Towards a minimal solution for the relative pose between axial cameras

The problem of estimating the relative pose between axial cameras from pairwise point correspondences is still open to improvement. The state-of-the-art solutions are either too specific in its scope, assuming certain types of correspondences; too broad, dealing with all types of generalized cameras and failing to address the specific issues of axial cameras; or non-minimal linear solutions. The aim of this paper is to pursue new insights on axial cameras that can lead to a suitable minimal solution for this problem. We propose a new formulation for modeling the intersection of back-projection rays of axial cameras through a 5×5 essential matrix that enables a better understanding of some particular axial configurations and leads to a new set of polynomial equations that proves to be useful in constraining the motion estimation. These equations enable to compute a solution from 10 correspondences, an improvement over the 16-point algorithm, which is the state-of-the-art solution within our aimed scope. Both synthetic and real experiments show that our algorithm achieves a better performance than the 16-point algorithm in the context of robust optimization with RANSAC.