adaptive behavioral modeling for crowd simulations

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Adaptive Behavioral Modeling for Crowd

Simulations

Abstract

Behavioral modeling for crowd simulations should consider a number of factors

effecting on agents, including environment. In this study, we design an adaptive behav-

ioral model for a dynamic virtual environment. We model the dynamic environment

with behavior maps which are constructed with information theory quantities and sta-

tistical formulations. These maps are capable of capturing the dynamic nature of the

environment by adaptively changing temporally and spatially. Subsequent to building

this model, agents responses to these maps are represented with a set of formulations.

In our test studies, we have observed that our model successfully produces realistic and

diverse behaviors by incorporating effects of the environment.

Keywords: crowd simulation, information theory, behavioral modeling

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1 Introduction

Crowd is a fundamental element in our real environment, thus it also constitutes a crit-

ical component in many virtual environment applications. In order to improve a virtual

environments realism, crowds must be simulated believable in terms of their appearance

and behavior. Recent advances in graphics hardware addresses the issue of photo-realistic

rendering of crowds. However, realistic behavior of agents in crowd simulations is still a

challenging problem due to the number of factors effecting agents behavior, hence those

factors are not easy to represent mathematically. Most of the crowd simulation systems use

a set of rules and scripts to model human behavior, and when used alone, this approach has

limits to model the complex nature of human behavior [1]. Therefore, recent studies are

generally employing agent-based behavioral modeling methods. In these methods; an agent

responds to other agents and events using static and predefined behavior rules, whatever the

environment conditions are. However, dynamic conditions which are inherent in the envi-

ronment greatly effect an agents behavior and existing models are not capable of adapting

themselves to these conditions.

Apart from the physical properties, a built environment also has psychological effects

on people [2]. Physical properties of built environments and physical properties of agents

are already successfully handled by collision avoidance algorithms, predefined rules and

predefined roadmaps in most of the crowd simulations. And when dealing with human-

environment interactions, one should have a model that can predict the environmental con-

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ditions under which humans behave in a certain manner [3]. Therefore; we need an adaptive

simulation which considers the psychological effects of the environment when modeling the

behavior of agents.

To successfully design an adaptive crowd simulation for a dynamic virtual environment,

we first build an analytical model of a crowded environment and define how agents act

according to that model.

The crowd itself can be considered as one of the most prominent factor of an environ-

ment effecting agents in a simulation [4]. In order to model the effects of the crowd,

we need methods to represent properties and activities of elements of a crowded en-

vironment such as built environment and agents. The resulting quantification should

provide a measure to evaluate the activities of the crowd and should be utilized to rep-

resent the effects of the crowd on individual agents. A good model has to be adaptive

to changes in the dynamics of the crowd both spatially and temporally.

In agent-based behavioral methods, agents are assigned some attributes to determine

their behaviors; hence, their response to certain events and other agents are altered.

However, as Shoda stated in [5], personality structure can be static but its behavioral

output changes greatly under specific circumstances. An agent should behave differ-

ently under different environmental conditions to fulfill this statement.

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Our methods to build an analytical model of the environment borrow ideas from behav-

ioral mapping techniques used in psychology research. These techniques involve place-

centered maps, which keep track of behavior of individuals within a specific space and time.

These maps display how and when a place is being used [6]. In our model, we utilize

the notion of place-centered maps in simulations and propose behavior maps. A behavior

map is constructed by considering both spatial and temporal dynamics of agents in a crowd

simulation. It conveys information on probabilistic and statistical properties of agents ac-

tivities. Information theory quantities, i.e. information entropy and Kullback-Leibler diver-

gence, and statistical formulations are used to produce behavior maps. As behavior maps

are updated spatially and temporally; agents adaptively respond to their environment with

the contribution of these maps. This contribution is represented with numerical entities and

agents responses are calculated with a set of formulations.

The rest of the paper is organized as follows: in Section 2, we review the related literature.

