# Radially Distorted Homographies, Revisited

## TL;DR

This paper introduces a unified, fast, and accurate method for estimating homographies with radial lens distortion in images, addressing three distinct distortion configurations simultaneously, and demonstrating superior speed over existing methods.

## Contribution

It presents a novel unified approach and minimal solvers for radially distorted homographies applicable to three different distortion scenarios, improving speed while maintaining accuracy.

## Key findings

- Solvers are faster than state-of-the-art methods.
- Maintains similar accuracy to existing approaches.
- Effective on fisheye camera images.

## Abstract

Homographies are among the most prevalent transformations occurring in geometric computer vision and projective geometry, and homography estimation is consequently a crucial step in a wide assortment of computer vision tasks. When working with real images, which are often afflicted with geometric distortions caused by the camera lens, it may be necessary to determine both the homography and the lens distortion-particularly the radial component, called radial distortion-simultaneously to obtain anything resembling useful estimates. When considering a homography with radial distortion between two images, there are three conceptually distinct configurations for the radial distortion; (i) distortion in only one image, (ii) identical distortion in the two images, and (iii) independent distortion in the two images. While these cases have been addressed separately in the past, the present paper provides a novel and unified approach to solve all three cases. We demonstrate how the proposed approach can be used to construct new fast, stable, and accurate minimal solvers for radially distorted homographies. In all three cases, our proposed solvers are faster than the existing state-of-the-art solvers while maintaining similar accuracy. The solvers are tested on well-established benchmarks including images taken with fisheye cameras. A reference implementation of the proposed solvers is made available as part of HomLib (https://github.com/marcusvaltonen/HomLib).