Minimal Solutions to Uncalibrated Two-view Geometry with Known Epipoles

Gaku Nakano; Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 2023, pp. 13361-13370

This paper proposes minimal solutions to uncalibrated two-view geometry with known epipoles. Exploiting the epipoles, we can reduce the number of point correspondences needed to find the fundamental matrix together with the intrinsic parameters: the focal length and the radial lens distortion. We define four cases by the number of available epipoles and unknown intrinsic parameters, then derive a closed-form solution for each case formulated as a higher-order polynomial in a single variable. The proposed solvers are more numerically stable and faster by orders of magnitude than the conventional 6- or 7-point algorithms. Moreover, we demonstrate by experiments on the human pose dataset that the proposed method can solve two-view geometry even with 2D human pose, of which point localization is noisier than general feature point detectors.