Minimal Relative Pose Estimation Using Translation-Decoupled Rotation for Planar Scenario

The minimal calibrated relative pose estimation in a planar scenario, which uses four 2-D–2-D image correspondences, has been effectively addressed through homography decomposition. Nonetheless, homography estimation through direct linear transformation (DLT) suffers from vulnerability to image noise when three points are (almost) collinear. To mitigate this issue, this article proposes four alternative minimal relative pose solvers for the planar scenario. The proposed method separates rotation estimation from translation using the coplanar line constraint. To achieve this, the line directions are expressed in terms of the relative rotation using four image point correspondences. Enforcing the line coplanarity constraint on these lines results in two distinct sets of multivariate polynomial equations. The equation systems are subsequently solved using the hidden variable technique and Gröbner bases approach, yielding four relative rotation solvers. Apart from the relative rotation recovery for the general planar scene, rotation estimation with an available common reference direction is further considered. Once the relative rotation arrives, a unified formulation retrieves the translation and plane normal. To benchmark the proposed method against existing methods, simulations, and real-world experiments were conducted under various planar scenarios and camera motion patterns. The results demonstrate that the proposed methods are 2–8 times more accurate than multiple existing methods regarding rotation estimates, and the translation estimation accuracy for these methods remains similar. In cases of degeneracy where three points are (almost) collinear, the proposed solvers effectively reduce rotation errors from 90° via the homography decomposition to approximately 7°. Overall, this article offers a promising alternative for relative pose estimation in planar scenarios.