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miSFM: On combination of Mutual Information and Social Force Model towards simulating crowd evacuation
Neurocomputing ∎ (∎∎∎∎) ∎∎∎–∎∎∎
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miSFM: On combination of Mutual Information and Social Force Model towards simulating crowd evacuation Mingliang Xu a, Yunpeng Wu a, Pei Lv n,a, Hao Jiang b, Mingxuan Luo a, Yangdong Ye a a b
School of Information Engineering, Zhengzhou University, Zhengzhou, China Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China
art ic l e i nf o
a b s t r a c t
Article history: Received 14 January 2015 Received in revised form 19 May 2015 Accepted 20 May 2015 Communicated by: Yue Gao
In this paper we propose a novel technique termed miSFM for the simulation of crowd evacuation. miSFM take merits of both Mutual Information (MI) and Social Force Model (SFM). More specifically, MI of interacting agents is adopted to determine the level of order within a crowd during an evacuation. In such a way, SFM can be improved by adapting the forces involved at microscopic level between mutually interacting agents. The key innovation lies in highlighting how the dynamic adjustment of SFM parameters reveals much more realistic crowd movements for the evacuation simulation. Extensive experiments over several alternative and state-of-the-art works demonstrate the advantages of the proposed algorithm. & 2015 Elsevier B.V. All rights reserved.
Keywords: Crowd simulation Evacuation Mutual Information Social Force Model
1. Introduction Crowd simulation is becoming a research hot spot with emerging applications in psycho-social study, entertainment, as well as education [1]. Crowds can be regarded as the circumstance in which individual people are grouped together to reveal their social behaviors. Among various crowd situations, the disaster and emergency crowd behaviors have attracted extensive research focus due to its dangerousness. Such situations may arise at various social events, for instance urgent egress or evacuation, in which the crowd density are extremely high. In this case, the situation may get out of control into unordered running and collision, which may result in hazardously high crowd densities and bottlenecks [2]. For example, crowd evacuation in fires typically causes very dangerous, competitive behaviors among individuals. For a case study, almost 1400 people died during evacuation in 1990 in Mecca, Saudi Arabi, due to a power blackout in a pedestrian tunnel. See [3] for more crowd disaster reported recently. Computational modeling and simulation retains one fundamental solution toward avoiding crowd evacuation disasters [4]. It has been receiving ever increasing research interest recently [5–8], with very success applications in the widely used commercial softwares, such as EXODUS, Simulex, Legion, and Myriad. However, due to the complex nature of human behaviors in the crowd, it is still widely regarded as an open problem. The key issue is how n
Corresponding author.
to accurately understand the collective behavior of crowds. Thus, a possible solution is to find rules that individual pedestrians unconsciously follow to navigate crowded spaces. One promising solution towards computational modeling is the Social Force Model (SFM) [9,10]. To model user behaviors during evacuation, SFM describes human crowd behavior with a mixture of socio-psychological attributes and physical forces. Comparing to other model [4–8], SFM can better reflect the phenomenon of pedestrian traffic especially in evacuation situations. While promising results have been reported, there exists one essential issue in SFM model, i.e., the model parameters are hard to be adaptively determined, which has to be fixed and cannot tackle the dynamic crowd environments. In this paper, we propose a novel model coined miSFM (i.e. mutual information Social Force Model) for simulating crowd evacuation. The main novelty of our approach is to use information theory to improve the adaptation of the SFM (Social Force Model) [9,10] during the evacuation. We employ mutual information to evaluate the disorder of the escaping crowd. In response to the mutual information feedback of the current crowd situation, our miSFM can dynamically adjust the key parameters of the SFM to achieve an optimal evacuation simulation. The remainder of the paper is organized as follows. In Section 2, we review the related work. In Section 3 we present the details of miFSM. In Section 4 we discuss our experiments and the results obtained with miFSM for different simulation scenarios. In Section 5, we conclude the paper and outline our future work.
http://dx.doi.org/10.1016/j.neucom.2015.05.074 0925-2312/& 2015 Elsevier B.V. All rights reserved.
Please cite this article as: M. Xu, et al., miSFM: On combination of Mutual Information and Social Force Model towards simulating crowd evacuation, Neurocomputing (2015), http://dx.doi.org/10.1016/j.neucom.2015.05.074i
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2. Related work 2.1. Understanding crowd behavior It is likely to demonstrate some common patterns from complex human behaviors. For example, people incline to find the more direct and easiest way when walking and typically avoid detours even if the route is crowded. It refers to the so-called “least effort principle”, i.e., everyone tries to reach his destination with least energy and time. Also in non-emergency situation, people prefer to be apart from each other [1,9], which results in relatively low crowd density. Referring to crowd behaviors in non-panic situations, an interesting observation is an oscillating phenomena appearing at doors or narrow passages, i.e., given the same mass of people on both sides of the door, when one side is using the door to pass through it, one of the masses decreases until the other one has enough “force” to get through the door. Another observation is the “repulsing force”, i.e., if we consider again people walking in opposite directions in a narrow pathway, soon we will get a stable state which includes people walking in lanes instead of forcing their way through the oncoming crowd. Referring to crowd behaviors in panic situations, an interesting observation is that, their desired velocity increases. However, the more tense people in a crowd get, the less they care about finding the most convenient and shortest way, which may show herding, flocking, or arching (a large crowd with a high desired velocity tries to pass through a door) [1]. For instance, in the arching case, the door gets clogged and the crowd pattern forms an arch shape around the door, resulting in pushing interactions [1,9]. Recent research in crowd simulation was able to recreate these behaviors and effects and propose explanations for their occurrences and measure their impacts.
