A convex relaxation optimization algorithm for multi-camera calibration with 1D objects

Accurate calibration is a pre-requisite for applications of a multi-camera system. The one-dimensional calibration method is highly suitable for multi-camera systems because a one-dimensional object is easy to construct and without self-occlusions. However, the progress made in one-dimensional calibration has primarily focused on reducing the constraints on the motion of one-dimensional objects, and the calibration accuracy still needs to be improved. In this paper, an accurate algorithm for multi-camera calibration with one-dimensional objects that is based on the convex relaxation techniques is proposed. First, constraints on the absolute conic of each camera are constructed. Next, the optimal solution for each absolute conic is found using convex relaxation, and the intrinsic parameters of each camera are computed. Finally, the extrinsic parameters of the multi-camera system are computed using simple matrix operations. Compared with existing algorithms, the proposed algorithm is more accurate and converges faster. Experiments with both synthetic and real image data validate the proposed algorithm.