Investigating Cultural Aspects in the Fundamental Diagram using Convolutional Neural Networks and Simulation
Rodolfo M. Favaretto, Roberto R. Santos, Marcio Ballotin, Paulo Knob, Soraia R. Musse, Felipe Vilanova, Angelo B. Costa
IInvestigating Cultural Aspects in the FundamentalDiagram using Convolutional Neural Networks andSimulation
Rodolfo M. Favaretto a, ∗ , Roberto R. Santos a , Marcio Ballotin a , Paulo Knob a ,Soraia R. Musse a , Felipe Vilanova b , ˆAngelo B. Costa b a Virtual Human Simulation Laboratory VHLab – Graduate Course on Computer Science,Pontifical Catholic University of Rio Grande do Sul, Porto Alegre, RS - Brazil b Graduate Course on Psychology, Pontifical Catholic University of Rio Grande do Sul,Porto Alegre, RS - Brazil
Abstract
This paper presents a study regarding group behavior in a controlled experimentfocused on differences in an important attribute that vary across cultures - thepersonal spaces - in two Countries: Brazil and Germany. In order to coherentlycompare Germany and Brazil evolutions with same population applying sametask, we performed the pedestrian Fundamental Diagram experiment in Brazil,as performed in Germany. We use CNNs to detect and track people in videosequences. With this data, we use Voronoi Diagrams to find out the neighborrelation among people and then compute the walking distances to find out thepersonal spaces. Based on personal spaces analyses, we found out that peoplebehavior is more similar, in terms of their behaviours, in high dense populationsand vary more in low and medium densities. So, we focused our study oncultural differences between the two Countries in low and medium densities.Results indicate that personal space analyses can be a relevant feature in orderto understand cultural aspects in video sequences. In addition to the culturaldifferences, we also investigate the personality model in crowds, using OCEAN.We also proposed a way to simulate the FD experiment from other countries (cid:73)
Thanks to Office of Naval Research Global (USA) and Brazilian agencies: CAPES, CNPQand FAPERGS. ∗ Corresponding author
Email address: [email protected] (Rodolfo M. Favaretto)
Preprint submitted to Neurocomputing October 26, 2020 a r X i v : . [ c s . OH ] S e p sing the OCEAN psychological traits model as input. The simulated countrieswere consistent with the literature. Keywords:
Group behaviors, Cultural aspects, Convolutional NeuralNetworks
1. Introduction
Crowd analysis is a phenomenon of great interest in a large number of ap-plications. Surveillance, entertainment and social sciences are fields that canbenefit from the development of this area of study. Literature dealt with differ-ent applications of crowd analysis, for example counting people in crowds [1, 2],group and crowd movement and formation [3, 4] and detection of social groupsin crowds [5, 6]. Normally, these approaches are based on personal tracking oroptical flow algorithms, and handle as features: speed, directions and distancesover time. Recently, some studies investigated cultural difference in videos fromdifferent countries using Fundamental Diagrams [7, 8, 9, 10, 11, 12].The Fundamental Diagrams – FD, originally proposed to be used in traf-fic planning guidelines [13, 14], are diagrams used to describe the relationshipamong three parameters: i) density of people (number of people per sqm), ii)speed (in meters/second) and iii) flow (time evolution) [9]. In Zhang’s work [15],FD diagrams were adapted to describe the relationship between pedestrian flowand density, and are associated to various phenomena of self-organization incrowds, such as pedestrian lanes and jams, such that when the density of peoplebecomes really high, the crowd stops moving. It is not the first time culturalaspects are connected with FD. Chattaraj and his collaborators [16] suggestthat cultural and population differences can also change the speed, density, andflow of people in their behavior.Favaretto and his colleagues discussed cultural dimensions according to Hof-stede analysis [17] and presented a methodology to map data from video se-quences to the dimensions of Hofstede cultural dimensions theory [18] and alsoa methodology to extract crowd-cultural aspects [19] based on the Big-five per-2onality model (or OCEAN) [20]. In his work, Favaretto [19] proposed a way tomap geometrical features (such as speed, angular variation and distances) frompedestrians tracking to OCEAN dimensions.In this paper, we want to investigate cultural aspects of people when analyz-ing the result of FD among two different Countries: Brazil and Germany. Weused the Pedestrian Fundamental Diagram experiment performed in Germanyand perform the experiment in Brazil, in order to compare these two differentpopulations. Our goal is to investigate the cultural aspects regarding distancesin personal space analyses. FD was chosen since the populations are performingthe same task in a controlled environment with same amount of individuals.We also propose a way to simulate other countries using OCEAN as input togenerate geometrical features (such as speed, angular variation, etc.) of eachpedestrian. The next section discusses the related work, and in Section 3 wepresent details about the proposed approach with a statistical analysis (Sec-tion 4), followed by the discussion and final considerations in Section 5.
