Recovering Planar Motion from Homographies Obtained using a 2.5-Point Solver for a Polynomial System

Abstract:
We present a minimal solver for a special kind of homography arising in applications with planar camera motion (e.g. mobile robotics applications). Since the camera motion we consider only has five degrees of freedom, an explicit parametrisation allows us to reduce the required number of point correspondences to 2.5. Using fewer point correspondences is beneficial when used together with RANSAC, but more importantly, the proposed special solver ensures that the estimated homography is of the correct type (in contrast to the DLT, which estimates a general homography). Our method works by enforcing eleven independent polynomial constraints on the elements of this kind of homography matrix, through the framework of the action matrix method for solving polynomial equations. Some analytical investigation using symbolic software has been conducted in order to understand the properties of the polynomial system, and these results have been used to help guide our design of the solver. Additionally, we provide a direct method to recover the sought motion parameters from the homography matrix. We demonstrate that it is possible to recover both the homography and its generating parameters efficiently and accurately.