This paper introduces the first minimal solvers that jointly estimate lens distortion and affine rectification from the image of rigidly-transformed coplanar features. The solvers work on scenes without straight lines and, in general, relax strong assumptions about scene content made by the state of the art. The proposed solvers use the affine invariant that coplanar repeats have the same scale in rectified space. The solvers are separated into two groups that differ by how the equal scale invariant of rectified space is used to place constraints on the lens undistortion and rectification parameters. We demonstrate a principled approach for generating stable minimal solvers by the Gröbner basis method, which is accomplished by sampling feasible monomial bases to maximize numerical stability. Synthetic and real-image experiments confirm that the proposed solvers demonstrate superior robustness to noise compared to the state of the art. Accurate rectifications on imagery taken with narrow to fisheye field-of-view lenses demonstrate the wide applicability of the proposed method. The method is fully automatic.

中文翻译：

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修正径向扭曲尺度和尺度变化的最小求解器

本文介绍了第一个从刚性变换的共面特征的图像中联合估计透镜畸变和仿射校正的最小求解器。求解器在没有直线的场景上工作，并且通常会放宽对现有技术所做的场景内容的强烈假设。建议的求解器使用仿射不变量，即共面重复在整流空间中具有相同的比例。求解器分为两组，不同之处在于如何使用校正空间的等标不变量来对镜头不失真和校正参数施加约束。我们展示了一种通过 Gröbner 基方法生成稳定最小求解器的原理方法，该方法通过对可行的单项式基进行采样以最大化数值稳定性来实现。合成和真实图像实验证实，与现有技术相比，所提出的求解器对噪声具有卓越的鲁棒性。对使用窄到鱼眼视场镜头拍摄的图像进行准确校正证明了所提出方法的广泛适用性。该方法是全自动的。