Trajectory reconstruction from non-overlapping surveillance cameras with relative depth ordering constraints

We present a method for reconstructing a trajectory of an object moving in front of non-overlapping fully or partially calibrated cameras. The non-overlapping setup turns that problem ill-posed as no point correspondences can be established which are necessary for the well known point triangulation. The proposed solution instead builds on the assumption of trajectory smoothness and depth ordering prior information. We propose a novel formulation with a consistent minimization criterion and a way to utilize the depth ordering prior reflected by the size change of a bounding box associated to an image point being tracked. Reconstructing trajectory minimizing the trajectory smoothness, its re-projection error and employing the depth priors is casted as the Second Order Cone Program yielding a global optimum. The new formulation together with the proposed depth prior significantly improves the trajectory reconstruction in sense of accuracy and topology, and speeds up the solver. Synthetic and real experiments validate the feasibility of the proposed approach.