基于 7 点或 5 点的线性基础矩阵估计
Linear Fundamental Matrix Estimation from 7 or 5 Points
提供首个针对 5 点共线特殊构型的线性最小解算器，可直接嵌入 RANSAC 或早期非最小拟合流程，替代 7 点/8 点非线性求解，降低两视图几何估计的延迟并提升数值稳定性。
原文依据 we provide the first linear solver for the minimal problem associated to this special configuration
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论我们重新审视一对透视相机的基础矩阵估计问题，这是几何计算机视觉的基石。众所周知，线性求解器至少需要 8 组点对应，而非线性最小求解器在未标定情形下仅需 7 组、在标定情形下仅需 5 组。本文考虑 7 点问题的一个特殊情形，即其中 5 个点被配置为位于两条直线上，此前已有工作表明该情形具有唯一解。作为理论贡献，我们对这种唯一性在标准 7 点算法中如何体现给出了完全初等的分析。在实践层面，我们为该特殊构型所对应的最小问题提供了首个线性求解器。此外，我们评估了一种基于虚拟中点构造的启发式 5 点基础矩阵求解器。当与早期非最小拟合相结合时，我们的求解器在多个基准上的运行时间与精度均与最优方法具有竞争力。代码见 https://github.com/CIVA-Lab/v-umlaut。
英文原文摘要 1097 字符
We revisit the problem of estimating the fundamental matrix of a pair of perspective cameras, a cornerstone of geometric computer vision. As is well-known, linear solvers require at least 8 point correspondences, whereas nonlinear minimal solvers require just 7 in the uncalibrated case or 5 in the calibrated case. In this paper, we consider a special case of the 7-point problem where 5 of the points are configured to lie on two lines, which has previously been shown to have a unique solution. As a theoretical contribution, we offer a completely elementary analysis of how this uniqueness manifests in the standard 7-point algorithm. On a practical level, we provide the first linear solver for the minimal problem associated to this special configuration. Additionally, we evaluate a heuristic 5-point fundamental matrix solver based on the construction of virtual midpoints. When combined with early non-minimal fitting, the runtime and accuracy of our solver is competitive with the state-of-the-art (SOTA) on multiple benchmarks. Code is available at https://github.com/CIVA-Lab/v-umlaut.