Planar metric rectification by algebraically estimating the image of the absolute conic

A new metric rectification method for planar homography is proposed based on a closed form algebraic solution of the image of the absolute conic on the image plane. Our solution allows shape measurement to be made directly on the image plane without explicitly computing the homography matrix or recoreringing the rectified image. We show that the invariance property of the relationship between the circular points and the absolute conic under projective transformation can effectively do planar metric rectification. In this approach, the image of the absolute conic is solved algebraically to achieve metric rectification based only on the vanishing line and the image of one arbitrary circle on the world plane extracted automatically from the image plane. The process of conic solving introduces no errors and the performance of the method is mainly dependent on the robustness of the straight line and ellipse fitting processes. The fitting scheme suggested in the paper is robust and give good results in most cases.