destination nodes. There are two typical approaches in evacuation model [15–17], i.e., the first approach defines a set of optimal routes and evaluates performance measures simultaneously, and the second uses an analytical optimization to offer a routing policy to be evaluated with a traffic simulation model [18–20]. For other relevant work, the work in [1] introduces a MACES model concerning the evacuation case that individuals in the crowd have limited knowledge of the environment. First, in the high-level, a wayfinding system is proposed for communication of route knowledge between individuals, allowing them to coordinate their mental maps. Then, in the low-level, a social force panic-based evacuation simulation is introduced to exploit the high-level system's route finding behaviors. As its improved version, the HiDAC model [11] enhances the performance of MACES by reducing the scope of processing of neighboring agents to those within the same room. HiDAC also involves further psychological effects including on the low-level system controlling pushing and desired velocities. Information theory has also been introduced by Feixas et.al. [21] to measure scene complexity. Turkay et al. [22] used information theory based formulations to automatically control the virtual camera in a crowded environment. In [23,24], the same authors extended information theory based model proposed in [21] to control how agents behave in a crowd simulation. In [25], the same authors provided an excellent “early warning” indicator of the emergence of crush conditions. In this paper, we propose to integrate an information theory based model to SFM to adjust the parameter of the SFM. Our model is microscopic behavioral simulation by nature as SFM and MI involves the mutual interaction of neighboring agents. This work sheds a new light on the correlation between MI and SFM parameters
2.2. Crowd modeling and simulating evacuation 3. A mutual information based SFM model Crowd simulation has a long history in computer graphics. Popular models include, but not limited to, Rule-based Models, Social Force Models (SFM), Crowd Evacuation, Information Theory based Simulation etc [1]. Rules-based Models and SFM can be classified as microscopic models, while Crowd Evacuation and Information Theory based Models may involve both microscopic and macroscopic interaction, the latter of which is controlled by mutual information or psychological behavior between agents. Rule-based crowd models are flexible in simulating various crowd agents through a set of carefully-designed rules. For instance, Reynolds [11] presented the Boids concept that simulates flocks of birds and schools of fishes via several simple yet effective steering behavioral rules to keep the group cohesion, alignment and separation to avoid collisions. Force-based model proposed by Helbing and Molnár [9,10] was originally derived from human social force study,. This model solves Newton's equation to determine the position of each individual by considering repulsive interactions, friction forces, dissipation, and fluctuations. Later, this model was further applied and generalized to other simulation scenarios such as densely populated crowds [12], simulation of pedestrian evolution [13] and escape panic [9]. This model can well capture the phenomenon such as arching in the portals and the “faster-is-slower” effect [8]. Our crowd simulation model is based on SFM, and we will describe the model formally in Section 3.1. Evacuation models [14] was inspired by the field of operations research (OR) and transportation engineering (TE). OR approaches aim to minimize the total evacuation time for the whole system or for individual user. System optimization methods consider traffic as non-interrupted flows, which satisfy demand existing in
Our model provides global knowledge of crowd's activities and enables the crowd simulator to incorporate agent–crowd interactions to modify agents' behavior. As shown in Fig. 1, our model is built upon the basis of the environment maps, which record and represent crowd's and obstacle's position. Over this map, the Social Force Model is deployed for modeling the crowd behavior. And finally, we introduce the Mutual Information to dynamically refine the parameters used in SFM, which alleviates the scale difference between different disaster scenarios. Our method is summarized in Fig. 2. Since the first element is relatively simple, we skip its detail and focus on the rest two ones, which are detailed in Sections 3.1 and 3.2.
3.1. Social force model For all the agents in the crowd ( 8 a A C, a is an agent, C is the crowd), the Social Force Model describes human crowd behavior with a mixture of socio-psychological attributes and physical forces. There are the following force that affect the movement of each agent: the driving force f drive ðva Þ, the obstacle's force f obstacle ðγÞ, the repulse force by the other agents f repulse ðγ a ; γ b Þ and the resultant force F: f drive ðva Þ ¼
1 0 ðv ea va Þ τa a
f obstacle ðγ a ; γ o Þ ¼ Ae
jγ a γ o j B
ð1Þ ð2Þ
Please cite this article as: M. Xu, et al., miSFM: On combination of Mutual Information and Social Force Model towards simulating crowd evacuation, Neurocomputing (2015), http://dx.doi.org/10.1016/j.neucom.2015.05.074i
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Fig. 1. The map initialization of the environment.
jγa γb j Ae B f repulse ðγ a ; γ b Þ ¼ γa γb F ¼ f drive ðva Þ þ f obstacle ðγ a ; γ o Þ þ
ð3Þ X
f repulse ðγ a ; γ b Þ þ ξa
Environment Initialization
ð4Þ
aab
Feedback
where v0a is the desired velocity of a, ea is the ideal heading, va is the current velocity, τa is the relaxation parameter. γ a ; γ b are the position vectors of the agents and γ o is the position vector of the obstacle. γ a γ b is the distance between the agents and γ a γ o is the distance between agent and obstacle. A; B are constant and ξa is the fluctuation factor.
3.2. Our miSFM
IðA; BÞ ¼
X i;j
pðai ; bj Þ pðai ; bj Þlog n pðai Þpðbj Þ
Iv ¼
X pðxi ; vj Þ pðxi ; vj Þlog 2 pðx i Þpðvj Þ i;j
ð6Þ
IðY; vÞ ¼
X pðyi ; vj Þ pðyi ; vj Þlog 2 pðy i Þpðvj Þ i;j
ð7Þ
IðX; dirÞ ¼
X pðxi ; dir j Þ pðxi ; dir j Þlog 2 pðxi Þpðdir j Þ i;j
ð8Þ
IðY; dirÞ ¼
X pðyi ; dir j Þ pðyi ; dir j Þlog 2 pðyi Þpðdir j Þ i;j
ð9Þ
ð10Þ
X pðyi ; denj Þ pðyi ; denj Þlog 2 pðyi Þpðdenj Þ i;j
IðX; vÞ þ IðY; vÞ 2
I dir ¼
ð11Þ
ð12Þ
IðX; dirÞ þ IðY; dirÞ 2
ð13Þ
IðX; denÞ þIðY; denÞ 2
ð14Þ
I den ¼
IðX; vÞ ¼
X pðxi ; denj Þ pðxi ; denj Þlog 2 pðxi Þpðdenj Þ i;j
Fig. 2. Overview structure of our miSFM model.
ð5Þ
where pðai Þ, pðbj Þ, pðai ; bj Þ are the individual probability and joint probability distribution of A and B. For agent ai , variables in computation of the MI include: twodimensional position coordinates ðxi ; yi Þ and the velocity vi , the direction dir i and the density deni . Regarding the density, we divide the scene for transformation into same 2D small bins with the area Rbin Rbin , Rbin is the width of one bin. The number of the agents in this area is the density, and deni is the number of the agents which share the same bin with ai . We measure the MI parameters I v ; I dir ; I den as follows:
IðX; denÞ ¼
Monitor the Status with MI
IðY; denÞ ¼
Along with the simulation of the evacuation, we measure the independence of the location, velocity, direction and density to establish the monitoring element of the current crowd status. In general, the Mutual Information of two discrete time-series variables A and B are defined as:
SFM for simulation
From the experiments in Section 4.2, we can quantitatively assert that, some parameters such as the time of evacuation is very sensitive to I v ; I dir and I den . It indicates that there exists a special extreme point in the MI curve corresponding to the optimal time of evacuation. This point is also related to the least escape time. Furthermore, we have also found that the parameter R in the SFM, which is the threshold of safe distance between two agents to avoid collision, is significantly related with the I v ; I dir ; I den . Moreover, the parameter V 0 in the SFM is implicitly determined by the I v when the least evacuation time occurs. Therefore, we can quantify the potential relationships between the SFM parameters and the MI values. From the beginning of the evacuation to the current time t, we sample the instant MI value of I v ðt i Þ; I dir ðt i Þ and I den ðt i Þ at every interval Δt time slice, where t i ¼ i U Δt and i ¼ 0; 1; 2; ⋯; t=Δt. Then, we compute the average sampled MI values of I v ðt i Þ; I dir ðt i Þ and I den ðt i Þ at the current time t, and denote the average values as: Pi ¼ t=Δt I v ðt i Þ ð15Þ I v ðtÞ ¼ i ¼ 0 t=Δt Pi ¼ t=Δt I dir ðtÞ ¼
I dir ðt i Þ t=Δt
i¼0
ð16Þ
Pi ¼ t=Δt I den ðtÞ ¼
I den ðt i Þ t=Δt
i¼0
ð17Þ
Please cite this article as: M. Xu, et al., miSFM: On combination of Mutual Information and Social Force Model towards simulating crowd evacuation, Neurocomputing (2015), http://dx.doi.org/10.1016/j.neucom.2015.05.074i
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Fig. 3. The classic situation for the evacuation (Top). The initialization of the simulation (Middle). The persons begin gather at the door for panic. (Bottom) The “arc” is presented.
