# Radially-Distorted Conjugate Translations

arXiv: https://arxiv.org/abs/1711.11339 · HTML: https://mlsanity.com/paper/1711.11339/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2017.

## Built on by (most cited first, 9 of 9)

- [AnyCalib: On-Manifold Learning for Model-Agnostic Single-View Camera Calibration](https://mlsanity.com/paper/2503.12701/) (2025)
- [GPU-Based Homotopy Continuation for Minimal Problems in Computer Vision](https://mlsanity.com/paper/2112.03444/) (2021)
- [A Deep Perceptual Measure for Lens and Camera Calibration](https://mlsanity.com/paper/2208.12300/) (2022)
- [Rethinking Generic Camera Models for Deep Single Image Camera Calibration to Recover Rotation and Fisheye Distortion](https://mlsanity.com/paper/2111.12927/) (2021)
- [Relative Pose from SIFT Features](https://mlsanity.com/paper/2203.07930/) (2022)
- [Trust Your IMU: Consequences of Ignoring the IMU Drift](https://mlsanity.com/paper/2103.08286/) (2021)
- [Deep Single Image Camera Calibration by Heatmap Regression to Recover Fisheye Images Under Manhattan World Assumption](https://mlsanity.com/paper/2303.17166/) (2023)
- [Practical solutions to the relative pose of three calibrated cameras](https://mlsanity.com/paper/2303.16078/) (2023)
- [Matching with AffNet based rectifications](https://mlsanity.com/paper/2207.14660/) (2022)

## Abstract (arXiv)

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.