Single view metrology

We describe how 3D affine measurements may be computed from a single perspe ctive view of a scene given only minimal geometric information determined f rom the image. This minimal information is typically the vanishing line of a reference plane, and a vanishing point for a direction not parallel to th e plane. It is shown that affine scene structure may then be determined fro m the image, without knowledge of the camera's internal calibration (e.g. f ocal length), nor of the explicit relation between camera and world (pose). In particular, we show how to (i) compute the distance between planes paral lel to the reference plane (up to a common scale factor); (ii) compute area and length ratios on any plane parallel to the reference plane; (iii) dete rmine the camera's location. Simple geometric derivations are given for the se results. We also develop an algebraic representation which unifies the t hree types of measurement and, amongst other advantages, permits a first or der error propagation analysis to be performed, associating an uncertainty with each measurement. We demonstrate the technique for a variety of applications, including heigh t measurements in forensic images and 3D graphical modelling from single im ages.