Planar motion estimation from 1D homographies

This paper addresses the estimation of planar camera motion using 1D homographies. As contributions, we show analytically that, contrary to what occurs with the 2D homography, there is a family of infinite solutions to the 1D homography decomposition, and therefore infinite possible motion reconstructions. In addition, we propose a new method to compute the planar motion between two images from the information provided by two different 1D homographies, employing their associated homology transformations. Therefore, our approach computes a general planar camera motion from only two 1D views, when previous works needed three 1D views for this task. The use of 1D information makes the method particularly suitable for omnidirectional cameras, due to the wide field of view and precise angular information provided by this kind of sensors. The performance of our proposal is illustrated through simulations and experiments on real images.