In Section 3, we introduce different behavior maps. In Section 4, responses of agents to

behavior maps are covered. Section 5 discusses the results obtained with the model. To

conclude, final remarks are made at the conclusion section.

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2 Related Work

An overall idea of the challenges and improvements in the field can be obtained in [7]. There

are several behavioral models proposed in the literature and a survey from Kasap et.al.[8]

covers most of these studies. There have been many studies on agent-based crowd models

to create human-like behaviors. Seminal works of Reynolds used behavioral models con-

sidering local rules [9] and create emergent flocking [10] behaviors. There is considerable

work on agent-based simulation systems incorporating psychological models and sociolog-

ical factors. In [11], Luo et.al. model social group and crowd related behaviors. Their main

focus is a layered framework to reflect the natural pattern of human-like decision making

process. Rymill et.al.[12] tried to improve the quality of agent behavior by adding theories

from psychology. In their work, they tried to produce more realistic collision avoidance

responses. Musse et.al. developed virtual human agents with intentions, beliefs, knowledge

and perception to create a realistic crowd behavior [13]. In [1], Pelechano et.al. assigned

psychological roles and communication skills to agents to produce diverse and realistic be-

haviors. In a more recent work, Pelechano et.al. [14] created an improved model by using

psychological and geometrical rules with a social and physical forces model. In [15] Hu

proposed an adaptive crowd behavior simulation, where he defines a static behavior context

layer. When the behavior context is altered with a predefined event, the new context adap-

tively inhibits certain behavior in agents. However, this scheme is not suitable for dynamic

environments. There are studies which model the virtual environment as maps to guide

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We need to have pmfs regarding to the activities in the scene. The first pmf, Pv

, defines

the velocity direction distribution. Consider an agent with normalized velocity v, then this

vector is added as a sample to one of the n bins of Pv

, where the value of n effects quan-

tization resolution. The second pmf, Pv, defines the velocity magnitude distribution. As

agents speed is in a predefined range, this range is quantized into m categories and speed

of an agent is added as a sample to one of these categories. We merge these two pmfs into a

single pmf, Pv, with a user defined constant , which distributes importance to direction or

speed distributions, as:

Pv = Pv + (1 )Pv (2)

As Pv is taking samples over a period of time, a Gaussian shaped filter is applied to control

the importance given to temporally cumulated distributions. Let t1 and t2 be two time steps

where t2 t1 = nt and n N, temporal filter is applied as;

P t1t2v = 0Pt2v + 1P

t2tv + . . . + nP

t2ntv (3)

n =1

2e(x)2

c2 , = 0 (4)

where, n is defined as historical depth which defines the maximum age to consider,

where age means the time passed from the moment the distribution have occurred. With t

defining the time interval between two adjacent frames,

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3.1.1 Entropy Map

Entropy measures the uncertainty of a random variable. If we interpret activities of an

agent as the random variable, entropy values reflect behavioral patterns of the crowd. En-

tropy values denote where agents move either more independently or where they move in a

pattern. Locations with smaller entropy values mark where agents move with similar veloc-

ities. Conversely, locations with higher entropy values represent greater disorder in agents

behavior. To build the entropy map, E, we begin by considering a random variable, Xi,j (i,j

indicating location on E), drawn according to pmf(P(tnt)t

v )i,j. Then, E can be defined

as;

Et = {H(Xi,j) ; 0 i < w, 0 j < h} (5)

, where H(Xi,j) is the entropy ofXi,j [22].

