Bus surveillance: how many and where cameras should be placed

Public transport safety is an important issue that has recently gained substantial attention, especially with the increasing number of violent incidents occurring abroad. To avoid such incidents and to perform post-incident investigations, many buses today are equipped with surveillance cameras. These cameras are usually installed in key places such as doors, the front and the middle of the bus. This camera placement is often performed manually based on human intuition and knowledge; however, there is no scientific basis to justify: (1) how many cameras would be sufficient, and (2) where (location) and how (with what orientation) they should be placed, to increase the area of coverage at the minimum cost. This paper addresses this issue by breaking it down into two separate problems: MaxGain and MinCost. The MaxGain problem is aimed to maximize the overall coverage with a specific number of cameras; while the MinCost problem attempts to minimize the number of cameras to cover a specified area in the bus. The solutions to these two problems are presented. The proposed method computes the approximate coverage of a camera inside the 3D bus model. Furthermore, in order to improve the efficiency of the solution, an algorithm called SmartMax is proposed. The proposed solution advises precise locations and orientations (pan and tilt angles) of required cameras and can be used to validate the current camera installations in various types of public transit buses.