For the MI of velocity I v ðtÞ, the former t Δt time and the later t þ Δt, the slope for the two segments ðt Δt; tÞ; ðt; t þ ΔtÞ is as follows: K v1 ¼
I v ðtÞ I v ðt ΔtÞ Δt
ð18Þ
K v2 ¼
I v ðt þ ΔtÞ I v ðtÞ Δt
ð19Þ
We adjust the parameter R according to the K v1 and K v2 : ( R þ θv ; jK v1 j 4 jK v2 j R¼ R θv ; jK v1 j jK v2 j
R¼
: R θden
; K den1 4 K den2 ; K den1 K den2
V0
; K v1 dK v2 o 0
ð23Þ
where λv is the adjustment factor of the parameter V 0 . The validity of the formula (17)–(20) is demonstrated in Section 4.2. With this method, we can control the overall SFM simulation according to the MI of the crowd in real time, which is the aim and contribution of our miSFM model.
ð20Þ 4. Results and discussion
where θv is the adjustment factor of the parameter R with the I v . Similarly, we can also determine 8 < R þ θdir ; K dir1 4 K dir2 R¼ ð21Þ : R θdir ; K dir1 K dir2
8 < R þ θden
And for the parameter V 0 , in the same way, we have 8 < V 0 þ λv ; K v1 4 0; K v2 4 0 V0 ¼ : V 0 λv ; K v1 o 0; K v2 o0
ð22Þ
We have developed a simulation system and run a series of evacuations experiments. All the experiments are conducted on an Intel Core (TM) i5 2.27 GHZ CPU with 4 GB memory and an ATI Mobility Radeon HD 5730 graphics card. Our platform is an extension of OpenSteer [26]. To determine the initial position of the persons, the only thing needs to specify is the bitmap files of the environment. It's automatic and very convenient. We use 3D character model to represent people in the crowd for a more realistic effect. In our platform, model's importing and rendering are supported by the FBX SDK [27].
Please cite this article as: M. Xu, et al., miSFM: On combination of Mutual Information and Social Force Model towards simulating crowd evacuation, Neurocomputing (2015), http://dx.doi.org/10.1016/j.neucom.2015.05.074i
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4.1. Results Evaluation of the evacuation typically involves measuring the escape time and the validity of the simulation for diverse environments set by the user. Over both factors, our experiments quantitatively demonstrate that the effect of the SFM is improved by the introduction of the Mutual Information. Scenario 1. As shown in Fig. 3, this scenario is the classic evacuation, i.e., from a single room with one door only. And our later experiments are expanded from this initial basic model. This scenario illustrates the arching phenomenon. Table 1 Comparison of SFM and miSFM for simulation time and average of the force in each update of the runtime.
Simulation time for escape Average of force on x-axis Average of force on y-axis
SFM
miSFM
10.76 s 17.204 15.287
8.95 s 13.597 12.248
220 SFM miSFM
200 180 160
Unsafe People
Fig. 4. The evacuation for more complex environments.
140 120 100 80 60 40 20 0
0
2
4
6
8
10
12
Time Fig. 5. The environment of the experiment reported in Table 1.
Fig. 7. The statistics of the people who are still in the dangerous place for SFM and miSFM respectively.
Fig. 6. The contrast of the effect of the SFM and miSFM. The top row is our miSFM, and the bottom is the original SFM (Left) time: 2 s, (Middle) time: 5 s, (Right) time: 8 s.
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time involves a more efficient crow evacuation, with less force being used and corresponding to a safer escape for the agents. In Fig. 7, we also report the difference of the statistics involving the people who are still unsafe for SFM and miSFM. We can see that miSFM leads to a faster reduction of the number of unsafe people than SFM.
Scenario 2. In this scenario, as shown in Fig. 4, we demonstrate a complex environment for evacuation in which there are many rooms and exits. The results show that the simulation is effective for a complex environment specified at user's discretion. The simulation also exhibits the arching phenomenon at each exit, showing the model and platform allow for a scalable simulation, with consistent results.
4.2. Discussion Scenario 3. In this scenario, we compare the performance of the miSFM model with the original SFM from the perspective of simulation time and the used force by each agent in the crowd. The parameter of the SFM is set by default and constant, while in our miSFM, the parameter is self-adapting (This is shown in Figs. 5 and 6 and Table 1). We can observe that a smaller escape
To illustrate the validity of our miSFM, we have performed a serial of experiments, from which we come up with the following observations:
4.2.1. The changes of the MI have relation with the parameter in SFM To discover the potential relationship between the MI and R, we fix the other parameter, compute the MI for different R, and observe the change of the MI with the less simulation time. In such a way, we can monitor the MI and then adjust R for a better simulation effect. To fully improve the simulation result, we carry out 3 groups of experiments with a different constant V 0 , it is the desired velocity for each person in SFM, and then change the value of R. The following is the details. As shown in Fig. 9, we can observe that the occurrence of the least escape time corresponds with the inflexion of the MI value. As a result, the proposed approach can monitor the sudden change of the MI value. That is to say, when the MI value is not stable, we can gain the parameter R as illustrated in Fig. 7, the lower R may lead to the slope of the curve. It is similar that we also analyze the parameter V 0 , and at this time, the variable is not R but V 0 , and we carry out 3 groups of experiments with the constant value for parameter V max , which shows the limit of the velocity in SFM to prevent the overload increment of the instant velocity. Fig. 10 shows the correlation between V 0 and MI values when the least simulation time appeared. W can observe that the
1000 200persons 500persons 1000persons
900 800
Unsafe People
700 600 500 400 300 200 100 0
0
30
60
90
120
150
180
Time
Fig. 8. The statistics of the people who are still in the dangerous place with different scales respectively. 0.9
Iv Idir Iden
0.85 0.8 0.75
0.7
0.7
MI
0.75
0.65
0.8 0.75 0.7
0.65
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0.6
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0.4 78 10
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R(V0 = 8)
R(V0 = 5) 42
30
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19
Time
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24
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70
R(V0 = 10)
18 17.5
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Time
17 36
22
16.5 16
34
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30
19 78 10
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50
70
78 10
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30
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50
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14 78 10
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R(V0 = 10)
Fig. 9. The relation between R and MI (Left column). In this situation, V 0 ¼ 5. When R ¼ 10, it has the least evacuation time and inflexion appeared in the curve of the three MI value, and after the inflexion, the MI value become stable. (Middle column) V 0 ¼ 8, when R ¼ 10, it has the best effect. (Right column) V 0 ¼ 10, when R ¼ 15, it has the best effect.
