Algorithms for Computing a Planar Homography from Conics in Correspondence

This paper presents two new algorithms for computing a planar homography from conic correspondences. Firstly, we propose a linear algorithm for computing the homography when there are three or more conic correspondences. In this case, we get an overdetermined set of linear equations and the solution that minimizes the algebraic distance is obtained by the singular value decomposition. Secondly, we propose another algorithm for determining the homography from only two conic correspondences. Unlike the previous algorithms our approach uses only linear algebra and does not require solving high-degree polynomial equations. Hence, the proposed formulation leads to an algorithm that is efficient and easy to implement. In addition, our approach incorporates the computation of the two projective invariants for a pair of conics. These invariants provide a condition for the existence of a homography between the pairs of conics. We evaluate the characteristics and robustness of the proposed algorithms in experiments with synthetic and real data.