A Alessandro Corbetta

High Statistics Measurements of Pedestrian Dynamics

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 Kinect™ 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).

Parameter estimation of social forces in pedestrian dynamics models via a probabilistic method

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.

Fluctuations around mean walking behaviors in diluted pedestrian flows

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.

From individual behaviour to an evaluation of the collective evolution of crowds along footbridges

This paper proposes a crowd dynamic macroscopic model grounded on microscopic phenomenological observations which are upscaled by means of a formal mathematical procedure. The actual applicability of the model to real-world problems is tested by considering the pedestrian traffic along footbridges, of interest for Structural and Transportation Engineering. The genuinely macroscopic quantitative description of the crowd flow directly matches the engineering need of bulk results. However, three issues beyond the sole modelling are of primary importance: the pedestrian inflow conditions, the numerical approximation of the equations for non trivial footbridge geometries and the calibration of the free parameters of the model on the basis of in situ measurements currently available. These issues are discussed, and a solution strategy is proposed.

Asymmetric pedestrian dynamics on a staircase landing from continuous measurements

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.

Frame vs. trajectory analyses of pedestrian dynamics asymmetries in a staircase landing

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.

Weakly supervised training of deep convolutional neural networks for overhead pedestrian localization in depth fields

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.

Comparing First-Order Microscopic and Macroscopic Crowd Models for an Increasing Number of Massive Agents

A comparison between first-order microscopic and macroscopic differential models of crowd dynamics is established for an increasing number of pedestrians. The novelty is the fact of considering massive agents, namely, particles whose individual mass does not become infinitesimal when grows. This implies that the total mass of the system is not constant but grows with . The main result is that the two types of models approach one another in the limit , provided the strength and/or the domain of pedestrian interactions are properly modulated by at either scale. This is consistent with the idea that pedestrians may adapt their interpersonal attitudes according to the overall level of congestion.

TurBase: A Software Platform for Research in Experimental and Numerical Fluid Dynamics

We present a software infrastructure for the research community working on turbulence and complex flows (TurBase), an easily accessible web platform for high quality data. Its main goal is to host, standardize and manage a large collections of heterogeneous experimental and numerical data sets from high-end European fluid dynamics experimental facilities and from High Performance Computational centres. TurBase offers scalable performances when accessing/uploading/searching data, providing at the same time maximum flexibility and power (through Jupyter notebooks) when doing online computation directly on big datasets