Rectification from Radially-Distorted Scales

This paper introduces the first minimal solvers that jointly estimate lens distortion and affine rectification from repetitions of rigidly transformed coplanar local features. The proposed solvers incorporate lens distortion into the camera model and extend accurate rectification to wide-angle images that contain nearly any type of coplanar repeated content. We demonstrate a principled approach to generating stable minimal solvers by the Grobner basis method, which is accomplished by sampling feasible monomial bases to maximize numerical stability. Synthetic and real-image experiments confirm that the solvers give accurate rectifications from noisy measurements when used in a RANSAC-based estimator. The proposed solvers demonstrate superior robustness to noise compared to the state-of-the-art. The solvers work on scenes without straight lines and, in general, relax the strong assumptions on scene content made by the state-of-the-art. Accurate rectifications on imagery that was taken with narrow focal length to near fish-eye lenses demonstrate the wide applicability of the proposed method. The method is fully automated, and the code is publicly available at https://github.com/prittjam/repeats.