Single view metrology

We describe how 3D affine measurements may be computed from a single perspective view of a scene given only minimal geometric information determined from the image. This minimal information is typically the vanishing line of a reference plane and a vanishing point for a direction not parallel to the plane. It is shown that affine scene structure may then be determined from the image, without knowledge of the camera´s internal calibration (e.g. focal length), nor of the explicit relation between camera and world (pose). In particular we show how to: compute the distance between planes parallel to the reference plane (up to a common scale factor); compute area and length ratios on any plane parallel to the reference plane; determine the camera´s (viewer´s) location. Simple geometric derivations are given for these results. We also develop an algebraic representation which unifies the three types of measurement and, amongst other advantages, permits a first order error propagation analysis to be performed, associating an uncertainty with each measurement. We demonstrate the technique for a variety of applications, including height measurements in forensic images and 3D graphical modelling from single images