arXiv:2508.21190cs.CV2025-08

统一求解带径向畸变的单应变换,速度更快更稳定。

Radially Distorted Homographies, Revisited

  • 提出统一方法处理三种径向畸变情形
  • 新解法在三个场景下均比现有最快方法快
  • 适合需要高精度图像对齐的研究者使用

单应变换是几何计算机视觉与射影几何中最常见的变换之一,其估计是众多计算机视觉任务的关键步骤。在真实图像中,相机镜头常引入几何畸变,尤其径向畸变,此时需同时估计单应变换与镜头畸变以获得可靠结果。针对两幅图像间的径向畸变单应变换,存在三种概念上不同的畸变配置:(i)仅一幅图像有畸变,(ii)两幅图像具有相同畸变,(iii)两幅图像畸变独立。尽管过去已分别处理这些情况,本文提出一种新颖且统一的方法,可覆盖全部三种情形。我们展示了该方法如何构建新的快速、稳定且精确的最小解法。在所有三种情况下,新解法均比现有最先进方法更快,且保持相近精度。所提解法在包括鱼眼相机拍摄图像在内的多个标准基准上进行了测试。相关参考实现已作为HomLib库的一部分开源(https://github.com/marcusvaltonen/HomLib)。

原文摘要 · Abstract (English)

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).

单应变换径向畸变图像对齐

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