About conditions for recovering the metric structures of perpendicular planes from the single ground plane to image homography

The absolute conic is the key for recovering the Euclidean structure in 3D space. The image of the absolute conic can be parametrized by the set of three vanishing points corresponding to orthogonal directions in space with two independent additional factors. Whereas a single plane to image homography only allows the image to inherit two vanishing points and one of these factors, we describe a method which recovers the metric structures of any perpendicular plane to the ground from the ground to image homography matrix. Indeed, under the assumption of a natural camera, we demonstrate that the third vanishing point lies on a line that we call central line. A direct solution is found with an additional constraint relevant to the application we deal with: a “pseudo-parallelism” between one of the camera axis and the ground plane. Direct applications on video MPEG-encoded images are presented in the experiment section showing a very satisfactory accuracy