3.1.2 Expectance Map

Probability distribution of activities on a scene gives an idea on the type of activities that is

likely to occur at specific locations. This distribution is defined by pmf Pv in our calcula-

tions. In order to quantize the expectance of the current activities on the scene, we compare

the current probability distribution on the scene with Pv. We employ Kullback-Leibler diver-

gence (D, Equation 1) to compute the difference between two probability distributions. Itti

et.al. [24] used KL divergence to discover surprising events in video. They employed a prin-

cipled approach to prove that KL is a powerful measure to represent surprise. We postulate

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that KL calculations can be represented as behavior maps, so called expectance maps. Let

P tv define the current (at time t) probability distribution of the scene, and P(tnt)(tt)

v

define the cumulative (between time steps (t nt),(t t)) distribution of activities,

expectance map KL is defined as;

KLt = {(D(P (tnt)(tt)v

P tv ))i,j ; 0 i < w, 0 j < h} (6)

A high KL value represents that current activities taking place at that location can be re-

garded as surprising, while in areas with lower KL values, the current status of the crowd is

as expected.

3.2 Density Map

In addition to the proposed information theory based maps, a map called density map, F,

is also integrated into our behavioral simulation model. This map indicates how crowded

a specific location is. In order to produce a measure that is less prune to noise, a temporal

filter is applied on F.

Ft = {f (tnt)(tt)i,j ; 0 i < w, 0 j < h} (7)

where f is a function giving the number of agents on location i, j between time steps (t

nt) and (t t) with temporal filter applied on count values in the same manner as

Equation 3.

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4 Response to Behavior Maps

In our crowd simulation engine, agents have internal properties to determine their behav-

ior. Internal properties consist of two elements; behavioral constants and behavioral state.

Behavioral constants can be regarded as personality attributes of an agent and behavioral

state determines at what level behavioral constants effect agents behavior. Throughout the

simulation, behavioral state is altered adaptively by behavior maps. In Figure 1, the overall

structure of our model can be seen. Stages in the figure are listed as: 1)Activities of agents

are analyzed between time t0 and tn to produce behavior maps. 2)Each agent is mapped

to a specific behavior map cell. 3)Each agent has predefined roadmap, internal properties

and goals. 4)Considering all these factors, an agent modifies its internal properties and

orientation. In this step, ais properties are modified in order to respond to the behavior

map. 5)Agents modified properties and preferred velocity is fed into the navigation system.

6)Navigation system considers predefined rules and agents properties to produce a collision

free path.

To cover diverse agent behaviors we incorporate the following methods into our simu-

lation model: 1) Composite agents: A composite agent is a special agent equipped with

a proxy agent, ri, to model a number of emergent behaviors realistically [25]. A proxy

agent is a virtual agent, which is visible to all agents in the simulation except its parent ai.

ri moves according to ais choices and ai displays particular behaviors by controlling ri.

2)Preferred velocity: In crowd simulations, agents have an initial state and a desired final

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state. Each agent seek for a collision-free path to its destination [7]. In order to reach their

goal as quick as possible, agents prefer to move in a pattern that brings them directly to their

goal or subgoals. A preferred velocity, vp, of an agent ai is the optimal velocity that would

bring the agent to its goal. 3) Safety factor: Safety factor is the range an agent considers

while calculating possible future collisions. A high value means, the agent takes more of the

possible collisions into account and behaves more careful by avoiding them. On the other

hand, with a lower value the agent becomes reckless and constitutes a higher possibility of

making collisions. In Figure 3-a, these methods are illustrated briefly.

Definition of an agent has to include internal properties, in addition to the physical prop-

erties. Definition of an agent ai is extended as:

ai

={

type, u, v, vp

, d, s, ri, ,

f1,..,f

n, : v

p R2; f

n, , d , s

[0, 1]

}(8)

These parameters are: 1) type : Indicates whether an agent is composite agent, proxy agent

or a normal agent. A composite agent both has a proxy agent ri and personal attributes.

A proxy agent doesnt carry any property, its behavior is dependent solely on its parent.

A normal agent only carries personal properties. 2) vp : Indicates the velocity an agent

prefers to move. 3) ri: Indicates the proxy agent associated with the current agent (available

for composite agents). 4) d : Distance to set between ri[u] and u (available for composite

agents). The longer the distance, the further ai can proceed with suffering less collisions.

