Linear pose estimate from corresponding conics

We propose here a new method to recover the orientation and position of a plane by matching at least three projections of a conic lying on the plane itself. The procedure is based on rearranging the conic projection equations such that the non linear terms are eliminated. It works with any kind of conic and does not require that the shape of the conic is known a-priori. The method was extensively tested using ellipses, but it can also be used for hyperbolas and parabolas. It was further applied to pairs of lines, which can be viewed as a degenerate case of hyperbola, without requiring the correspondence problem to be solved first. Critical configurations and numerical stability have been analyzed through simulations. The accuracy of the proposed algorithm was compared to that of traditional algorithms and of a trinocular vision system using a set of landmarks.

► Recovering orientation of a conic from a trinocular vision system leads to a non linear problem. ► Here we propose a linear solution to estimate the conic orientation. ► The method can be applied to any kind of conic, including the degenerated cases. ► Tests on both simulated and real data demonstrate the feasibility of the method. ► Critical configurations are also analyzed by a geometrical/numerical point of view.