Skip to main content
SpringerLink
Log in

Single View Metrology

  • Published:
International Journal of Computer Vision Aims and scope Submit manuscript

Abstract

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 (i) compute the distance between planes parallel 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) determine the camera'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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Alberti, L.B. 1980. De Pictura. 1435. Reproduced by Laterza.

  • Barnard, S.T. 1983. Interpreting perspective images. Artificial Intelligence, 21(3):435–462.

    Google Scholar 

  • Berger, M. 1987. Geometry II. Springer-Verlag.

  • Canny, J.F. 1986. A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 8(6):679–698.

    Google Scholar 

  • Caprile, B. and Torre, V. 1990. Using vanishing points for camera calibration. International Journal of Computer Vision, 127–140.

  • Clarke, J.C. 1998. Modelling uncertainty:Aprimer. Technical Report 2161/98, University of Oxford, Dept. Engineering Science.

  • Collins, R.T. and Weiss, R.S. 1990. Vanishing point calculation as a statistical inference on the unit sphere. In Proc. 3rd International Conference on Computer Vision, Osaka, pp. 400–403.

  • Criminisi, A., Reid, I., and Zisserman, A. 1999a. A plane measuring device. Image and Vision Computing, 17(8):625–634.

    Google Scholar 

  • Criminisi, A., Reid, I., and Zisserman, A. 1999b. Single view metrology. In Proc. 7th International Conference on Computer Vision Kerkyra, Greece, pp. 434–442.

  • Devernay, F. and Faugeras, O.D. 1995. Automatic calibration and removal of distortion from scenes of structured environments. The International Society for Optimal Engineering. In SPIE, Vol. 2567, San Diego, CA.

  • Faugeras, O.D. 1993. Three-Dimensional Computer Vision: A Geometric Viewpoint. MIT Press.

  • Golub, G.H. and Van Loan, C.F. 1989. Matrix Computations, 2nd edn. The John Hopkins University Press: Baltimore, MD.

    Google Scholar 

  • Horry, Y., Anjyo, K., and Arai, K. 1997. Tour into the picture: Using a spidery mesh interface to make animation from a single image. In Proceedings of the ACM SIGGRAPH Conference on Computer Graphics, pp. 225–232.

  • Kim, T., Seo, Y., and Hong, K. 1998. Physics-based 3D position analysis of a soccer ball from monocular image sequences. In Proc. International Conference on Computer Vision, pp. 721–726.

  • Koenderink, J.J. and van Doorn, A.J. 1991. Affine structure from motion. J. Opt. Soc. Am. A, 8(2):377–385.

    Google Scholar 

  • Liebowitz, D., Criminisi, A., and Zisserman, A. 1999. Creating architectural models from images. In Proc. EuroGraphics, Vol. 18, pp. 39–50.

    Google Scholar 

  • Liebowitz, D. and Zisserman, A. 1998. Metric rectification for perspective images of planes. In Proceedings of the Conference on Computer Vision and Pattern Recognition, pp. 482–488.

  • McLean, G.F. and Kotturi, D. 1995. Vanishing point detection by line clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(11):1090–1095.

    Google Scholar 

  • Proesmans, M., Tuytelaars, T., and Van Gool, L.J. 1998. Monocular image measurements. Technical Report Improofs-M12T21/1/P, K.U. Leuven.

  • Quan, L. and Mohr, R. 1992. Affine shape representation from motion through reference points. Journal of Mathematical Imaging and Vision 1:145–151.

    Google Scholar 

  • Reid, I.D. and North, A. 1998. 3D trajectories from a single viewpoint using shadows. In Proc. British Machine Vision Conference.

  • Reid, I. and Zisserman, A. 1996. Goal-directed video metrology. In Proc. 4th European Conference on Computer Vision, LNCS 1065 R. Cipolla and B. Buxton (Eds.). Vol. 2, Springer: Cambridge, pp. 647–658.

    Google Scholar 

  • Robert, L. and Faugeras, O.D. 1993. Relative 3D positioning and 3D convex hull computation from a weakly calibrated stereo pair. In Proc. 4th International Conference on Computer Vision, Berlin pp. 540–544.

  • Shapiro, L.S. and Brady, J.M. 1995. Rejecting outliers and estimating errors in an orthogonal regression framework. Philosophical Transactions of the Royal Society of London, SERIES A, 350:407–439.

    Google Scholar 

  • Shufelt, J.A. 1999. Performance and analysis of vanishing point detection techniques. IEEE Transactions on Pattern Analysis and Machine Intelligence, 21(3):282–288.

    Google Scholar 

  • Springer, C.E. 1964. Geometry and Analysis of Projective Spaces. Freeman.

  • Stewart, G.W. and Sun, J. 1990. Matrix Perturbation Theory. Academic Press Inc., USA.

    Google Scholar 

  • Sturm, P. and Maybank, S. 1999. A method for interactive 3D reconstruction of pieceware planar objects from single images. In Proc. 10th British Machine Vision Conference, Nottingham.

  • Van Gool, L., Proesmans, M., and Zisserman, A. 1998. Planar homologies as a basis for grouping and recognition. Image and Vision Computing, 16:21–26.

    Google Scholar 

  • Viéville, T. and Lingrand, D. 1999. Using specific displacements to analyze motion without calibration. International Journal of Computer Vision, 31(1):5–30.

    Google Scholar 

  • Weng, J., Huang, T.S., and Ahuja, N. 1989. Motion and structure from two perspective views: Algorithms, error analysis and error estimation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(5):451–476.

    Google Scholar 

  • Wilkinson, J.H. 1965. The Algebraic Eigenvalue Problem. Clarendon Press, Oxford.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Engineering Science, University of Oxford, Parks Road, Oxford, OX1 3PJ, UK

    A. Criminisi, I. Reid & A. Zisserman

Authors
  1. A. Criminisi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. Reid
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Zisserman
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Criminisi, A., Reid, I. & Zisserman, A. Single View Metrology. International Journal of Computer Vision 40, 123–148 (2000). https://doi.org/10.1023/A:1026598000963

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1026598000963

Search

Navigation