Corners are popular features for relative pose computation with 2D-2D point correspondences. Stable corners may be formed by two 3D rays sharing a common starting point. We call such elements ray-point-ray (RPR) structures. Besides a local invariant keypoint given by the lines' intersection, their reprojection also defines a corner orientation and an inscribed angle in the image plane. The present paper investigates such RPR features, and aims at answering the fundamental question of what additional constraints can be formed from correspondences between RPR features in two views. In particular, we show that knowing the value of the inscribed angle between the two 3D rays poses additional constraints on the relative orientation. Using the latter enables the solution of the relative pose problem with as few as 3 correspondences across the two images. We provide a detailed analysis of all minimal cases distinguishing between 90-degree RPR-structures and structures with an arbitrary, known inscribed angle. We furthermore investigate the special cases of a known directional correspondence and planar motion, the latter being solvable with only a single RPR correspondence. We complete the exposition by outlining an image processing technique for robust RPR-feature extraction. Our results suggest high practicality in man-made environments, where 90-degree RPR-structures naturally occur.

中文翻译：

---

使用射线-点-射线特征的最小情况相对位姿计算


角点是使用 2D-2D 点对应进行相对姿态计算的常用特征。稳定的角可以由共享公共起点的两条 3D 射线形成。我们将此类元素称为射线-点-射线（RPR）结构。除了由线的交点给出的局部不变关键点之外，它们的重投影还定义了图像平面中的角方向和内切角。本文研究了此类 RPR 特征，旨在回答两个视图中 RPR 特征之间的对应关系可以形成哪些附加约束的基本问题。特别是，我们表明，了解两条 3D 射线之间的内切角值会对相对方向造成额外的约束。使用后者可以用两幅图像中少至 3 个对应项来解决相对位姿问题。我们对所有最小情况进行了详细分析，区分 90 度 RPR 结构和具有任意已知内切角的结构。我们还研究了已知方向对应和平面运动的特殊情况，后者只需单个 RPR 对应即可求解。我们通过概述用于鲁棒 RPR 特征提取的图像处理技术来完成阐述。我们的结果表明在人造环境中具有很高的实用性，在这种环境中自然会出现 90 度 RPR 结构。