Please cite this article as: M. Xu, et al., miSFM: On combination of Mutual Information and Social Force Model towards simulating crowd evacuation, Neurocomputing (2015), http://dx.doi.org/10.1016/j.neucom.2015.05.074i
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0.65 Iv
Iv
Iv
0.65
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0.6
0.55
MI
MI
MI
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= 5)
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= 10)
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28 26
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= 5)
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= 15)
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22 35
30
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Time
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= 10)
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= 15)
Fig. 10. The relation between V 0 and one of MI value Iv (Left column). In this situation, V max ¼ 5. When V 0 ¼ 20, it has the less evacuation time and minimum value in the curve of the I v . (Middle column) V max ¼ 10, when V 0 ¼ 25, it has the best effect. (Right column) V max ¼ 15, when V 0 ¼ 50, it has the least simulation time.
Fig. 11. Different scales of the persons (Top) 200, persons (Middle) 500, persons (Bottom) 1000 persons.
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smallest value of I v corresponds to the lower evacuation time. Therefore, the adjustment of the parameter V 0 can be done by monitoring value I v . It is worth mentioning that there are also other parameters which are sensitive to some MI values. Such parameters would also make contribution to improving the miSFM model. 4.2.2. The different scales of the evacuation We run a series of experiments with different scales of agents number. The results of these experiments show that our model is available to diverse numbers of the persons. As shown in Fig. 8, this result illustrates that the different scales did not cause a larger variation of the escape rate. In Fig. 11, we present the different simulations.
5. Conclusion and future work In this paper we present a novel approach for crowd evacuation using the miSFM model. Our approach is designed by information theory with the well-established social force model to improve the accuracy and robustness of the proposed crowd behavior algorithm. The main idea behind this approach is to automatically adjust the parameter of SFM with the MI's feedback to achieve a better effect for evacuation. It is also convenient that the environment is user-specified. We have shown that our method is effective scalable and flexible for different crowd scales and diverse environments. Certain limitations still exist in the current work. The discovery of the correlation between the mutual information and the SFM parameter can be further extended. Also, the utilization of the MI can be further investigated, e.g. by considering other properties beyond velocity, direction and density. It would be also beneficial to improve the environment set-up to support irregular shape of the rooms, halls, and so on.
[9] D. Helbing, I. Farkas, T. Vicsek, Simulating dynamical features of escape panic, Nature 407 (2000) 487–490. [10] D. Helbing, P. Molnar, Social force model for pedestrian dynamics, Phys. Rev. E Stat. Phys. Plasmas Fluids. Relat. Interdiscip. Top. 51 (5) (1995) 4282–4286. [11] C.W. Reynolds, Flocks, Herds and Schools: A Distributed Behavioral Model, ACM, Anaheim, California, 1987. [12] N. Pelechano, J. Allbeck, N. Badler, Controlling Individual Agents in HighDensity Crowd Simulation, Eurographics Association, SanDiego, California, 2007. [13] T.I. Lakoba, D. Kaup, N.M. Finkelstein, Modifications of the Helbing–Molnar– Farkas–Vicsek social force model for pedestrian evolution, Simulation 81 (5) (2005) 339–352. [14] O. Oguz, et al., Emergency crowd simulation for outdoor environments, Comput. Graph. 34 (2) (2010) 136–144. [15] F. Southworth, L. Army, Installations, and Environment, Regional evacuation modeling: A State-of-the-art Review, Oak Ridge National Laboratory. Center for Transportation Analysis, 1991. [16] S. Algers, et al., Review of micro-simulation models. Smartest Project deliverable D, Vol. 3, 1997. [17] G. Santos and B.E. Aguirre, A critical review of emergency evacuation simulation models, 2004. [18] K. Talebi, J.M.G. Smith, Stochastic network evacuation models, Comput. Oper. Res. 12 (6) (1985) 559–577. [19] J. Smith, Multi-objective routing in stochastic evacuation networks. DZ Duand PM Pardalos (Eds.), Network Optmization Problem, 1992, 2, pp. 263–281. [20] J.M.G. Smith, Application of state-dependent queues to pedestrian/vehicular network design, Oper. Res. 42 (3) (1994) 414–427. [21] M. Feixas, et al., An information Theory Framework for the Analysis of Scene Complexity, Wiley Online Library, 1999. [22] C. Turkay, E. Koc, S. Balcisoy, An information theoretic approach to camera control for crowded scenes, Vis. Comput. 25 (5) (2009) 451–459. [23] C. Turkay, E. Koc, S. Balcisoy, An information theory based behavioral model for agent-based crowd simulations, 2010. [24] C. Turkay, E. Koc, S. Balcisoy, Integrating information theory in agent-based crowd simulation behavior models, Comput. J. 54 (11) (2011) 1810–1820. [25] P. Harding, S. Gwynne, M. Amos, Mutual information for the detection of crush, PloS One 6 (12) (2011) e28747. [26] C. Reynolds, Online 〈http://opensteer.sourceforge.net〉, 2003. [27] 〈http://www.autodesk.com/products/fbx〉.
Ming-Liang Xu is an associate professor in the School of Information Engineering of Zhengzhou University, China. His research interests include computer graphics and computer vision. Xu got his Ph.D. degree in computer science and technology from the State Key Lab of CAD&CG at Zhejiang University.
Acknowledgments This work was in part supported by the National Natural Science Foundation of China (NSFC) (Grant Nos. 61202207 and 61472370), the China Post-doctoral Science Foundation (Grant nos. 2012M520067 and 2013T60706), the National Key Technology Research and Development Program of China (Grant no. 2013BAH23F01), and the Research Fund for the Doctoral Program of Higher Education of China (Grant no. 20124101120005). We also would like to thank the anonymous reviewers for their constructive comments.
Yunpeng Wu received his Bachelor of Engineering in Computer Science and Technology from the Zhengzhou University, Zhengzhou, in 2010. He is currently a Ph.D. candidate in the Department of Information Engineering at Zhengzhou University. His research interests include machine learning and crowd simulation.
References [1] M.-L. Xu, et al., Crowd simulation and its applications: recent advances, J. Comput. Sci. Technol. 29 (5) (2014) 799–811. [2] J. Bohannon, Directing the herd: crowds and the science of evacuation, Science 310 (5746) (2005) 219. [3] D. Helbing, et al., Simulation of pedestrian crowds in normal and evacuation situations, Pedestr. Evacuat. Dyn. 21 (2002) 21–58. [4] N. Pelechano, N.I. Badler, Modeling crowd and trained leader behavior during building evacuation, Comput. Graph. Appl. IEEE 26 (6) (2006) 80–86. [5] Armel Ulrich Kemloh Wagoum, M. Chraibi, Efficient and validated simulation of crowds for an evacuation assistant, Comput. Animat. Virtual Worlds 23 (2012) 3–15. [6] A. Wagoum, A. Seyfried, S. Holl, Modelling dynamic route choice of pedestrians to assess the criticality of building evacuation, Adv. Complex Syst. 15 (2012) 1250029. [7] A. Borrmann, et al., Bidirectional coupling of macroscopic and microscopic pedestrian evacuation models, Saf. Sci. 50 (2012) 1695–1703. [8] S.J. Guy, et al., Least-effort trajectories lead to emergent crowd behaviors, Phys. Rev. E 85 (1) (2012) 016110.
