用于检测临界两视图配置的单应参数化
Homaloidal parametrization for detecting critical two-view configurations
提出一种基于二次变换线性估计的退化配置检测方法，可替代传统依赖基础矩阵的检测方式，提升两视图几何估计的鲁棒性。
原文依据 we propose a novel degeneracy test for detecting points on the critical surface
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考虑在从（至少）8 个点对应中估计基础矩阵时识别退化配置的问题。已知此类配置对应于基础矩阵的病态估计，因此在实际中识别它们很重要。到目前为止，实用的退化检测仅适用于平面场景和纯旋转的情况，而一般临界曲面（例如包含 3D 点和相机中心的双曲面/锥面/柱面）的情况研究较少，唯一可用的方法高度不稳定，且涉及预先计算的基础矩阵。在本文中，我们提出了一种新的退化检测方法，用于检测临界曲面上的点。通过利用所谓的“圆锥曲线单应网”的几何性质，我们能够设计一个简单且非常实用的检测方法，该方法仅需从图像对应中线性估计一个二次变换。我们的检测不需要预先计算基础矩阵，并且在合成和真实退化配置上的实验表明，它比最接近的竞争方法更稳定。
英文原文摘要 1159 字符
We consider the problem of identifying degenerate configurations while estimating the fundamental matrix from (at least) 8 point correspondences. It is known that such configurations correspond to an ill-posed estimation of the fundamental matrix, so it is important to identify them in practice. So far, a practical degeneracy test is only available for the cases of planar scenes and pure rotation, while the case of the general critical surface (e.g., a hyperboloid/cone/cylinder containing 3D points and camera centres) is less studied, and the only available method is highly unstable, involving a pre-computed fundamental matrix. In this paper, we propose a novel degeneracy test for detecting points on the critical surface. By exploiting the geometry of the so-called "homaloidal net of conics", we are able to design a simple and very practical test that requires the linear estimation of a quadratic transformation from image correspondences. Our test does not require a fundamental matrix in advance and turns out to be more stable than its closest competitor, as shown in our experiments on both synthetic and real-world degenerate configurations.