In this paper, how to calibrate a fixed multi-camera system and simultaneously achieve a Euclidean reconstruction from a set of segments is addressed. It is well known that only a projective reconstruction could be achieved without any prior information. Here, the known segment lengths are exploited to upgrade the projective reconstruction to a Euclidean reconstruction and simultaneously calibrate the intrinsic and extrinsic camera parameters. At first, a DLT(Direct Linear Transformation)-like algorithm for the Euclidean upgrading from segment lengths is derived in a very simple way. Although the intermediate results in the DLT-like algorithm are essentially equivalent to the quadric of segments (QoS), the DLT-like algorithm is of higher accuracy than the existing linear algorithms derived from the QoS because of a more accurate way to extract the plane at infinity from the intermediate results. Then, to further improve the accuracy of Euclidean upgrading, two weighted DLT-like algorithms are presented by weighting the linear constraint equations in the original DLT-like algorithm. Finally, using the results of these linear algorithms as the initial values, a new weighted nonlinear algorithm for Euclidean upgrading is explored to recover the Euclidean structure more accurately. Extensive experimental results on both the synthetic data and the real image data demonstrate the effectiveness of our proposed algorithms in Euclidean upgrading and multi-camera calibration. 
Euclidean upgrading from segment lengths: DLT-like algorithm and its variants