Plane based relative structure recovery

In this paper we provide a novel linear algorithm to estimate the direction of translation and the normal to the scene plane, given a stereo pair with known correspondences between the corners in the images. Planar parallax which arises naturally in planar scenes (and can also be defined with respect to virtual planes), is exploited to achieve this. Based on the parallax vectors and the homography induced by the scene plane we calculate the direction of translation and the normal to the scene plane. We also calculate the relative heights of points on the object with respect to the scene plane, given the height of the camera above the plane. The accuracy of the estimated normal with respect to noise in input data is also analyzed empirically.