The planar two point algorithm

Vision-based localization, mapping and navigation is often performed by searching for corresponding image points and estimating the epipolar geometry. It is known that the possible relative poses of a camera mounted on a mobile robot that moves over a planar ground floor, has two degrees of freedom. This report provides insight in the problem of estimating the exact planar robot pose difference using only two image point correspondences. We describe an algorithm which uses this minimal set of correspondences termed the Two-point algorithm. It is shown that sometimes two non-degenerate correspondences do not define a unique relative robot pose, but lead to two possible real solutions. The algorithm is especially useful as hypothesis generator for the well known RANSAC (RANdom SAmple Consensus) method. The algorithm is evaluated using both simulated data and data acquired by a mobile robot equipped with an omnidirectional camera. The improvement over existing methods is analogous to the improvement of the well known Five-point algorithm over other algorithms for general non-planar camera motions.