Abstract
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 Gröbner-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-ofthe-art and demonstrate significantly better rectifcations on
noisy measurements. Qualitative results on diverse imagery
demonstrate high-accuracy undistortion and rectification