A new algorithm for linearly reconstructing the infinite homography matrix and intrinsic parameter matrix of a camera

By deriving the formula to directly determine the infinite homography matrix from a pair of fundamental matrixes, a new linear restoration algorithm of the homography matrix of the plane at infinity from feature point-pair sets extracted from three views under a pair of linearly independent motions is developed in this paper. Then, in terms of the similar decomposition of the infinite homography matrix, we prove that as soon as an additional orthogonal constraint to the pair of linearly independent motions is imposed on, the intrinsic parameter matrix of the camera to be self-calibrated can be linearly and uniquely determined. So, a new linear self-calibration algorithm from feature point-pair sets extracted from three views under a pair of orthogonal motions is successfully developed. Experiments show that the new algorithm has the advantages of simple realization, high computation speed, excellent restoration precision and strong antinoise ability.