2. Related Work
Cultural influence can be considered in crowds attributes as personal spaces,speed, pedestrian avoidance side and group formations [21]. Personal spacerefers to the preferred distance from others that an individual maintains withina given setting. This area surrounding a persons body into which intruders maynot come is the personal space [22]. It serves mainly to two main functions: (i)communicating the formality of the relationship between the interactants; and(ii) protecting against possible psychologically and physically uncomfortablesocial encounters [23]. People from various cultural backgrounds differ withregard to their personal space [24]. These differences reflect the cultural normsthat shape the perception of space and guide the use of space within differentsocieties [25].Recently, a study on personal space employing a projective technique wasconducted in 42 countries [26]. Participants had to answer a graphic task mark-3ng which distance they would feel comfortable when interacting with: a) astranger, b) an acquaintance, and c) a close person. This way the authors couldevaluate the projected metric distance for a) social distance, b) personal dis-tance and c) intimate distance. The number of countries assessed in the study ofSorokowska and colleagues [26] promote conclusions from different cultures andindicated some new possible categorization of the cultures but also to designobjects or implement changes in the real world. The project of public trans-portations, for example, can be improved by the analysis of real personal spacein different countries, since the invasion of the personal space in trains elicitspsychophysiological responses of stress [27]. Furthermore, the project of human-robots has also been improved through the analysis of personal space [28]. Asit is important that robots do not invade the personal space of its users, theconfiguration of its distances might benefit from studies that employ analysis ofdaily preferred interpersonal distances across different countries.Our idea here is to identify different aspects among populations from Braziland Germany regarding distances in individual’s personal space. However, dif-ferently from the projective technique proposed by [26], we want to use videosequences, real populations and computer vision techniques to proceed with per-sonal space analyses. Next section presents the methodology adopted to detectand track the individuals in the experiment and how we perform the statisticinformation extraction.
3. The proposed approach
We propose a 2-step methodology responsible for trajectories detection andstatistical data extraction/analysis. The first part aims to obtain the individ-ual trajectories of observed pedestrians in real videos using machine learningalgorithms. We performed the Fundamental diagram experiment in Brazil, asillustrated in Figure 1.This experiment in Brazil was conducted as described in [16]. With the samepopulations (N=1, 15, 20, 25, 30 and 34) and physical environment setup. In4 igure 1: Sketch of the FD experimental setup according to [16]. addition, we obtained from Germany video with populations (N=1, 15, 25 and34), so N=20 and 30 were not used in our analysis.The corridor was built up with markers and tape on the ground. Its sizeand shape is presented in Figure 1. The length of the corridor is l corr = 17 . m .The width of the passageway is w corr = 0 . m , which is sufficient for a singleperson walk. In addition, we can observe a rectangle of 2 x 0.8 meters whichillustrates the Region of Interest (ROI) where the populations were captured tobe analyzed, as proposed in [16].For the experiment, the camera was positioned in the top, eliminating thevideo perspective. All the individuals were initially uniformly distributed in thecorridor. After the starting instruction, every individual should walk aroundthe corridor twice and then leave the environment while keep walking for areasonable distance away, eliminating the tailback effect. Figure 2 shows theexperiment performed in Brazil and Germany, with N = 34 (where N is thenumber of people).In the first step of our method, the people detection and tracking is per- We have access to such videos thanks to the authors of database of PED experiments,available at http://ped.fz-juelich.de/db/ . a) Brazil(b) GermanyFigure 2: Some pictures extract from the experiment: (a) performed in Brazil with N = 34and (b) performed in Germany with N = 34. formed using Convolutional Neural Networks (CNNs). In the second step, thestatistical information is obtained from trajectories and analyzed in order tofind neighbor individuals and compute distances among them. These modules6re presented in sequence. Since our goal was to accurately track the issues involved in the FD experi-ment, we decided to use the recent convolutional neural networks (CNNs). Weuse the real-time detection framework, Yolo with reference model Darknet [29].Initially, we used trained models with public datasets, named COCO [30] andPASCAL VOC [31]. However, due to very different camera position in the videosequences, the tracking did not work well, as can be seen in Figure 3(a).So, we proceed with a dataset generation to be used for the network training.We used the videos with 20 and 30 people performed in Brazil. We choose thistwo experiments (with 20 and 30 pedestrian) for training process because we donot have the corresponding amount of people from the Germany dataset. Weincluded in the training dataset one image at each 50 frames, resulting in 45images for movie with 20 people and 83 for video with 30 people. Table 1 showsthe number of images used in training, validation and testing phases. Obtainedaccuracy in our method for videos from Brazil was 98.2 % with 15 people, 98.4% with 25 people and 97.8 % with 34 people. Table 2 demonstrates the accuracyof both Countries in the respective videos.
