Localization and Optimization Problems for Camera Networks

In the framework of networked control systems, we focus on networks of autonomous PTZ cameras. A large set of cameras communicating each other through a network is a widely used architecture in application areas like video surveillance, tracking and motion. First, we consider relative localization in sensor networks, and we tackle the issue of investigating the error propagation, in terms of the mean error on each component of the optimal estimator of the position vector. The relative error is computed as a function of the eigenvalues of the network: using this formula and focusing on an exemplary class of networks (the Abelian Cayley networks), we study the role of the network topology and the dimension of the networks in the error characterization. Second, in a network of cameras one of the most crucial problems is calibration. For each camera this consists in understanding what is its position and orientation with respect to a global common reference frame. Well-known methods in computer vision permit to obtain relative positions and orientations of pairs of cameras whose sensing regions overlap. The aim is to propose an algorithm that, from these noisy input data makes the cameras complete the calibration task autonomously, in a distributed fashion. We focus on the planar case, formulating an optimization problem over the manifold SO(2). We propose synchronous deterministic and distributed algorithms that calibrate planar networks exploiting the cycle structure of the underlying communication graph. Performance analysis and numerical experiments are shown. Third, we propose a gossip-like randomized calibration algorithm, whose probabilistic convergence and numerical studies are provided. Forth and finally, we design surveillance trajectories for a network of calibrated autonomous cameras to detect intruders in an environment, through a continuous graph partitioning problem.