Brief Introduction on Computational Modeling of Crowd Behavior
Generally speaking, based to the subjectiveness and objectiveness of methodology, there are two major approaches for computational modeling of crowd behavior. From the objective perspective, there are physics-based approach, which regard individuals in the crowd as physical particles corresponding to some physics laws; and from the subjective perspective, there are agent-based approach, which model the individuals in the crowd as autonomous agents who would do decision making and interaction according to some rules.
I, Physics-based approach
The crowd is treated as physical fluid and particles, thus a lot of analytical methods from statistical mechanics and thermodynamics are introduced. Here are some typical research works from this kind of approach.
- S. Ali and M. Shah. Floor fields for tracking in high density crowd scenes. In Proc. ECCV, 2008.
- R. Hughes. The flow of human crowds. Annual Review of Fluid Mechanics, 2003.
- A. Treuille, S. Cooper, and Z. Popovi´c. Continuum crowds. In ACM SIGGRAPH, 2006.
II, Agent-based modeling approach
Different from the physics-based approach which assumes individuals in the crowd as non-thinking physical particles, the agent_based modeling considers the individuals in the crowd as autonomous agents which actively sense the environment and make decision according to some predefined rules. This kind of approach is also close related to game theory, complex systems, emergence, and Monte Carlo simulations. Here is a nice survey on agent_based modeling,
- E. Bonabeau. Agent_based modeling: Methods and techniques for simulating human systems. Proc. National Academy of Sciences of the United States of America, 2002.
Recently there is an online free course Model Thinking which lectured by Prof. Scott Pages from University of Michigan. I have introduced Prof. Scott’s research works on complex systems and the nice books Complexity and Diversity, the Dfference and Complex Adaptive Systems written by him in this weblog (I finish reading these three books with great inspiration). Personally I enjoy this course quite a lot, since it not only specifically introduces the classical agent_based models used in economics, social sciences, but also generally highlight how to formulate some real-life problems from scratches using the framework of model thinking. And each lectures in the course are shorted into video clips with 15 min length (I know you would easily distract your attentions when the lecture last too long) and the contents are easy to follow and not technically intense. I sincerely recommend it to you all! Besides, this course discusses the meaning of model in real life and theoretic scientific research, on which I am meditating a lot during these time, later on I would write a article on this.
In recent years there are gradually a lot of agent_based models proposed for modeling the crowd. Here I outline two famous agent-based models in crowd behavior analysis: the social-force model proposed by Dirk Helbing and the Self-propelled particles (SPP) model proposed by Tamas Vicsek.
Social-force model is proposed to formulate the behavioral process of autonomous agents, from perceiving the environments and making decision. The general framework of this process is shown in Figure 1. Furthermore, social-force model can be used to simulate the crowd panic as shown in Figure 2.
Here are the two seminal papers on social-force model:
- Helbing, Dirk; Molnár Péter . Social force model for pedestrian dynamics.Physical Review E 51, 1995
- D. Helbing, I. Farkas, and T. Vicsek. Simulating dynamical features of escape panic. Nature, 2000
And you could find a lot of resource on social-force model in the following two pages maintained by Prof. Dirk Helbing and his research teams on crowd behavior analysis:
In computer vision community, the social force model is introduced for multi-target tracking , abnormality detection , and analysis of pedestrian action and mutual interaction 
-  R. Mehran, A. Oyama, and M. Shah. Abnormal crowd behavior detection using social force model. In Proc.CVPR, 2009.
-  S. Pellegrini, A. Ess, K. Schindler, and L. Van Gool. You’ll never walk alone: Modeling social behavior for multi-target tracking. In Proc. ICCV, 2010.
-  P. Scovanner and M. Tappen. Learning pedestrian dynamics from the real world. In Proc. ICCV, 2009.
Self-propelled particles (SPP) model
SPP model is proposed to model the interaction of individual in the crowd the and the formation of collective motion.
The model itself is very simple, at each time step, the individuals would coordinate its velocity directions with its neighbor individuals. When the coordination level is high, there is collective motion of the crowd emerging. as shown in Figure 3.
Here is the seminal paper on SPP.
Vicsek, T.; Czirok, A.; Ben-Jacob, E.; Cohen, I. & Shochet, O. Novel type of phase transition in a system of self-driven particles. Physical review letters, 1995.
In this paper, Vicsek further discussed the influence of noise on the coordination level and the phenomena of phase transition, that is, how the phase of random movements of individuals is transformed into the phase of collective motion of individuals. It is related some important topics, such as self-organization and emergence.
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