Pei Lv is an assistant professor in the School of Information Engineering of Zhengzhou University, China. His research interests include character animation, crowd simulation and tracking. He received his Ph. D in 2013 from the State Key Lab of CAD&CG, Zhejiang University, China. Before that, he received his B.S. degree in computer science, from Zhengzhou University, Zhengzhou, China, in 2008.
Please cite this article as: M. Xu, et al., miSFM: On combination of Mutual Information and Social Force Model towards simulating crowd evacuation, Neurocomputing (2015), http://dx.doi.org/10.1016/j.neucom.2015.05.074i
M. Xu et al. / Neurocomputing ∎ (∎∎∎∎) ∎∎∎–∎∎∎ Hao Jiang is an assistant professor with Beijing Key Lab of Mobile Computing and Pervasive Devices, Institute of Computing Technology, Chinese Academy of Sciences, China. He received the Ph.D. degree in computer science from Chinese Academy of Sciences in 2011. His research interests include crowd simulation, virtual reality and intelligent human–computer interaction. He is a member of CCF, IEEE and ACM.
9 Yangdong Ye is currently a professor in the School of Information Engineering at Zhengzhou University, China. His research interests include database systems, machine learning, and intelligent systems. Ye has a PhD in computer science from China Academy of Railway Science.
Mingxuan Luo received his Bachelor of Engineering in Software Engineering from the Northwestern Polytechnical University, Xi'an, in 2013. He is currently a Master candidate in the Department of Information Engineering at Zhengzhou University. His research interests include computer graphics and traffic simulation.
Please cite this article as: M. Xu, et al., miSFM: On combination of Mutual Information and Social Force Model towards simulating crowd evacuation, Neurocomputing (2015), http://dx.doi.org/10.1016/j.neucom.2015.05.074i
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Neurocomputing journal homepage: www.elsevier.com/locate/neucom
miSFM: On combination of Mutual Information and Social Force Model towards simulating crowd evacuation Mingliang Xu a, Yunpeng Wu a, Pei Lv n,a, Hao Jiang b, Mingxuan Luo a, Yangdong Ye a a b
School of Information Engineering, Zhengzhou University, Zhengzhou, China Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China
art ic l e i nf o
a b s t r a c t
Article history: Received 14 January 2015 Received in revised form 19 May 2015 Accepted 20 May 2015 Communicated by: Yue Gao
In this paper we propose a novel technique termed miSFM for the simulation of crowd evacuation. miSFM take merits of both Mutual Information (MI) and Social Force Model (SFM). More specifically, MI of interacting agents is adopted to determine the level of order within a crowd during an evacuation. In such a way, SFM can be improved by adapting the forces involved at microscopic level between mutually interacting agents. The key innovation lies in highlighting how the dynamic adjustment of SFM parameters reveals much more realistic crowd movements for the evacuation simulation. Extensive experiments over several alternative and state-of-the-art works demonstrate the advantages of the proposed algorithm. & 2015 Elsevier B.V. All rights reserved.
Keywords: Crowd simulation Evacuation Mutual Information Social Force Model
1. Introduction Crowd simulation is becoming a research hot spot with emerging applications in psycho-social study, entertainment, as well as education [1]. Crowds can be regarded as the circumstance in which individual people are grouped together to reveal their social behaviors. Among various crowd situations, the disaster and emergency crowd behaviors have attracted extensive research focus due to its dangerousness. Such situations may arise at various social events, for instance urgent egress or evacuation, in which the crowd density are extremely high. In this case, the situation may get out of control into unordered running and collision, which may result in hazardously high crowd densities and bottlenecks [2]. For example, crowd evacuation in fires typically causes very dangerous, competitive behaviors among individuals. For a case study, almost 1400 people died during evacuation in 1990 in Mecca, Saudi Arabi, due to a power blackout in a pedestrian tunnel. See [3] for more crowd disaster reported recently. Computational modeling and simulation retains one fundamental solution toward avoiding crowd evacuation disasters [4]. It has been receiving ever increasing research interest recently [5–8], with very success applications in the widely used commercial softwares, such as EXODUS, Simulex, Legion, and Myriad. However, due to the complex nature of human behaviors in the crowd, it is still widely regarded as an open problem. The key issue is how n
Corresponding author.
to accurately understand the collective behavior of crowds. Thus, a possible solution is to find rules that individual pedestrians unconsciously follow to navigate crowded spaces. One promising solution towards computational modeling is the Social Force Model (SFM) [9,10]. To model user behaviors during evacuation, SFM describes human crowd behavior with a mixture of socio-psychological attributes and physical forces. Comparing to other model [4–8], SFM can better reflect the phenomenon of pedestrian traffic especially in evacuation situations. While promising results have been reported, there exists one essential issue in SFM model, i.e., the model parameters are hard to be adaptively determined, which has to be fixed and cannot tackle the dynamic crowd environments. In this paper, we propose a novel model coined miSFM (i.e. mutual information Social Force Model) for simulating crowd evacuation. The main novelty of our approach is to use information theory to improve the adaptation of the SFM (Social Force Model) [9,10] during the evacuation. We employ mutual information to evaluate the disorder of the escaping crowd. In response to the mutual information feedback of the current crowd situation, our miSFM can dynamically adjust the key parameters of the SFM to achieve an optimal evacuation simulation. The remainder of the paper is organized as follows. In Section 2, we review the related work. In Section 3 we present the details of miFSM. In Section 4 we discuss our experiments and the results obtained with miFSM for different simulation scenarios. In Section 5, we conclude the paper and outline our future work.
http://dx.doi.org/10.1016/j.neucom.2015.05.074 0925-2312/& 2015 Elsevier B.V. All rights reserved.
Please cite this article as: M. Xu, et al., miSFM: On combination of Mutual Information and Social Force Model towards simulating crowd evacuation, Neurocomputing (2015), http://dx.doi.org/10.1016/j.neucom.2015.05.074i
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2. Related work 2.1. Understanding crowd behavior It is likely to demonstrate some common patterns from complex human behaviors. For example, people incline to find the more direct and easiest way when walking and typically avoid detours even if the route is crowded. It refers to the so-called “least effort principle”, i.e., everyone tries to reach his destination with least energy and time. Also in non-emergency situation, people prefer to be apart from each other [1,9], which results in relatively low crowd density. Referring to crowd behaviors in non-panic situations, an interesting observation is an oscillating phenomena appearing at doors or narrow passages, i.e., given the same mass of people on both sides of the door, when one side is using the door to pass through it, one of the masses decreases until the other one has enough “force” to get through the door. Another observation is the “repulsing force”, i.e., if we consider again people walking in opposite directions in a narrow pathway, soon we will get a stable state which includes people walking in lanes instead of forcing their way through the oncoming crowd. Referring to crowd behaviors in panic situations, an interesting observation is that, their desired velocity increases. However, the more tense people in a crowd get, the less they care about finding the most convenient and shortest way, which may show herding, flocking, or arching (a large crowd with a high desired velocity tries to pass through a door) [1]. For instance, in the arching case, the door gets clogged and the crowd pattern forms an arch shape around the door, resulting in pushing interactions [1,9]. Recent research in crowd simulation was able to recreate these behaviors and effects and propose explanations for their occurrences and measure their impacts.
