On camera calibration with linear programming and loop constraint linearization

A technique for calibrating a network of perspective cameras based on their graph of trifocal tensors is presented. After estimating a set of reliable epipolar geometries, a parameterization of the graph of trifocal tensors is proposed in which each trifocal tensor is linearly encoded by a 4-vector. The strength of this parameterization is that the homographies relating two adjacent trifocal tensors, as well as the projection matrices depend linearly on the parameters. Two methods for estimating these parameters in a global way taking into account loops in the graph are developed. Both methods are based on sequential linear programming: the first relies on a locally linear approximation of the polynomials involved in the loop constraints whereas the second uses alternating minimization. Both methods have the advantage of being non-incremental and of uniformly distributing the error across all the cameras. Experiments carried out on several real data sets demonstrate the accuracy of the proposed approach and its efficiency in distributing errors over the whole set of cameras.