Minimal Case Relative Pose Computation using Ray-Point-Ray Features

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.