Table 1: Configuration of the Dataset used in the experiment.
Goal Images Annotations CountryTrain 128 3833 BrazilValid 96 1536 BrazilTest - 15 people 1596 23530 BrazilTest - 25 people 3124 73250 BrazilTest - 34 people 5580 178448 BrazilTest - 15 people 2372 71846 GermanyTest - 25 people 3322 74005 GermanyTest - 34 people 3504 110500 Germany7 a) Test using VOC(b) Training ResultsFigure 3: Test using VOC and trained pattern configuring (a). Training Results in a videofrom Brazil (b).
As a result of tracking process, described in last section, we obtained the 2Dposition (cid:126)X i of person i (meters), at each timestep in the video. Positions areused to compute the Fundamental Diagram.We adopted the already used hy-8 able 2: Accuracy (%) obtained. Country 15 people 25 people 34 peopleBrazil 98.2% 98.4% 97.8%Germany 93.0% 92.3% 91.0%pothesis [32] to approximate the personal space using a Voronoi Diagram (VD).Indeed, we use the output of VD to compute the neighbor of each individual inorder to calculate the pairwise distances. As our pedestrian tracking could notbe applied to find out the order of pedestrians in the video (we do not know theorder in which the pedestrians were tracked, e.g. i and i + 1), we use the outputof the Voronoi Diagram to compute the neighbour of each individual (pedes-trians in front and behind) to calculate distances between each pedestrian andhis/her predecessor. So, the distance between individual i and the one in frontof him/her i + 1 is considered the personal space of i , in this work. So, wecompute such distances in the ROI, at the first moment the second individualentries in the ROI illustrated in Figure 1.Once we have computed all personal spaces for all individuals from the twopopulations, we conducted the following analysis. First, we show in Figure 4 themean distances observed in each population. As expected, the personal spacereduces as the density increases.The correlations of distances among the twopopulations are shown in Figure 5.As can be observed in Figure 5, the Pearson’s correlations among the pop-ulations increase as the densities increase too. Based on this affirmation, ourhypothesis is that in high densities, people act more as a mass and less as indi-viduals [33], which ultimately affects behaviors according to their own culture.This assumption is coherent with one of the main literatures on mass behav-ior [34].Figure 6 shows an analysis of the Probability Distribution Function (PDF)applied on the personal spaces. The three plots represent the probability of dis-9 igure 4: Mean personal distances observed in each population. tributions for each observed personal space in the interval [0 − .
