Large uncontrollable crowds have the potential to cause serious injuries, and even death.

1. Large uncontrollable crowds have the potential to cause serious injuries, and even death. In a disaster, escape paths can be blocked by frightened dense crowds of people trying to push their way out. This type of behavior has been shown to cause injuries and death. During competitions where people must run closely together, someone can trip and potentially get trampled. A way to prevent these disasters from happening is to set up cameras where dense crowds form and monitor the area. The system would count the number of people passing through the vision of the camera and calculate the crowd’s speed, pressure, and other useful data that can be used to notify a security personnel that a negative event is about to occur. Problem The goal of this research is to find a way to calculate the number of people in a dense crowd with only its flow field. Below are a number of methods that were tested to count people in crowds. Method 1: Number of local maxima of flow field. To explain why this is useful, an example is given; imagine watching a fish swimming in water. The water molecules around the fish will be moving slightly slower than the rest of the fish. The number of local maxima contained in the flow field comprising the fish’s movement would be very close to “1.” Now imagine counting the number of local maxima in the flow field of a school of fish. This number would be proportional to the number fish in the school. Method 2: Fluid dynamics. As crowds get more and more dense, they begin to look like particles interacting with each other. Dense crowds show granular particle behavior. Fluid dynamics could shed some insight on what the density may look like depending on the interactions between the particles. Method 3: Linear relationship between density and velocity. This method follows the simple idea that if a crowd slows down its density is increasing, while speeding up indicates density is decreasing. People will move faster if there is space to fill, and slower if obstacles are in their path. Methodology Method 1: Step 1) Obtain the optical flow of the video, u and v. Step 2) Compute the magnitude of the velocity from u and v. Step 3) Locate all of the local maxima. Step 4) Count the all of the local maxima. Step 5) Divide all of the resulting numbers by the same threshold value (7 was used for the example shown below). Process Results Dataset: Many videos retrieved from YouTube, REU students, graduate students, and other various sources from the Internet. The percent error is based on an average of 25 density computed frames from one video. Each method was tested on the same 25 frames. Future Research Finish working on the fluid dynamics method. There is possibly a way to relate the different accelerations calculated using a homogeneous first-order linear partial differential equation. Although, further research is needed to see if an estimation is possible from solving it. Continuous particle advection with aging and energy fields. Fluid dynamics open systems. Research Experience for Undergraduates 2012, University of Central Florida Carlos Garcia (carlos.m.garcia7@gmail.com) , WaqasSultani (waqas5163@gmail.com) Estimating Crowd Density from Optical Flow Acknowledgements Thank you for your support and helpful advice: Dr. Mubarak Shah Dr. Nielsda Vitoria Lobo WaqasSultani EraldoRibeiro Method 2: Step 1) Compute the optical flow of the video. Step 2) Use the equations below to estimate the acceleration due to pressure, viscosity, social forces, and convection. Step 3) Use this information to estimate the density (have not completed this yet; still working on it). Method 3: Step 1) Compute the optical flow of the video. Step 2) Compute the magnitude of the velocity. Step 3) Use linear equation recovered from research paper to estimate the density. Conclusion Method #1 is an incredibly simple algorithm. 11% is pretty good considering the algorithm will never catch a person standing still. These methods will only work when velocity is present. Method #2 was not tested because it is not completed yet. Method #3 did very poorly on the testing because of the conversions and parameters needed to compute the density. Further testing is needed to fine-tune that particular algorithm.