3-D visual coverage based on gradient descent algorithm on matrix manifolds and its application to moving objects monitoring

This paper investigates coverage control for visual sensor networks based on gradient descent techniques on matrix manifolds. We consider the scenario that networked vision sensors with controllable orientations are distributed over 3-D space to monitor 2-D environment. Then, the decision variable must be constrained on the Lie group SO(3). The contribution of this paper is two folds. The first one is technical, namely we formulate the coverage problem as an optimization problem on SO(3) without introducing local parameterization like Euler angles and directly apply the gradient descent algorithm on the manifold. The second technological contribution is to present not only the coverage control scheme but also the density estimation process including image processing and curve fitting while exemplifying its effectiveness through simulation of moving objects monitoring.