5] meters. Thered lines represent the probabilities from Brazil while the blue line representsthe probabilities from Germany. The individuals from Germany keep a higherdistance from each other than individuals from Brazil.The distances performed by Brazilian individuals seems to have a lowerstandard deviation than distances performed by individuals from Germany (thewidth of the Gaussian curve is smaller in Brazil). The distances from the in-dividuals in both countries gets more similar (the red and the blue lines aremore similar when N = 34 than N = 15), corroborating with the mass idea.Also in Figure 7, we present the Kullback-Leibler divergence from the proba-bility distribution of distances among the countries. The KullbackLeibler (KL)divergence [35] (also called relative entropy) is a measure of how one probabilitydistribution diverges from a second. It is interesting to see that as the densityincreases, the KL divergence decreases. In this section we describe our proposal to simulate the Fundamental Dia-gram. Our idea is to simulate FD experiments with varied populations. Once inlast section we analyzed the FD in two Countries, our main goal here is to inves-10 igure 5: Correlations of personal space among the countries. tigate if we can simulate FD for other Countries in a coherent way, if comparedwith the literature. That is why we chosen OCEAN (Openness, Conscientious-ness, Extraversion, Agreeableness and Neuroticism) psychological traits model,proposed by Goldberg [36] to serve as input in our method. In addition, it ishas been already used in the context of simulation. For instance, Durupinar etal. [37] developed a simulation model based on psychological traits aiming torepresent emotions and emotion contagion between agents in an effective way.Therefore, there is a specific literature presenting the OCEAN of differentCountries [38] that can inform input values in our method. As mentioned before,Favaretto et al. [19] comprehends equations to map pedestrian behavior, fromvideo sequence, to OCEAN individual values. So, we extended this model topropose a way to, having the OCEAN as input, find out geometrical informationregarding how people evolve in simulations. We decided to use three parametersto simulate FD, that are achieved based on equations proposed by Favaretto [19]: collectivity , angular variation and linear speed .Collectivity is related to the group cohesion, i.e. the higher is the cohesionmore collective behaviors the population has [39]. According to Dyaram etal. [40], members of a strongly cohesive group tends to stay together, not leavingthe group, as well to be an active part of it. Angular variation is computed11 a) N = 15 (b) N = 25(c) N = 34Figure 6: Probability distribution function (PDF) from the distances between the individualsin the experiment with, respectively: (a) N = 15, (b) N = 25 and (c) N = 34. as a function of the vector that represents the goal direction of agent i andthe third parameter represents the linear speed of i . These three parameterswere proposed in Favaretto [19] and are inversely mapped, in this work, to becomputed having OCEAN values as input, as described in following equations.Equation 1 describes collectivity φ i of agent i as a function of E i , A i and N i that state for some of input OCEAN parameters for i : φ i = 2 A i + N i − + 2 E i + 2(1 − N i )7 . (1)12 igure 7: Kullback-Leibler divergence from the distributions of distances in Figure 6. Equation 2 describes the angular variation of i as a function of O i , A i and φ i parameters: α i = 1 − O i + 1 . − φ i − E . (2)And Equation 3 refers to linear speed of agent i and it is impacted by E i , C i and α i parameters: s i = . C i − (4 α i ) − + E − α i +12 . (3)Table 3 shows a summarization of the relations among OCEAN and geomet-ric parameters. Collectivity is related to Extraversion, Agreeableness and Neu-roticism traits; Angular Variation is related to agent Openness, Extraversionand cohesion, and finally Speed is dependent on Consciousness, Extraversionand angular variation.It is important to notice that the Extraversion trait is related to all features.As mentioned in Favaretto [19], the Extraversion trait comprehends the majority13 able 3: Relationship between the agent features and input OCEAN dimensions. Agent Features Related inputCollectivity ( φ i ) E, A, NAngular Variation ( α i ) O, E, φ i Speed ( s i ) C, E, α i of items related to crowd behavior, so, being necessary for all equations asproposed in the present work.We use φ i , α i and s i of agent i to impact its motion in FD. Virtual humansare modeled to move in a pre-defined order in FD scenario having α and s asangular and linear speed, respectively. The agent collectivity is used to definethe cohesion of the group which the agent is a member. A group’s cohesion willbe calculated as the mean value of its participants collectivity factor φ B . Groupswith cohesion close to one, have stronger bounds between their participants andwill be harder to separate over the simulation conditions and the opposite istrue for cohesion value close to zero.In our method, a cohesion value ζ g is set to define how much a group g tends to stay together, in the interval [0 , µ g is defined to represent themaximum distance an agent can be away from the rest of the group g , withoutleaving it and break the group structure. This cohesion distance is calculatedas follows in Equation 4: µ g = H s − ( ζ g ( H s − H p ζ max )) , (4)where H p is the Hall’s personal space and H s is the Hall’s social space. This14istance spaces are described by Hall [41] which defines regions that a personfeels comfortable to maintain at each specific personal or social levels. ζ max valuestands for Maximum Cohesion ( ζ max = 3) and represents the higher cohesionvalue a group can achieve.For instance, if ζ g = 0 for a certain low cohesive group g , then µ g = 3 . ζ g = 3 then µ g = 1 .
