Exact algorithms for non-overlapping 2-frame problem with non-partial coverage for networked robotic cameras

We report our algorithmic development on the 2-frame problem that addresses the need of coordinating two networked robotic pan-tilt-zoom (PTZ) cameras for n, (n > 2), competing rectangular observation requests. We assume the two camera frames have no overlap on their coverage. A request is satisfied only if it is fully covered by a camera frame. The satisfaction level for a given request is quantified by comparing its desirable observation resolution with that of the camera frame which fully covers it. We propose a series of exact algorithms for the solution that maximizes the overall satisfaction. Our algorithms solve the 2-frame problem in O(n²), O(n²m) and O(n³) times for fixed, m discrete and continuous camera resolution levels, respectively. We have implemented all the algorithms and compared them with the existing work.