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 a 3D scene and a 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 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 robustness and computational savings, e.g., as a minimal engine within ransac. In addition, algorithms are developed to find a practical solution shown to effectively recover camera pose using synthetic and real datasets. This technology is intended as a building block of curve-based structure from motion systems, allowing new views to be incrementally registered to a core set of views for which relative pose has been computed.