Minimal Solvers for Rectifying from Radially-Distorted Conjugate Translations

TL;DR

This paper presents minimal solvers that simultaneously correct radial lens distortion and perform affine-rectification using local features, improving robustness and efficiency in rectifying images of coplanar textures in man-made environments.

Contribution

The paper introduces novel minimal solvers that jointly address radial distortion correction and affine-rectification, accommodating various feature types with state-of-the-art algebraic methods.

Findings

Solvers are stable, small, and fast.

Outperform existing methods in robustness to noise.

Effective on challenging real-world imagery.

Abstract

This paper introduces minimal solvers that jointly solve for radial lens undistortion and affine-rectification using local features extracted from the image of coplanar translated and reflected scene texture, which is common in man-made environments. The proposed solvers accommodate different types of local features and sampling strategies, and three of the proposed variants require just one feature correspondence. State-of-the-art techniques from algebraic geometry are used to simplify the formulation of the solvers. The generated solvers are stable, small and fast. Synthetic and real-image experiments show that the proposed solvers have superior robustness to noise compared to the state of the art. The solvers are integrated with an automated system for rectifying imaged scene planes from coplanar repeated texture. Accurate rectifications on challenging imagery taken with narrow to wide field-of-view lenses demonstrate the applicability of the proposed solvers.