Camera Pose Estimation Using First-Order Curve Differential Geometry

This paper considers and solves the problem of estimating camera pose given a pair of point-tangent correspondences between the 3D scene and the projected image. The problem arises when considering curve geometry as the basis of forming correspondences, computation of structure and calibration, which in its simplest form is a point augmented with the curve tangent. We show that while the standard resectioning problem is solved with a minimum of three points given the intrinsic parameters, when points are augmented with tangent information only two points are required, leading to substantial computational savings, e.g., when used as a minimal engine within RANSAC. In addition, computational algorithms are developed to find a practical and efficient solution shown to effectively recover camera pose using both synthetic and realistic datasets. The resolution of this problem is intended as a basic building block of future curve-based structure from motion systems, allowing new views to be incrementally registered to a core set of views for which relative pose has already been computed.