In this paper, we derive a linear constraint for planar motion leveraging scale- and orientation-covariant features, e.g., SIFT, which is used to create a novel minimal solver for planar motion requiring only a single covariant feature. We compare the proposed method to traditional point-based solvers and solvers relying on affine correspondences in controlled synthetic environments and well-established datasets for autonomous driving. The proposed solver is integrated into a modern robust estimation framework, where it is shown to accelerate the complete estimation pipeline more than 25 \(\times \) , compared to state-of-the-art affine-based minimal solvers, with negligible loss in precision (Code available here: https://github.com/EricssonResearch/eccv-2024 ).