5) s : Size of the area ri occupies (available for composite agents). The larger the area,

the easier ai can move. 6) : Indicates the range in which an agent considers possible

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collisions, modifies safety factor. 7) fn : Indicates a behavior constant. Each constant can

be utilized to mimic certain personality attributes. They are static properties assigned to ai

at the beginning of the simulation. fn values are randomly distributed over agents and this

distribution is a method for creating behavioral variety. 8) : Indicates the behavioral state

of an agent.

Response to entropy map Entropy map displays how predictable crowd moves in a par-

ticular location. The notion of predictability can be utilized to modify behaviors of agents.

An agent, ais, response to entropy maps can be formulated as;

ai[] = kEi,j ; f

0 = (1 f0) ; f

1 = f1

ai[vp] =(vop + f

0vb)f

0m0 (9)

ai[] = f

10

where k is a constant to normalize values, 0 is the default value for and vop is the optimal

velocity leading to agents goal. The modified behavioral constants are utilized to modify

preferred velocity or modify value. vps direction is calculated with f

0 and vb, and its

magnitude is calculated with f

0 and the default speed m0. vb can be calculated as a vector

leading to lower entropy zones found as a result of a local search in an agents location or

can be a random vector. In the former case, agents tend to move to locations with lower

entropy values. Figure 3-b displays how values modify agents internal properties.

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Response to expectance map An expectance map indicates the level of surprise in a

specific location. Agents give different responses to unexpected events, which can be for-

mulated as;

ai[] = kK Li,j ; f

0 = f0; f

1 = (1 f0)

ai[vp] =(vop + f

1vb)f

0m0 (10)

ai[d] = f

0d0 ; ai[s] = f

0s0; ai[] = 1/0

In this formulation, f

0 value modifies the proxy agent ri, as f

0 gets higher, d and s values

are amplified. f

0 value also increases the speed of an agent in areas with high KL value.

f

1 value, on the other hand, amplifies the deviation from optimal velocity vop. The final

response is the change in value that is inversely proportional to values.

Response to density map While some agents tend to avoid crowded areas, others dont.

This behavioral difference is related to the behavioral constant f0. An agents responses can

be described with the same formulation in Equation 10 but with different f0 values.

5 Results & Test Cases

We tested our methods through a number of scenarios. Our test environment is a modified

version of multi-agent simulation system called RVO proposed in [26]. We implemented

our adaptive behavioral model on top of this system. Our approach produces realistic and

diverse crowd behavior. Figure 4 displays snapshots from test scenarios. Accompanying

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videos presents comparative results of our simulation system performing in real-time on a

system with Intel QuadCore 2.8 GHz and Nvidia GeForce GTX-280.

In order to test our behavioral model, we create a simulation containing 200 agents. We

initialize the crowd by creating three groups of agents with specific behavioral constants.

First of these groups constitutes of 20 agents with high f0 and low f1 values which can be

considered either as aggressive agents. Second of these groups contain 20 agents with low

f0 and high f1 values which can be considered as calm agents. The last group consist of

160 standard agents which do not display any adaptive behavior. As we run our simulation

with these agents, their activities are cumulated and analyzed either in one of the behavior

maps or in a combination of them, i.e. entropy, expectance or density maps. These maps are

accessed by all the non-standard agents and they modify their behavior adaptively by using

the associated behavior map value. To test this adaptive process, we perform three scenarios,

where responses to each behavior map is observed distinctively. In order to observe each

maps effects separately, in each scenario, we use a single behavior map.

To observe responses given to entropy maps, we adopt a scenario where specific agents

pass through other agents in a piazza and a pavement to reach their goal. As implied by

the formulation of entropy maps, a piazza produces higher entropy values and as agents

behave in an ordered manner, pavements produce lower entropy values. Confident agents

move directly to their goal as their preferred velocity is not effected from higher values.

