Radially Distorted Homographies, Revisited

2025-08-28

AI Summary

This paper addresses homography estimation under radial distortion, unifying the modeling and solution of three distortion configurations: single-sided distortion, identical distortion on both views, and independent distortion on each view. Existing methods require separate designs for each case; in contrast, we propose the first unified algebraic framework that reduces all three problems to minimal solvers. Leveraging geometric constraints and polynomial system solving techniques, we construct an efficient and numerically stable closed-form solver requiring only the minimal number of point correspondences—typically four. Experiments on standard benchmarks and fisheye imagery demonstrate that our solver achieves state-of-the-art accuracy while running 2–5× faster. The approach thus offers both theoretical unification and practical deployability.

Technology Category

• Intelligent Robots: State Estimation
• Computer Vision: Other Foundations of Computer Vision
• Machine Learning: Multi-instance/Multi-view Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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. The source code for our solvers will be made available in the event our paper is accepted for publication.

Problem

• Estimating homography with radial distortion simultaneously
• Addressing three distinct radial distortion configurations
• Developing unified minimal solvers for accurate estimation

Innovation

• Unified approach for radial distortion cases
• Fast minimal solvers for homography estimation
• Accurate simultaneous homography and distortion computation