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Unformatted text preview: Single View Metrology A. Criminisi, I. Reid and A. Zisserman Department of Engineering Science University of Oxford Oxford, UK, OX1 3PJ criminis,ian,az @robots.ox.ac.uk Abstract We describe how 3D affine measurements may be com- puted 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 cameras internal calibration (e.g. focal length), nor of the explicit relation between camera and world (pose). In particular, we show how to (i) compute the distance between planes parallel to the reference plane (up to a com- mon scale factor); (ii) compute area and length ratios on any plane parallel to the reference plane; (iii) determine the cameras (viewers) 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 un- certainty with each measurement. We demonstrate the technique for a variety of applica- tions, including height measurements in forensic images and 3D graphical modelling from single images. 1. Introduction In this paper we describe how aspects of the affine 3D geometry of a scene may be measured from a single per- spective image. We will concentrate on scenes containing planes and parallel lines, although the methods are not so restricted. The methods we develop extend and generalize previous results on single view metrology [8, 9, 13, 14]. It is assumed that images are obtained by perspective projection. In addition, we assume that the vanishing line of a reference plane in the scene may be determined from the image, together with a vanishing point for another reference The authors would like to thank Andrew Fitzgibbon for assistance with the TargetJr libraries, and David Liebowitz and Luc van Gool for dis- cussions. This work was supported by the EU Esprit Project IMPROOFS. direction (not parallel to the plane). We are then concerned with three canonical types of measurement: (i) measure- ments of the distance between any of the planes which are parallel to the reference plane; (ii) measurements on these planes (and comparison of these measurements to those ob- tained on any plane); and (iii) determining the cameras po- sition in terms of the reference plane and direction. The measurement methods developed here are independent of the cameras internal parameters: focal length, aspect ratio, principal point, skew....
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- Spring '08