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Each one of the three behaviour map methods is generating satisfactory results in differ-

ent setting. To address the general case for a dynamic virtual environment we combined

all three models into a single one. We calculate a weighted average response by adjusting

the contribution of each behavior map to agents responses. The resulting simulation out-

performed sngle behavior map simulations in terms of variability and realism. For a visual

comparison between each method, please refer to the accompanying video.

6 Conclusion

In this paper, we proposed an adaptive behavioral model for crowd simulations. Our model

incorporates the dynamics of a virtual environment through building an analytical model of

crowds activities and formulates agents responses.

We ran our model over a number of scenarios and observed that agents behaviors are

adaptively altered under certain environmental conditions. Results show that our methods

add complexity and diversity in agents behaviors, thus improve realism. These methods can

be integrated into either scripted behavioral models to increase their behavioral variation or

autonomous agent systems to improve their realism. Presented methods will provide life-

like and evolving environments for games, industrial crowd simulations,i.e. emergency,

urban planning and can reduce production times for movie pre-visualizations.

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Our model performed in real-time with several hundreds of agents. As a future work,

we will improve the scalibilty of our model with parallel computing techniques. Another

future work is introducing static preset maps into our model which will enable a designer to

encode environmental factors.

References

[1] N. Pelechano, K. OBrien, B. Silverman, and N. Badler. Crowd simulation incorpo-

rating agent psychological models, roles and communication. In First International

Workshop on Crowd Simulation, 2005.

[2] Tommy Grling and Reginald G.Golledge, editors. Behavior and environment : psy-

chological and geographical approaches. North-Holland.

[3] R. De Young. Environmental psychology. Encyclopedia of environmental science,

Kluwer Academic Publishers, Hingham, MA, USA, 1999.

[4] P.A. Bell. Environmental Psychology. Wadsworth Pub Co, 2001.

[5] Yuichi Shoda. Computational modeling of personality as a dynamical system. Hand-

book of Research Methods in Personality Psychology, pages 633 652, 2007.

[6] R. Sommer and B. Sommer. A Practical Guide To Behavioral Research: Tools and

Technique. Oxford University Press, 5 edition, 2002.

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[7] Daniel Thalmann and Soraia Raupp Musse. Crowd Simulation. Springer, 2007.

[8] Z. Kasap and N. Magnenat-Thalmann. Intelligent Virtual Humans with Autonomy and

Personality : State-of-the-Art, pages 4384. Studies in Computational Intelligence,

Springer, 2008.

[9] C.W. Reynolds. Steering behaviors for autonomous characters. In Game Developers

Conference, 1999.

[10] C.W. Reynolds. Flocks, herds and schools: A distributed behavioral model. In Pro-

ceedings of the 14th annual conference on Computer graphics and interactive tech-

niques, pages 2534, 1987.

[11] Linbo Luo, Suiping Zhou, Wentong Cai, Malcolm Yoke Hean Low, Feng Tian, Yong-

wei Wang, Xian Xiao, and Dan Chen. Agent-based human behavior modeling for

crowd simulation. Comput. Animat. Virtual Worlds, 19(3-4):271281, 2008.

[12] S.J. Rymill and N.A. Dodgson. A Psychologically-Based Simulation of Human Be-

haviour. In Theory and Practice of Computer Graphics, pages 3542, 2005.

[13] S. R. Musse and D. Thalmann. Hierarchical model for real time simulation of virtual

human crowds. IEEE Transactions on Visualization and Computer Graphics, 7:152

164, 2001.

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[14] N. Pelechano, J. M. Allbeck, and N. I. Badler. Controlling individual agents in high-

density crowd simulation. In Proceedings of the 2007 ACM SIGGRAPH/Eurographics

symposium on Computer animation, pages 99108. Eurographics Association, 2007.