4. Experimental Results
In this section we present results about FD investigation firstly based onvideo sequences, then based on simulations.
We performed a comparison among the preferred distance people keep fromothers evaluated in a study performed by Sorokowska [26] and the results ob-tained from the experiment performed in our approach. In the Sorokowska’swork, the answers were given on a distance (0-220 cm) scale anchored by twohuman-like figures, labeled A and B. Participants were asked to imagine that heor she is Person A. The, the participant was asked to rate how close a Person Bcould approach, so that he or she would feel comfortable in a conversation withPerson B.Figures 8 show the comparison of four different FD scenarios, containingrespectively 15, 20, 25 and 30 people. In our approach we measure the dis-tances a person A keeps from a person B right in front of he or she. As saidbefore, we used VD to determine which person is the neighbor of the other.For the comparison, in the Sorokowska’s approach we select the evaluation fromacquaintance people, where the people are not close neither strangers, similarto people in our experiment. 15 a) When N = 15 (b) When N = 20(c) When N = 25 (d) When N = 30Figure 8: Our approach versus Sorokowska [26] with different number of people in the exper-iment. As we can see in Figure 8, in spite of the fact that distances from our ap-proach are higher than the ones from Sorokowska, the proportion is similar in allthe scenarios. People from Brazil keeps higher distances from others than peoplefrom Germany (according to our approach, in the N = 15 configuration, peoplefrom Brazil are about 0.5m more distant from each other than in Germany,while in the Sorokowska approach, people from Brazil are 0.8m more distant).It’s interesting to notice that as the number of people increases, more similar tothe values obtained by Sorokowska it gets (When N = 30 the values are quitesimilar). Although they are different experiments, our method proves in a realscenario that people actually behave according to the preferences answered inSorokowska’s research. We modeled the fundamental diagram experiment similar to the measuresof Chatarraj et al. [42], using the BioCrowds simulator [43]. In BioCrowds,16ach agent in the environment perceives a set of markers (dots) on the ground(described through space subdivision) within its observational radius and movesforward to its goal based on such markers (unoccupied and closest to the agentthan any other one). This is the main feature of the BioCrowds simulator, whichsupports main behaviours observed from crowd simulations (e.g., lanes and arcsformation).As output, BioCrowds measures the position of each agent at each frame,similar the tracking process performed with the FD videos. For more infor-mation on BioCrowds, please refer to [43]. In this work we simulated an FDusing BioCrowds for the same population tested using the similar environmentalsetup, as described in [16], adding goal (represented as red flags) at every cornerof the scenario, as shown in Figure 9.
Figure 9: Example of Fundamental diagram experiment in BioCrowds with goals and 15agents.
The agents are programed to seek the next goal anticlockwise, this way theykeep looping. Knowing the agent in front of it, we are able to calculate theEuclidean distance between them, this distance is the personal distance of thisagent. With this method we are able to determinate the personal distance ofevery agent during the simulation.Based on Favaretto et al. [19] experiment, we executed simulations usingthe OCEANs presented by McCrae [38] for Germans and Hispanic Americansgroups. For Germany, the used inputs are: O = 56 . C = 46 . E = 47 . A =179 . N = 52 .
8. For Brazil, we assumed the Hispanic Americans values: O =51 . C = 51 . E = 47 . A = 47 . N = 49 .
5. With this setup, we collectedthe personal distances of all agents during the simulation and calculated themean personal distance value of all agents. Figure 10 shows a comparison chartbetween the results obtained by each study for both cultures.
Figure 10: Comparison between the personal distances found by Favaretto et al. videos [19],Sorokowska study [26] and our method for Brazilian and German cultures.
