Multiple-camera tracking of rigid objects

In this paper we describe a method for tracking rigid objects using one or several cameras. The tracking process consists of aligning a 3-D model representation of an object with image contours by measuring and minimizing the image error between predicted model points and image contours. The tracker behaves like a visual servo loop where the internal and external camera parameters are updated at each new image acquisition. We study in detail the Jacobian matrix associated with this minimization process in the presence of both point-to-point and point-to-contour matches. We establish the minimal number of matches that are needed as well as the singular configurations leading to a rank-deficient Jacobian matrix. We find a mathematical link between the point-to-point and point-to-contour cases. Based on this link we show that the latter has the same kind of singularities as the former. Moreover we study multiple-camera configurations which optimize the robustness of the method in the presence of single-camera singularities, bad, noisy, or missing data. Extensive experiments done with a complex ship part and with up to three cameras validate the method. In particular we show that the tracker may well be used as a camera calibration procedure.