Radially-Distorted Conjugate Translations

TL;DR

This paper presents minimal solvers that jointly estimate affine-rectification and radial lens distortion from coplanar repeated patterns, enabling accurate wide-angle image rectification even with moderate distortion.

Contribution

It introduces the first minimal solvers that incorporate radial lens distortion into rectification from coplanar repeated patterns, extending accuracy to wide-angle imagery.

Findings

Significantly better rectifications on noisy measurements.

High-accuracy undistortions demonstrated on diverse imagery.

Fast and stable solvers derived from Grobner-basis method.

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 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.