destination nodes. There are two typical approaches in evacuation model [15–17], i.e., the first approach defines a set of optimal routes and evaluates performance measures simultaneously, and the second uses an analytical optimization to offer a routing policy to be evaluated with a traffic simulation model [18–20]. For other relevant work, the work in [1] introduces a MACES model concerning the evacuation case that individuals in the crowd have limited knowledge of the environment. First, in the high-level, a wayfinding system is proposed for communication of route knowledge between individuals, allowing them to coordinate their mental maps. Then, in the low-level, a social force panic-based evacuation simulation is introduced to exploit the high-level system's route finding behaviors. As its improved version, the HiDAC model [11] enhances the performance of MACES by reducing the scope of processing of neighboring agents to those within the same room. HiDAC also involves further psychological effects including on the low-level system controlling pushing and desired velocities. Information theory has also been introduced by Feixas et.al. [21] to measure scene complexity. Turkay et al. [22] used information theory based formulations to automatically control the virtual camera in a crowded environment. In [23,24], the same authors extended information theory based model proposed in [21] to control how agents behave in a crowd simulation. In [25], the same authors provided an excellent “early warning” indicator of the emergence of crush conditions. In this paper, we propose to integrate an information theory based model to SFM to adjust the parameter of the SFM. Our model is microscopic behavioral simulation by nature as SFM and MI involves the mutual interaction of neighboring agents. This work sheds a new light on the correlation between MI and SFM parameters
2.2. Crowd modeling and simulating evacuation 3. A mutual information based SFM model Crowd simulation has a long history in computer graphics. Popular models include, but not limited to, Rule-based Models, Social Force Models (SFM), Crowd Evacuation, Information Theory based Simulation etc [1]. Rules-based Models and SFM can be classified as microscopic models, while Crowd Evacuation and Information Theory based Models may involve both microscopic and macroscopic interaction, the latter of which is controlled by mutual information or psychological behavior between agents. Rule-based crowd models are flexible in simulating various crowd agents through a set of carefully-designed rules. For instance, Reynolds [11] presented the Boids concept that simulates flocks of birds and schools of fishes via several simple yet effective steering behavioral rules to keep the group cohesion, alignment and separation to avoid collisions. Force-based model proposed by Helbing and Molnár [9,10] was originally derived from human social force study,. This model solves Newton's equation to determine the position of each individual by considering repulsive interactions, friction forces, dissipation, and fluctuations. Later, this model was further applied and generalized to other simulation scenarios such as densely populated crowds [12], simulation of pedestrian evolution [13] and escape panic [9]. This model can well capture the phenomenon such as arching in the portals and the “faster-is-slower” effect [8]. Our crowd simulation model is based on SFM, and we will describe the model formally in Section 3.1. Evacuation models [14] was inspired by the field of operations research (OR) and transportation engineering (TE). OR approaches aim to minimize the total evacuation time for the whole system or for individual user. System optimization methods consider traffic as non-interrupted flows, which satisfy demand existing in
Our model provides global knowledge of crowd's activities and enables the crowd simulator to incorporate agent–crowd interactions to modify agents' behavior. As shown in Fig. 1, our model is built upon the basis of the environment maps, which record and represent crowd's and obstacle's position. Over this map, the Social Force Model is deployed for modeling the crowd behavior. And finally, we introduce the Mutual Information to dynamically refine the parameters used in SFM, which alleviates the scale difference between different disaster scenarios. Our method is summarized in Fig. 2. Since the first element is relatively simple, we skip its detail and focus on the rest two ones, which are detailed in Sections 3.1 and 3.2.
3.1. Social force model For all the agents in the crowd ( 8 a A C, a is an agent, C is the crowd), the Social Force Model describes human crowd behavior with a mixture of socio-psychological attributes and physical forces. There are the following force that affect the movement of each agent: the driving force f drive ðva Þ, the obstacle's force f obstacle ðγÞ, the repulse force by the other agents f repulse ðγ a ; γ b Þ and the resultant force F: f drive ðva Þ ¼
1 0 ðv ea va Þ τa a
f obstacle ðγ a ; γ o Þ ¼ Ae
jγ a γ o j B
ð1Þ ð2Þ
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Fig. 1. The map initialization of the environment.
jγa γb j Ae B f repulse ðγ a ; γ b Þ ¼ γa γb F ¼ f drive ðva Þ þ f obstacle ðγ a ; γ o Þ þ
ð3Þ X
f repulse ðγ a ; γ b Þ þ ξa
Environment Initialization
ð4Þ
aab
Feedback
where v0a is the desired velocity of a, ea is the ideal heading, va is the current velocity, τa is the relaxation parameter. γ a ; γ b are the position vectors of the agents and γ o is the position vector of the obstacle. γ a γ b is the distance between the agents and γ a γ o is the distance between agent and obstacle. A; B are constant and ξa is the fluctuation factor.
3.2. Our miSFM
IðA; BÞ ¼
X i;j
pðai ; bj Þ pðai ; bj Þlog n pðai Þpðbj Þ
Iv ¼
X pðxi ; vj Þ pðxi ; vj Þlog 2 pðx i Þpðvj Þ i;j
ð6Þ
IðY; vÞ ¼
X pðyi ; vj Þ pðyi ; vj Þlog 2 pðy i Þpðvj Þ i;j
ð7Þ
IðX; dirÞ ¼
X pðxi ; dir j Þ pðxi ; dir j Þlog 2 pðxi Þpðdir j Þ i;j
ð8Þ
IðY; dirÞ ¼
X pðyi ; dir j Þ pðyi ; dir j Þlog 2 pðyi Þpðdir j Þ i;j
ð9Þ
ð10Þ
X pðyi ; denj Þ pðyi ; denj Þlog 2 pðyi Þpðdenj Þ i;j
IðX; vÞ þ IðY; vÞ 2
I dir ¼
ð11Þ
ð12Þ
IðX; dirÞ þ IðY; dirÞ 2
ð13Þ
IðX; denÞ þIðY; denÞ 2
ð14Þ
I den ¼
IðX; vÞ ¼
X pðxi ; denj Þ pðxi ; denj Þlog 2 pðxi Þpðdenj Þ i;j
Fig. 2. Overview structure of our miSFM model.
