Investigating cultural aspects in the fundamental diagram using convolutional neural networks

This paper presents a study regarding group behavior in a controlled experiment focused on differences in an important attribute that vary across cultures - the personal spaces - in two Countries: Brazil and Germany. In order to coherently compare Germany and Brazil evolutions with same population applying same task, we performed the pedestrian Fundamental Diagram experiment in Brazil, as performed in Germany. We use convolutional neural networks to detect and track people in video sequences. With this data, we use Voronoi Diagrams to find out the neighbor relation among people and then compute the walking distances to find out the personal spaces. Based on personal spaces analyses, we found out that people behavior is more similar in high dense populations. So, we focused our study on cultural differences between the two Countries in low and medium densities. Results indicate that personal space analyses can be a relevant feature in order to understand cultural aspects in video sequences even when compared with data from self-reported questionnaires.

Crowd analysis is a phenomenon of great interest in a large number of 2 applications. Surveillance, entertainment and social sciences are fields that can 3 benefit from the development of this area of study. Literature dealt with 4 different applications of crowd analysis, for example counting people in 5 crowds [1,2], group and crowd movement and formation [3,4] and detection of 6 social groups in crowds [5,6]. Normally, these approaches are based on personal 7 tracking or optical flow algorithms, and handle as features: speed, directions 8 and distances over time. Recently, some studies investigated cultural difference 9 in videos from different countries using Fundamental Diagrams. 10 June 8, 2018 1/9 The Fundamental Diagrams -FD, originally proposed to be used in traffic 11 planning guidelines [7,8], are diagrams used to describe the relationship among 12 three parameters: i) density of people (number of people per sqm), ii) speed (in 13 meters/second) and iii) flow (time evolution) [9]. In Zhang's work [10], FD 14 diagrams were adapted to describe the relationship between pedestrian flow and 15 density, and are associated to various phenomena of self-organization in crowds, 16 such as pedestrian lanes and jams, such that when the density of people 17 becomes really high, the crowd stops moving. It is not the first time cultural 18 aspects are connected with FD. Chattaraj and his collaborators [11] suggest that 19 cultural and population differences can also change the speed, density, and flow 20 of people in their behavior. 21 Favaretto and his colleagues discussed cultural dimensions according to 22 Hofstede typology [12] and presented a methodology to map data from video 23 sequences to the dimensions of Hofstede cultural dimensions theory [13] and also 24 a methodology to extract crowd-cultural aspects [14] based on the Big-five 25 personality model (or OCEAN) [15]. 26 In this paper, we want to investigate cultural aspects of people when 27 analyzing the result of FD among two different Countries: Brazil and Germany. 28 We used the Pedestrian Fundamental Diagram experiment performed in 29 Germany and perform the experiment in Brazil, in order to compare these two 30 different populations. Our goal is to investigate the cultural aspects regarding 31 distances in personal space analyses. FD was chosen since the populations are 32 performing the same task in a controlled environment with same amount of 33 individuals. The next section discusses the related work, and in Section 2 we 34 present details about the proposed approach with a statistical analysis, followed 35 by the discussion and final considerations in Section 3. Cultural influence in crowds can consider attributes such as personal spaces, 38 speed, pedestrian avoidance side and group formations [16]. Personal space 39 refers to the preferred distance from others that an individual maintains within 40 a given setting. This area surrounding a person's body into which intruders may 41 not come is the personal space [17]. It serves mainly to two main functions: (i) 42 communicating the formality of the relationship between the interactants; and 43 (ii) protecting against possible psychologically and physically uncomfortable 44 social encounters [18]. People from various cultural backgrounds differ with 45 regard to their personal space [19]. These differences reflect the cultural norms 46 that shape the perception of space and guide the use of space within different 47 societies [20].

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Recently, a study on personal space employing self-report questionaries was 49 conducted in 42 countries [21]. Participants had to answer a graphic task of Sorokowska and colleagues [21] indicate possible categorization of cultures 55 regarding this group behavior.

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Still, as different analitical techniques could produce different results and the 57 use of objective measures of personal space has been encouraged in the 58 literature [18], the interactive analysis methods may be the most appropriate 59 not only to further develop new possible categorization of cultures but also to 60 design virtual environments or implement changes in the real world.

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The project of public transportations, for example, can be improved by the 62 analysis of personal space in different countries, since the invasion of the 63 personal space in trains elicits psychophysiological responses of stress [22]. 64 Furthermore, the project of human-robots has also been improved through the 65 analysis of personal space [23], as it is important that robots do not invade the 66 personal space of its users -the configuration of its distances might benefit from 67 studies that employ analysis of daily preferred interpersonal distances across 68 different countries.

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Our idea here is to identify different aspects among populations from Brazil 70 and Germany regarding distances in individual's personal space. However, 71 differently from the projective technique proposed by [21], we want to use video 72 sequences, real populations and computer vision techniques to proceed with 73 cultural personal space analyses. Next section presents the methodology 74 adopted to detect and track the individuals in the experiment and how we 75 perform the statistic information extraction.  [11]. The length of the corridor is l corr = 17.3m and the width of the passageway is w corr = 0.8m. This experiment in Brazil was conducted as described in [11]. With the same 83 populations (N=1, 15, 20, 25, 30 and 34) and physical environment setup. In 84 addition, we obtained from Germany (we have access to such videos thanks to 85 the authors of database of PED experiments ) video with populations (N=1, 15, 86 25 and 34), so N=20 and 30 were not used in our analysis.

