  This paper introduces the first minimal solvers that jointly solve for
affine-rectification and radial lens distortion from coplanar repeated
patterns. Even with imagery from moderately distorted lenses, plane
rectification using the pinhole camera model is inaccurate or invalid. The
proposed solvers incorporate lens distortion into the camera model and extend
accurate rectification to wide-angle imagery, which is now common from consumer
cameras. The solvers are derived from constraints induced by the conjugate
translations of an imaged scene plane, which are integrated with the division
model for radial lens distortion. The hidden-variable trick with ideal
saturation is used to reformulate the constraints so that the solvers generated
by the Grobner-basis method are stable, small and fast.
  Rectification and lens distortion are recovered from either one conjugately
translated affine-covariant feature or two independently translated
similarity-covariant features. The proposed solvers are used in a \RANSAC-based
estimator, which gives accurate rectifications after few iterations. The
proposed solvers are evaluated against the state-of-the-art and demonstrate
significantly better rectifications on noisy measurements. Qualitative results
on diverse imagery demonstrate high-accuracy undistortions and rectifications.
The source code is publicly available at https://github.com/prittjam/repeats.
