Step 3.1: Implementation - Identifying Regions with High Human Activity.

Given the 3D geometry of the environment, the goal is to find the location and orientation of cameras to construct an effective surveillance scenario as described in Step 1. A two stage approach is considered to solve this problem.

1. Identify regions in the geometry that might have high human activity.
2. Optimize camera placement to maximize the view of these regions.

Identifying regions of High Human Activity: 

Given an infrastructure we assume that humans follow trajectories with the goal of reaching a destination like an entrances, exit or a doorways. Let these destination be called nodes, based on the purpose a node serves in the infrastructure there is a certain probability associated with accessing it. For example, at an airport the ticket counter might have an higher probability of access than a coffee shop or a restroom. The knowledge of this probability can help us estimate the likely human motion activity in the infrastructure. Given the geometry of the environment along with the nodes and their assigned probabilities, the likely human motion in the scenario are simulated to identify regions of high human activity. The steps involved in this process are

1. Identify nodes and assign probabilities
2. Sample start and end nodes based on the probabilities
3. Simulate trajectories from the starting node to the end node
4. Calculate occupancy map from the trajectories
5. Cluster regions based on their occupancy

Let us consider the following floor plan. 

Figure 1

Identify nodes and assign probabilities: 

In Figure 1, we would like to install a camera network that provides effective surveillance in the hallway. The nodes identified are numbered as shown. Given this geometry and the nodes, the first task is to assign the probabilities. The probability of accessing a node is defined by its purpose in the scenario. In this case, we assume that it is proportional to the accommodation capacity of the room.  Which means the higher the capacity of a room to seat humans, the higher is the probability of accessing it. The following probabilities were assigned. 

Node	Capacity	Probability
0	60	0.46
1	10	0.07
2	10	0.07
3	10	0.07
4	-	entry/exit
5	10	0.07
6	20	0.15
7	-	entry/exit
8	10	0.07

Assuming that all humans entering an infrastructure will exit at some point, the nodes marked as entry/exit points are not assigned a probability.

Sample start and end nodes based on the probabilities:

We assume that any human entering the hallway will exit at some point of time. First an entry (4,7) was chosen with equal probability, then a node was chosen that is not an exit based on the probability assigned as shown in the table. Now that the human has transitioned to the node, the human can either choose to transition to another node or exit with equal probabilities. If the human chooses to exit, the closest exit is chosen else, the human chooses to go another node based on a calculated probability. The probability of choosing the second node changes because the node that the human is currently in is eliminated when calculating the probability for other nodes. Sample output obtained from simulating this scenario is shown in Figure 2.

Figure 2