Hybrid and Non-minimal Planar Motion Estimation from Point Correspondences

We address the problem of relative camera pose estimation in the context of planar motion, where the rotation axis and translation vectors are orthogonal to each other. For such scenarios, it is common to assume a known motion plane to leverage the reduced algebraic structure and geometric parameterization of the ensuing epipolar constraints. In this work, we focus on the general prior-free case, in which no assumptions about the plane of motion are made. While current solvers estimate planar motion from homogeneous (i.e. 2D-2D or 3D-3D) point correspondences, leveraging hybrid (i.e. combinations of 2D-2D, 2D-3D, and 3D-3D) point correspondences remains an open problem. We explore the solution space for the general planar motion problem and propose three novel minimal solvers from hybrid point correspondences, as well as a triplet of new non-minimal solvers from 2D-2D point correspondences bridging the theoretical gap from minimal to linear solutions. Experiments on both synthetic data and standard benchmark sequences of real-world imagery demonstrate that our proposed solvers can provide better pose estimates than homogeneous planar motion solvers (with or without motion plane prior), while achieving competitive run times.