## 3 Related Works
### Crowd Monitoring  
Large events may be seen as a \"concentrate of urbanity\". The number of participants at top world events can reach more than a million people and issues such as mobility and physical security are of paramount importance to guarantee the success of the event and to avoid serious problems. Planning the pedestrian flows and capacity plays a key role to prevent major troubles. Various techniques of estimation are used to plan pedestrian flows and capacities [10]. The required level of security can be achieved combining a precise study of the arrangement of the natural and artificial physical featuresof the event (_i.e._, the topography of the event), for instance using a simulator, and real-time monitoring of the crowd [11]. Common sense suggests that the first rule should be to avoid as much as possible architectural barriers on the event site (such as obstacles, bottlenecks, hairpin turn, _etc._), with particular attention to the emergency routes. Crowd simulators may help to detect flows in the topography of the event otherwise difficult to notice. Many types of simulators exist. Depending on the level of the detail that they take into account, simulators may be based on three different modeling approaches: microscopic, mesoscopic, and macroscopic. Macroscopic and mesoscopic approaches remove certain complexities from the equation to lower computational costs and speed up computations. On the contrary, microscopic approaches try to provide a very detailed simulation to the individuals' behavior and, even, psychological phenomena that may link each other. An example of a macroscopic crowd simulator is represented by the use of the cellular automaton approach [12]. A cellular automaton represents the scene using a grid of cells that can be either occupied by one individual or they can be empty. [PERSON] _et al._[12] used this approach by defining a \"static\" floor field to direct the general movement towards an area of the grid and a \"dynamic\" floor field left by the pedestrians. The dynamic field was used to simulate the \"herding\" phenomenon [13] in which, during evacuation situations, individuals follow others individuals before them. They found that this type of simulation can recreate real pedestrian's behavior but the grid overlay may generate lockups. Due to the abstraction and restriction of movement to a grid, the computational load is low. Example of the mesoscopic approach may be found in the works of [PERSON] _et al._ [PERSON] used \"hydrodynamics\" to describe the crowd's movement [14]. Then, in later work, he investigated social forces as a modeling approach for pedestrian crowd simulation and its use in normal and evacuation situations [15; 16]. Essentially, considering social forces means taking into account that all individuals want to reach their destination as comfortable as possible and other social factors such as: the individuals' preference to keep a certain distance from one another (e.g., to avoid collision but also to respect the private sphere), the friends preference to move as a group, _etc._ Another interesting mesoscopic approach is described by the work of [PERSON] _et al._[PERSON] _et al._ [17]. They presented a hybrid system consisting of a single-agent and fluid dynamics. In their algorithm, they overlaid a grid on the simulation scene and they used a crowd flow mechanism (called \"unilateral incompressibility constraint\") that calculated the flow in the grid modeling the crowd as a combination of compressible and incompressible fluid. Solving the flow for all cells of the grid provided a flow field that was used to model the velocity vector of the agents in the direction allowed by the system. This approach permitted to avoid collisions and to make the individual agents respect a minimal distance from each other. This simulation approach proved to be very performing, running a simulation with one million agents at three frames per second on an Intel Core i7 standard home computer.