Though obtained values are different for every approach, we observe a similarbehavior in all of them, Brazilian personal distances are slightly greater thanGermans in all approaches, i.e. in the video analysis (as presented by Favarettoet al. [19]), in social literature (as described by Sorokowska et al. [26] ) andindicates that our method can be comparable to the real life.This way, our method successfully represented the proxemics of both cul-tures. About the difference of the obtained values, we believe the small differenceobtained between Favaretto’s et al. [19] and our work results can be explaineddue the involved simulation parameters. These parameters would require extratuning to represent the reality with more accuracy as we used literature to setthe majority of parameters, e.g. the agent markers-detection radius R i and thehuman average walk speed s avg .Also in the experiment conducted by Sorokowska [26], the individuals wereasked to answer their comfort distances in an image, in a survey and maybe the18 igure 11: Comparison between personal distances obtained in our method and Sorokowskaet al. [26] work. Such data was obtained simulating 20 agents in the virtual FD and comparedwith Sorokowska et al. [26] results in 10 Countries. difference indicates that Physical space is not accurate with virtual abstractions.Although the results show a similar behavior, the interviewed individuals lakedin visual and sensorial informations that could make them feel uncomfortable ina way they feel not by answering it on a paper, but we reinforce the behaviorsare indeed similar.Along with the comparison between real crowds and literature for CountriesBrazil and Germany, we executed simulations for other cultural groups (Coun-tries) represented both into Sorokowska et al. [26] and McCrae [38] studies. Bycomparing the simulated personal distances, obtained using McCrae [38] cul-tural OCEAN as input, with Sorokowska et al. [26] results, we formatted theobtained results in Figure 11.As showed in Figure 8, we compare our results for experiments with 15,20, and 25 pedestrians with Sorokowska’s et al. results. It is interesting tosee that the values are much more similar with 30 pedestrian than with 15.This is explained because the results obtained in Sorokowska et al. [26] workare related to personal distances, according to Hall [44], i.e. values from 45 cm to 120 cm . So, in a simulated in the environment with 30 agents, we present thesituation where people are in personal distances and results can be comparedwith Sorokowska’s et al. 19egarding the Figure 11, it is easy to see that in some Countries population,e.g. from Peruvians to Hispanic Americans (in X axes), the values of personalspaces are very similar. It indicates that the input according to McCrae [38]OCEAN values is correlated with the physical space occupied by agents in oursimulation, when compared to real pedestrians.
5. Discussions and Final Considerations
In this paper we presented some comparatives in cultural aspects of groupof people in video sequences from two countries: Brazil and Germany. Sinceone important aspect to be considered in behavior analysis is the context andenvironment where people are acting, we worked with Fundamental Diagramexperiment proposed by [16], in this way, people from both countries performedexactly the same task. Our hypothesis is that by fixing the environment setupand the task people should apply, we could evaluate the cultural variation ofindividual behavior.In the analysis, we found out that as the density of people increases, peopleare more homogeneous, as shown in PDF of distances (Figure 6) and Kullback-Leibler divergence in Figure 7 and in computed Pearson’s correlation in Figure 5.It indicates that people assumes group-level behavior instead of individual-levelbehavior according to his/her culture or personality. It is an interesting and con-crete proof of several theories about mass behavior as discussed in Vilanova [33]and Le Bon [34].We show some differences among Brazil and Germany in the personal spaceof the individuals in terms of distances between individuals. These differencesare evidences of cultural behavior of people from each country, mainly in lowdensity or small groups, when the individuals are not acting as a crowd.We performed a comparison among the personal spaces pedestrian keep fromothers in the videos of FD with the study proposed by Sorokowska [26]. It wasinteresting to see that the personal spaces observed in the videos from Braziland Germany in FD experiment are are in accordance with those presented20hrough subject answers given in the Sorokowska’s work.In addition, we proposed a way to simulate the FD experiment from othercountries. For this, we use the OCEAN of each country as input to discover thecollectivity, angular variation and linear speed of each agent in the simulation.We also used Sorokowska distances to compare the distances between agentsobtained in the simulations of each country. The results also are in accordancewhit Sorokowska [26].For future work, we intend to keep investigating the cultural aspects in videosequences, focused on medium and low densities, since it seems to be moredifferent in terms of culture at this densities of pedestrians. We also intend toincrease our set of video data, addressing another countries.
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