ð5Þ
where pðai Þ, pðbj Þ, pðai ; bj Þ are the individual probability and joint probability distribution of A and B. For agent ai , variables in computation of the MI include: twodimensional position coordinates ðxi ; yi Þ and the velocity vi , the direction dir i and the density deni . Regarding the density, we divide the scene for transformation into same 2D small bins with the area Rbin Rbin , Rbin is the width of one bin. The number of the agents in this area is the density, and deni is the number of the agents which share the same bin with ai . We measure the MI parameters I v ; I dir ; I den as follows:
IðX; denÞ ¼
Monitor the Status with MI
IðY; denÞ ¼
Along with the simulation of the evacuation, we measure the independence of the location, velocity, direction and density to establish the monitoring element of the current crowd status. In general, the Mutual Information of two discrete time-series variables A and B are defined as:
SFM for simulation
From the experiments in Section 4.2, we can quantitatively assert that, some parameters such as the time of evacuation is very sensitive to I v ; I dir and I den . It indicates that there exists a special extreme point in the MI curve corresponding to the optimal time of evacuation. This point is also related to the least escape time. Furthermore, we have also found that the parameter R in the SFM, which is the threshold of safe distance between two agents to avoid collision, is significantly related with the I v ; I dir ; I den . Moreover, the parameter V 0 in the SFM is implicitly determined by the I v when the least evacuation time occurs. Therefore, we can quantify the potential relationships between the SFM parameters and the MI values. From the beginning of the evacuation to the current time t, we sample the instant MI value of I v ðt i Þ; I dir ðt i Þ and I den ðt i Þ at every interval Δt time slice, where t i ¼ i U Δt and i ¼ 0; 1; 2; ⋯; t=Δt. Then, we compute the average sampled MI values of I v ðt i Þ; I dir ðt i Þ and I den ðt i Þ at the current time t, and denote the average values as: Pi ¼ t=Δt I v ðt i Þ ð15Þ I v ðtÞ ¼ i ¼ 0 t=Δt Pi ¼ t=Δt I dir ðtÞ ¼
I dir ðt i Þ t=Δt
i¼0
ð16Þ
Pi ¼ t=Δt I den ðtÞ ¼
I den ðt i Þ t=Δt
i¼0
ð17Þ
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Fig. 3. The classic situation for the evacuation (Top). The initialization of the simulation (Middle). The persons begin gather at the door for panic. (Bottom) The “arc” is presented.
For the MI of velocity I v ðtÞ, the former t Δt time and the later t þ Δt, the slope for the two segments ðt Δt; tÞ; ðt; t þ ΔtÞ is as follows: K v1 ¼
I v ðtÞ I v ðt ΔtÞ Δt
ð18Þ
K v2 ¼
I v ðt þ ΔtÞ I v ðtÞ Δt
ð19Þ
We adjust the parameter R according to the K v1 and K v2 : ( R þ θv ; jK v1 j 4 jK v2 j R¼ R θv ; jK v1 j jK v2 j
R¼
: R θden
; K den1 4 K den2 ; K den1 K den2
V0
; K v1 dK v2 o 0
ð23Þ
where λv is the adjustment factor of the parameter V 0 . The validity of the formula (17)–(20) is demonstrated in Section 4.2. With this method, we can control the overall SFM simulation according to the MI of the crowd in real time, which is the aim and contribution of our miSFM model.
ð20Þ 4. Results and discussion
where θv is the adjustment factor of the parameter R with the I v . Similarly, we can also determine 8 < R þ θdir ; K dir1 4 K dir2 R¼ ð21Þ : R θdir ; K dir1 K dir2
8 < R þ θden
And for the parameter V 0 , in the same way, we have 8 < V 0 þ λv ; K v1 4 0; K v2 4 0 V0 ¼ : V 0 λv ; K v1 o 0; K v2 o0
ð22Þ
We have developed a simulation system and run a series of evacuations experiments. All the experiments are conducted on an Intel Core (TM) i5 2.27 GHZ CPU with 4 GB memory and an ATI Mobility Radeon HD 5730 graphics card. Our platform is an extension of OpenSteer [26]. To determine the initial position of the persons, the only thing needs to specify is the bitmap files of the environment. It's automatic and very convenient. We use 3D character model to represent people in the crowd for a more realistic effect. In our platform, model's importing and rendering are supported by the FBX SDK [27].
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4.1. Results Evaluation of the evacuation typically involves measuring the escape time and the validity of the simulation for diverse environments set by the user. Over both factors, our experiments quantitatively demonstrate that the effect of the SFM is improved by the introduction of the Mutual Information. Scenario 1. As shown in Fig. 3, this scenario is the classic evacuation, i.e., from a single room with one door only. And our later experiments are expanded from this initial basic model. This scenario illustrates the arching phenomenon. Table 1 Comparison of SFM and miSFM for simulation time and average of the force in each update of the runtime.
Simulation time for escape Average of force on x-axis Average of force on y-axis
SFM
miSFM
10.76 s 17.204 15.287
8.95 s 13.597 12.248
220 SFM miSFM
200 180 160
Unsafe People
Fig. 4. The evacuation for more complex environments.
140 120 100 80 60 40 20 0
0
2
4
6
8
10
12
Time Fig. 5. The environment of the experiment reported in Table 1.
Fig. 7. The statistics of the people who are still in the dangerous place for SFM and miSFM respectively.
Fig. 6. The contrast of the effect of the SFM and miSFM. The top row is our miSFM, and the bottom is the original SFM (Left) time: 2 s, (Middle) time: 5 s, (Right) time: 8 s.
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time involves a more efficient crow evacuation, with less force being used and corresponding to a safer escape for the agents. In Fig. 7, we also report the difference of the statistics involving the people who are still unsafe for SFM and miSFM. We can see that miSFM leads to a faster reduction of the number of unsafe people than SFM.
Scenario 2. In this scenario, as shown in Fig. 4, we demonstrate a complex environment for evacuation in which there are many rooms and exits. The results show that the simulation is effective for a complex environment specified at user's discretion. The simulation also exhibits the arching phenomenon at each exit, showing the model and platform allow for a scalable simulation, with consistent results.
4.2. Discussion Scenario 3. In this scenario, we compare the performance of the miSFM model with the original SFM from the perspective of simulation time and the used force by each agent in the crowd. The parameter of the SFM is set by default and constant, while in our miSFM, the parameter is self-adapting (This is shown in Figs. 5 and 6 and Table 1). We can observe that a smaller escape
To illustrate the validity of our miSFM, we have performed a serial of experiments, from which we come up with the following observations:
4.2.1. The changes of the MI have relation with the parameter in SFM To discover the potential relationship between the MI and R, we fix the other parameter, compute the MI for different R, and observe the change of the MI with the less simulation time. In such a way, we can monitor the MI and then adjust R for a better simulation effect. To fully improve the simulation result, we carry out 3 groups of experiments with a different constant V 0 , it is the desired velocity for each person in SFM, and then change the value of R. The following is the details. As shown in Fig. 9, we can observe that the occurrence of the least escape time corresponds with the inflexion of the MI value. As a result, the proposed approach can monitor the sudden change of the MI value. That is to say, when the MI value is not stable, we can gain the parameter R as illustrated in Fig. 7, the lower R may lead to the slope of the curve. It is similar that we also analyze the parameter V 0 , and at this time, the variable is not R but V 0 , and we carry out 3 groups of experiments with the constant value for parameter V max , which shows the limit of the velocity in SFM to prevent the overload increment of the instant velocity. Fig. 10 shows the correlation between V 0 and MI values when the least simulation time appeared. W can observe that the
1000 200persons 500persons 1000persons
900 800
Unsafe People
700 600 500 400 300 200 100 0
0
30
60
90
120
150
180
Time
Fig. 8. The statistics of the people who are still in the dangerous place with different scales respectively. 0.9
Iv Idir Iden
0.85 0.8 0.75
0.7
0.7
MI
0.75
0.65
0.8 0.75 0.7
0.65
0.65
0.6
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0.55
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0.45 0.4
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0.4 78 10
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70
Iv Idir Iden
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MI
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MI
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Fig. 9. The relation between R and MI (Left column). In this situation, V 0 ¼ 5. When R ¼ 10, it has the least evacuation time and inflexion appeared in the curve of the three MI value, and after the inflexion, the MI value become stable. (Middle column) V 0 ¼ 8, when R ¼ 10, it has the best effect. (Right column) V 0 ¼ 10, when R ¼ 15, it has the best effect.