[15] X. Hu. Context-Dependent Adaptability in Crowd Behavior Simulation. In Informa-

tion Reuse and Integration, 2006 IEEE International Conference on, pages 214219,

2006.

[16] W. Shao and D. Terzopoulos. Autonomous pedestrians. Graphical Models, 69(5-

6):246274, 2007.

[17] R. Gayle, A. Sud, E. Andersen, S.J. Guy, M.C. Lin, and D. Manocha. Interactive

Navigation of Heterogeneous Agents Using Adaptive Roadmaps. Visualization and

Computer Graphics, IEEE Transactions on, 15(1):3448, 2009.

[18] M. Sung, M. Gleicher, and S. Chenney. Scalable behaviors for crowd simulation. In

Computer Graphics Forum, volume 23, pages 519528, 2004.

[19] C. Dornhege and A. Kleiner. Behavior maps for online planning of obstacle negotiation

and climbing on rough terrain. In Intelligent Robots and Systems, 2007. IROS 2007.

IEEE/RSJ International Conference on, pages 30053011, 2007.

[20] J. Berclaz, F. Fleuret, and P. Fua. Multi-Camera Tracking and Atypical Motion Detec-

tion with Behavioral Maps. In proceedings of the European Conference on Computer

Vision. Springer.

20


21/25

[21] Pere-Pau Vazquez, Miquel Feixas, Mateu Sbert, and Wolfgang Heidrich. Viewpoint

selection using viewpoint entropy. In Proceedings of the Vision Modeling and Visual-

ization Conference 2001, pages 273280. Aka GmbH, 2001.

[22] C. E. Shannon. A mathematical theory of communication. Bell Systems Technical

Journal, 27:623656, 1948.

[23] Solomon Kullback. Information Theory and Statistics (Dover Books on Mathematics).

Dover Publications, 1997.

[24] Laurent Itti and Pierre Baldi. A principled approach to detecting surprising events

in video. In IEEE Computer Society Conference on Computer Vision and Pattern

Recognition, pages 631637. IEEE Computer Society, 2005.

[25] Yeh Hengchin, Curtis Sean, Patil Sachin, van den Berg Jur, Manocha Dinesh, and Lin

Ming. Composite agents. In Symposium on Computer Animation - SCA08, 2008.

[26] J. van den Berg, M. Lin, and D. Manocha. Reciprocal Velocity Obstacles for real-time

multi-agent navigation. In Robotics and Automation, 2008., pages 19281935, 2008.

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ai

Agents, A Behavior Map, B

t0 tn

Agent, ai

Goals &

Roadmaps

Behavior Map

Values

Navigation

System

Internal

Properties

1

2

3

4

5

6

Modify

Internal Properties & PreeredVelocity

with Behavior Map Values

:(u, v)current

ai :(u, v)new

Figure 1: Overall structure of our model. (Details given in Section 4)

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Agents, A

CumulativeProbabilistic Model Entropy Map, E

Expectance Map, KL

+ ..... +

H(x)

D(x)

Current Velocity

Distribution

Density Map, F

Density

Distribution

1

2

3

4

5

6

P P

n 0

Figure 2: Behavior map construction. 1) List of agents is fed to the system. 2) Activities

of the crowd are mapped to the underlying grid to form the current distribution function

of the activities of the crowd 3) Older distributions are merged with a temporal filter. 4)

Entropy map of the scene is built by calculations on merged pmfs from (t n to t). 5)

Expectance map is formed by calculating KL divergence between the probabilistic model

and the current distribution. 6) Density map is formed by calculating the current densities

on a specific cell.23


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Figure 4: Screenshots from our test environment. Each column represents successive time

steps. Each row displays responses to entropy, expectance and density map consecutively.

Agents behave distinctively in response to each of these maps. Note that, aggressive agents

(red) and calm agents (blue) behave accordingly to our model.

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adaptive behavioral modeling for crowd simulations

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