Minimal Solution for Computing Pairs of Lines in Non-central Cameras

In non-central cameras, the complete geometry of a 3D line is mapped to each corresponding projection, therefore each line can be theoretically recovered from a single view. However, the solution of this problem is ill-conditioned due to the lack of effective baseline between rays. This limitation prevents from a practical implementation of the approach if lines are not close to the visual system. In this paper, we exploit additional geometric constraints to improve the results of line reconstruction from single images in non-central systems. In particular, we obtain the minimal solution for the case of a pair of intersecting orthogonal lines and for the case of a pair of parallel lines considering three rays from each line. The proposal has been evaluated with simulations and tested with real images.