Noname manuscript No. (will be inserted by the editor) On Camera Calibration with Linear Programming and Loop Constraint

Abstract A technique for calibrating a network of perspec-tive cameras based on their graph of trifocal tensors is pre-sented. After estimating a set of reliable epipolar geome-tries, 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 poly-nomials involved in the loop constraints whereas the sec-ond uses alternating minimization. Both methods have the advantage of being non-incremental and of uniformly dis-tributing the error across all the cameras. Experiments car-ried 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. Keywords structure from motion · camera calibration · sequential linear programmin