Linear Fundamental Matrix Estimation from 7 or 5 Points

Taci Ata Kucukpinar, Juan Mogollon, Joshua Fraser, Timothy Duff, Kannappan Palaniappan; Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2026, pp. 21464-21473

We revisit the problem of estimating the fundamental matrix of a pair of perspective cameras, a cornerstone of geometric computer vision. As is well-known, linear solvers require at least 8 point correspondences, whereas nonlinear minimal solvers require just 7 in the uncalibrated case or 5 in the calibrated case. In this paper, we consider a special case of the 7-point problem where 5 of the points are configured to lie on two lines, which has previously been shown to have a unique solution. As a theoretical contribution, we offer a completely elementary analysis of how this uniqueness manifests in the standard 7-point algorithm. On a practical level, we provide the first linear solver for the minimal problem associated to this special configuration. Additionally, we evaluate a heuristic 5-point fundamental matrix solver based on the construction of virtual midpoints. When combined with early non-minimal fitting, the runtime and accuracy of our solver is competitive with the state-of-the-art (SOTA) on multiple benchmarks. Code is available at https://github.com/CIVA-Lab/v-umlaut.