis we investigate the dynamics of pedestrian crowds in a fundamental and applied perspective. Envisioning a quantitative understanding we employ ad hoc largescale experimental measurements as well as analytic and numerical models. Moreover, we analyze current regulations in matter of pedestrians structural actions (structural loads), in view of the need of guaranteeing pedestrian safety in serviceable built environments. This work comes in three complementary parts, in which we adopt distinct perspectives and conceptually different tools, respectively from statistical physics, mathematical modeling and structural engineering. The statistical dynamics of individual pedestrians is the subject of the first part of this thesis. Although individual trajectories may appear random, once we analyze them in large ensembles we expect “preferred” behaviors to emerge. Thus, we envisage individual paths as fluctuations around such established routes. To investigate this aspect, we perform year-long 24/7 measurements of pedestrian trajectories in real-life conditions, which we analyze statistically and via Langevin-like models. Two measurement locations have been considered: a corridor-shaped landing in the Metaforum building at Eindhoven University of Technology and the main walkway within Eindhoven Train Station. The measurement technique we employ is based on overhead Microsoft Kinect™ 3D-range sensors and on ad hoc tracking algorithms. In the second part of the thesis, we zoom out from the perspective of individual pedestrians and we look at crowds, adopting a genuine mathematical modeling point of view. We establish a general background of crowd dynamics modeling, which includes an introduction to the modeling framework by Cristiani, Piccoli and Tosin (CPT). This framework is suitable to model systems governed by social interactions and stands on a first order measure-valued evolution equation. Measures enable a unified treatment of crowd flows at the microscopic (particle-like) and macroscopic (fluid-like) observation scales. In a Wasserstein space context, we wonder when the microscopic and macroscopic dynamics are consistent as the number of agents involved grows. In this comparison we consider agents whose mass (in a measure sense) is independent on the size of the crowd. Then, we focus on the modeling of crowds moving across footbridge-like (i.e. elongated) geometries. In these simple scenarios we are able to give a reasonable form to the CPT model components from phenomenological considerations and thus perform simulations. In the third part of the thesis, we consider crowd flows on footbridges in relation to the way the safety of pedestrians is ensured by the current building practice. We address crowd-footbridge systems in terms of featured uncertainties. We provide a review of the literature giving a synthetic comparison of uncertainties involved. In general, beside the uncertainties affecting the mechanical properties of the structure, the status of the crowd is itself uncertain. Taking inspiration from wind engineering, we approach the crowd dynamics through a distinction between the approaching traffic and the crossing traffic. In the review, we consider how building regulations address the crowd load. On one hand, no uncertainty, nor variability, is considered on the crowd state, therefore the roughest possible model (constant load) is typically retained. On the other hand, we notice how a large dissent is present in the prescribed load values, suggesting a possible inadequacy in regulations. Finally, we propose a framework to deal with uncertainties related to the crowd traffic, and specifically the crowd density.

Focusing on a specific crowd dynamics situation, including real life experiments and measurements, our paper targets a twofold aim: (1) we present a Bayesian probabilistic method to estimate the value and the uncertainty (in the form of a probability density function) of parameters in crowd dynamic models from the experimental data; and (2) we introduce a fitness measure for the models to classify a couple of model structures (forces) according to their fitness to the experimental data, preparing the stage for a more general model-selection and validation strategy inspired by probabilistic data analysis. Finally, we review the essential aspects of our experimental setup and measurement technique.

Aiming at a quantitative understanding of basic aspects of pedestrian dynamics, extensive and high-accuracy measurements of real-life pedestrian trajectories have been performed. A measurement strategy based on Microsoft KinectTM has been used. Specifically, more than 100.000 pedestrians have been tracked while walking along a trafficked corridor at the Eindhoven University of Technology, The Netherlands. The obtained trajectories have been analyzed as ensemble data. The main result consists of a statistical descriptions of pedestrian characteristic kinematic quantities such as positions and fundamental diagrams, possibly conditioned to the local crowd flow (e.g. co-flow or counter-flow).