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The corridor was built up with markers and tape on the ground. Its size and 88 shape is presented in Fig. 1. The length of the corridor is l corr = 17.3m. The 89 width of the passageway is w corr = 0.8m, which is sufficient for a single person 90 walk. In addition, we can observe a rectangle of 2 x 0.8 meters which illustrates 91 the Region of Interest (ROI) where the populations were captured to be 92 analyzed, as proposed in [11]. 93 For the experiment, the camera was positioned in the top, eliminating the 94 video perspective. All the individuals were initially uniformly distributed in the 95 corridor. After the starting instruction, every individual should walk around the 96 corridor twice and then leave the environment while keep walking for a 97 reasonable distance away, eliminating the tailback effect. Fig. 2  In the first step of our method, the people detection and tracking is 101 performed using Convolutional Neural Networks (CNNs). In the second step, 102 the statistical information is obtained from trajectories and analyzed in order to 103 find neighbor individuals and compute distances among them. These modules 104 are presented in sequence. 105

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Since our goal was to accurately track the issues involved in the FD experiment, 107 we decided to use the recent convolutional neural networks (CNNs). We use the 108 real-time detection framework, Yolo with reference model Darknet [24]. Initially, 109 we used trained models with public datasets, named COCO [25] and PASCAL 110 VOC [26]. However, due to very different camera position in the video 111 sequences, the tracking did not work well, as can be seen in Fig. 3 (left). So, we proceed with a dataset generation to be used for the network training. 113 We used the videos with 20 and 30 people performed in Brazil different 114 quantities, which were not used in the experiment, we will finally test with the 115 number of people used in the experiment scenarios We included in the dataset 116 one image at each 50 ones, resulting in 45 images for movie with 20 people and 117 83 for video with 30 people.  used to compute the Fundamental Diagram. We adopted the already used 126 hypothesis [27] to approximate the personal space using a Voronoi Diagram 127 (VD) [28]. Indeed, we use the output of VD to compute the neighbor of each 128 individual in order to calculate the pairwise distances. So, the distance between 129 individual i and the one in front of him/her i + 1 is considered the personal 130 space of i, in this work. So, we compute such distances in the ROI, at the first 131 moment the second individual entries in the ROI illustrated in Fig. 1.

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Once we have computed all personal spaces for all individuals from the two 133 populations, we conducted the following analysis. First, we show in Fig. 4 the 134 mean distances observed in each population. As expected, the personal space 135 reduces as the density increases. In addition, the differences are higher among 136 the population as the densities are lower. The correlations of distances among 137 the two populations are shown in Fig. 5.  populations increase as the densities increase too. Based on this affirmation, our 140 hypothesis is that in high densities, people act more as a mass and less as 141 individuals [29], which ultimately affects behaviors according to their own 142 culture. This assumption is coherent with one of the main literatures on mass 143 behavior [30].  155 Also in Fig. 6, in the right, we present the Kullback-Leibler divergence from the 156 probability distribution of distances among the countries. The Kullback-Leibler 157 (KL) divergence [31] (also called relative entropy) is a measure of how one 158 probability distribution diverges from a second. It is interesting to see that as 159 the density increases, the KL divergence decreases.  Analyzing both scenarios (N = 15 and N = 34), it is possible to notice that 168 in both cases, people from Brazil are more correlated with the first neighbor in 169 terms of the personal distance. It could be interpreted as a cultural trait, e.g. a 170 population that reacts more to the surround population. People from Germany, 171 on the other hand, are less correlated with the first neighbor (most people have 172 a negative correlation). In the same way, it could be interpreted as a cultural 173 trait, as a population that tries to behave independently of people around. 174 We also performed a comparison among the preferred distance people keep 175 from others evaluated in a study performed by [21] and the results obtained 176 from the experiment performed in our approach. Fig. 7 shows such comparison. 177 In the Sorokowska work, the answers were given on a distance (0-220 cm) scale 178 anchored by two human-like figures, labeled A and B. Participants were asked to 179 imagine that he or she is Person A. The participant was asked to rate how close 180 a Person B could approach, so that he or she would feel comfortable in a 181 conversation with Person B. In our approach we measure the distances a person A keeps from a person B 183 right in front of he or she. As said before, we used VD to determine which 184 person is the neighbor of the other. For the comparison, in our approach we use 185 the distances from the experiment N = 15 and from the Sorokowska's approach 186 we select the evaluation from acquaintance people, where the people are not 187 close neither strangers, similar to people in our experiment. As we can see in 188 Fig. 7, in spite of the fact that distances from our approach are higher than the 189 ones from Sorokowska, the proportion is similar in both scenarios. People from 190 Brazil keeps higher distances from others than people from Germany (according 191 to our approach, people from Brazil are about 0.5m more distant from each 192 other than in Germany, while in the Sorokowska approach, people from Brazil 193 are 0.8m more distant).

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Although they are different experiments, our method proves in a real scenario 195 that people actually behave according to the preferences answered in 196 Sorokowska's research.  [11], in this way, people from both countries performed 203 exactly the same task. Our hypothesis is that by fixing the environment setup 204 and the task people should apply, we could evaluate the cultural variation of 205 individual behavior.

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In the analysis, we found out that as the density of people increases, people 207 are more homogeneous, as shown in PDF of distances and Kullback-Leibler 208 divergence in Fig. 6 and in computed Pearson's correlation in Fig. 5. It 209 indicates that people assumes group-level behavior instead of individual-level 210 behavior according to his/her culture or personality. It is an interesting and 211 concrete proof of several theories about mass behavior as discussed in [29], [30]. 212 We show some differences among Brazil and Germany in the personal space 213 of the individuals in terms of distances between individuals. These differences 214 are evidences of cultural behavior of people from each country, mainly in low 215 density or small groups, when the individuals are not acting as a crowd. For 216 future work, we intend to keep investigating the cultural aspects in video 217 sequences, focused on medium and low densities. We also intend to increase our 218 set of video data, addressing another countries.