Please cite this article as: M. Xu, et al., miSFM: On combination of Mutual Information and Social Force Model towards simulating crowd evacuation, Neurocomputing (2015), http://dx.doi.org/10.1016/j.neucom.2015.05.074i
M. Xu et al. / Neurocomputing ∎ (∎∎∎∎) ∎∎∎–∎∎∎
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0.65 Iv
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Fig. 10. The relation between V 0 and one of MI value Iv (Left column). In this situation, V max ¼ 5. When V 0 ¼ 20, it has the less evacuation time and minimum value in the curve of the I v . (Middle column) V max ¼ 10, when V 0 ¼ 25, it has the best effect. (Right column) V max ¼ 15, when V 0 ¼ 50, it has the least simulation time.
Fig. 11. Different scales of the persons (Top) 200, persons (Middle) 500, persons (Bottom) 1000 persons.
Please cite this article as: M. Xu, et al., miSFM: On combination of Mutual Information and Social Force Model towards simulating crowd evacuation, Neurocomputing (2015), http://dx.doi.org/10.1016/j.neucom.2015.05.074i
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smallest value of I v corresponds to the lower evacuation time. Therefore, the adjustment of the parameter V 0 can be done by monitoring value I v . It is worth mentioning that there are also other parameters which are sensitive to some MI values. Such parameters would also make contribution to improving the miSFM model. 4.2.2. The different scales of the evacuation We run a series of experiments with different scales of agents number. The results of these experiments show that our model is available to diverse numbers of the persons. As shown in Fig. 8, this result illustrates that the different scales did not cause a larger variation of the escape rate. In Fig. 11, we present the different simulations.
5. Conclusion and future work In this paper we present a novel approach for crowd evacuation using the miSFM model. Our approach is designed by information theory with the well-established social force model to improve the accuracy and robustness of the proposed crowd behavior algorithm. The main idea behind this approach is to automatically adjust the parameter of SFM with the MI's feedback to achieve a better effect for evacuation. It is also convenient that the environment is user-specified. We have shown that our method is effective scalable and flexible for different crowd scales and diverse environments. Certain limitations still exist in the current work. The discovery of the correlation between the mutual information and the SFM parameter can be further extended. Also, the utilization of the MI can be further investigated, e.g. by considering other properties beyond velocity, direction and density. It would be also beneficial to improve the environment set-up to support irregular shape of the rooms, halls, and so on.
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Ming-Liang Xu is an associate professor in the School of Information Engineering of Zhengzhou University, China. His research interests include computer graphics and computer vision. Xu got his Ph.D. degree in computer science and technology from the State Key Lab of CAD&CG at Zhejiang University.
Acknowledgments This work was in part supported by the National Natural Science Foundation of China (NSFC) (Grant Nos. 61202207 and 61472370), the China Post-doctoral Science Foundation (Grant nos. 2012M520067 and 2013T60706), the National Key Technology Research and Development Program of China (Grant no. 2013BAH23F01), and the Research Fund for the Doctoral Program of Higher Education of China (Grant no. 20124101120005). We also would like to thank the anonymous reviewers for their constructive comments.
Yunpeng Wu received his Bachelor of Engineering in Computer Science and Technology from the Zhengzhou University, Zhengzhou, in 2010. He is currently a Ph.D. candidate in the Department of Information Engineering at Zhengzhou University. His research interests include machine learning and crowd simulation.
References [1] M.-L. Xu, et al., Crowd simulation and its applications: recent advances, J. Comput. Sci. Technol. 29 (5) (2014) 799–811. [2] J. Bohannon, Directing the herd: crowds and the science of evacuation, Science 310 (5746) (2005) 219. [3] D. Helbing, et al., Simulation of pedestrian crowds in normal and evacuation situations, Pedestr. Evacuat. Dyn. 21 (2002) 21–58. [4] N. Pelechano, N.I. Badler, Modeling crowd and trained leader behavior during building evacuation, Comput. Graph. Appl. IEEE 26 (6) (2006) 80–86. [5] Armel Ulrich Kemloh Wagoum, M. Chraibi, Efficient and validated simulation of crowds for an evacuation assistant, Comput. Animat. Virtual Worlds 23 (2012) 3–15. [6] A. Wagoum, A. Seyfried, S. Holl, Modelling dynamic route choice of pedestrians to assess the criticality of building evacuation, Adv. Complex Syst. 15 (2012) 1250029. [7] A. Borrmann, et al., Bidirectional coupling of macroscopic and microscopic pedestrian evacuation models, Saf. Sci. 50 (2012) 1695–1703. [8] S.J. Guy, et al., Least-effort trajectories lead to emergent crowd behaviors, Phys. Rev. E 85 (1) (2012) 016110.
Pei Lv is an assistant professor in the School of Information Engineering of Zhengzhou University, China. His research interests include character animation, crowd simulation and tracking. He received his Ph. D in 2013 from the State Key Lab of CAD&CG, Zhejiang University, China. Before that, he received his B.S. degree in computer science, from Zhengzhou University, Zhengzhou, China, in 2008.
Please cite this article as: M. Xu, et al., miSFM: On combination of Mutual Information and Social Force Model towards simulating crowd evacuation, Neurocomputing (2015), http://dx.doi.org/10.1016/j.neucom.2015.05.074i
M. Xu et al. / Neurocomputing ∎ (∎∎∎∎) ∎∎∎–∎∎∎ Hao Jiang is an assistant professor with Beijing Key Lab of Mobile Computing and Pervasive Devices, Institute of Computing Technology, Chinese Academy of Sciences, China. He received the Ph.D. degree in computer science from Chinese Academy of Sciences in 2011. His research interests include crowd simulation, virtual reality and intelligent human–computer interaction. He is a member of CCF, IEEE and ACM.
9 Yangdong Ye is currently a professor in the School of Information Engineering at Zhengzhou University, China. His research interests include database systems, machine learning, and intelligent systems. Ye has a PhD in computer science from China Academy of Railway Science.
Mingxuan Luo received his Bachelor of Engineering in Software Engineering from the Northwestern Polytechnical University, Xi'an, in 2013. He is currently a Master candidate in the Department of Information Engineering at Zhengzhou University. His research interests include computer graphics and traffic simulation.
Please cite this article as: M. Xu, et al., miSFM: On combination of Mutual Information and Social Force Model towards simulating crowd evacuation, Neurocomputing (2015), http://dx.doi.org/10.1016/j.neucom.2015.05.074i