3D reconstruction based on homography mapping

Previous work shows that based on the fundamental matrix from two views, 3D structures can be recovered up to an unknown projectivity. In this paper, we show that based on four coplanar correspondences of two externally uncalibrated cameras, 3D reconstruction can be achieved in Euclidean space with only one uniform scale factor and up to two real solutions. It is shown that this scale factor is the physical distance from the camera center to the plane formed by the four points in 3D space. Consequently, if this distance is known a priori, then the 3D structure can be completely determined. In order to disambiguate the two solutions, a third view is required in general to give a unique solution. In practice, since the real data are always corrupted with noise, more coplanar correspondences are used and a least squares solution is applied to obtain the estimation of the homography matrix. Experimental results on both simulated and real data show that this reconstruction algorithm works reasonably robustly, It is also shown that this algorithm is optimal both in terms of the minimum number of required correspondences and in terms of the assumption made for the internal calibration.