# Minimal Solvers for Rectifying from Radially-Distorted Scales and Change of Scales

## TL;DR

This paper presents novel minimal solvers that jointly estimate lens distortion and affine rectification from images of coplanar features, working without straight lines and relaxing scene assumptions, with demonstrated robustness and wide applicability.

## Contribution

The paper introduces the first minimal solvers for joint lens distortion and affine rectification estimation that do not require straight lines and are robust to scene content variations.

## Key findings

- Solvers outperform state-of-the-art in noise robustness
- Effective on images with narrow to fisheye lenses
- Fully automatic and applicable to diverse scenes

## Abstract

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 Gr\"obner 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.

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Source: https://tomesphere.com/paper/1907.11539