General Planar Motion from a Pair of 3D Correspondences

We present a novel 2-point method for estimating the relative pose of a camera undergoing planar motion from 3D data (e.g. from a calibrated stereo setup or an RGB-D sensor). Unlike prior art, our formulation does not assume knowledge of the plane of motion, (e.g. parallelism between the optical axis and motion plane) to resolve the under-constrained nature of SE(3) motion estimation in this context. Instead, we enforce geometric constraints identifying, in closed-form, a unique planar motion solution from an orbital set of geometrically consistent SE(3) motion estimates. We explore the set of special and degenerate geometric cases arising from our formulation. Experiments on synthetic data characterize the sensitivity of our estimation framework to measurement noise and different types of observed motion. We integrate our solver within a RANSAC framework and demonstrate robust operation on standard benchmark sequences of real-world imagery. Code is available at: https://github.com/jdibenes/gpm.