Skip to main content
SpringerLink
Log in

Linear Multi View Reconstruction and Camera Recovery Using a Reference Plane

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

Abstract

This paper presents a linear algorithm for simultaneous computation of 3D points and camera positions from multiple perspective views based on having a reference plane visible in all views. The reconstruction and camera recovery is achieved in a single step by finding the null-space of a matrix built from image data using Singular Value Decomposition. Contrary to factorization algorithms this approach does not need to have all points visible in all views. This paper investigates two reference plane configurations: Finite reference planes defined by four coplanar points and infinite reference planes defined by vanishing points. A further contribution of this paper is the study of critical configurations for configurations with four coplanar points. By simultaneously reconstructing points and views we can exploit the numerical stabilizing effect of having wide spread cameras with large mutual baselines. This is demonstrated by reconstructing the outsideand inside (courtyard) of a building on the basis of 35 views in one single Singular Value Decomposition.

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

  • Caprile, B. and Torre, V. 1990. Using vanishing points for camera calibration. Int. J. Computer Vision, 4:127–139.

    Google Scholar 

  • Carlsson, S. 1995. Duality of reconstruction and positioning from projective views. In IEEE Workshop on Representation of Visual Scenes, P. Anandan (Ed.), Boston, USA.

  • Carlsson, S. and Weinshall, D. 1998. Dual computation of projective shape and camera positions from multiple images. Int. J. Computer Vision, 27(3):227–241.

    Google Scholar 

  • Criminisi, A., Reid, I., and Zisserman, A. 1998. Duality, rigidity and planar parallax. In European Conf. Computer Vision, Springer-Verlag, Freiburg, Germany, pp. 846–861.

    Google Scholar 

  • Cross, G., Fitzgibbon, A.W., and Zisserman, A. 1999. Parallax geometry of smooth surfaces in multiple views. In Int. Conf. Computer Vision, Kerkyra, Greece, pp. 323–329.

  • Faugeras, O.D. 1992. What can be seen in three dimensions with an uncalibrated stereo rig? In European Conf. Computer Vision, D. Sandini (Ed.), Santa Margherita Ligure, Italy, Springer-Verlag, pp. 563–578.

    Google Scholar 

  • Faugeras, O.D. and Luong, Q.-T. 2001. The Geometry of Multiple Images. The MIT Press: Cambridge, MA.

    Google Scholar 

  • Fitzgibbon, A.W. and Zisserman, A. 1998. Automatic camera recovery for closed or open image sequences. In European Conf. Computer Vision, Freiburg, Germany, pp. 311–326.

  • Hartley, R. 1997. In defence of the 8-point algorithm. IEEE Transactions on Pattern Analysis and Machine Intelligence, 19(6):580–593.

    Google Scholar 

  • Hartley, R. 2000. Ambiguous configurations for 3-view projective reconstruction. In European Conf. Computer Vision, Dublin, Ireland, pp. 922–935.

  • Hartley, R. and Debunne, G. 1998. Dualizing scene reconstruction algorithms. In Workshop on 3D Structure from Multiple Images of Large-scale Environments (SMILE-98), R. Koch and L. Van Gool, (Eds.), LNCS, vol. 1506, Springer-Verlag: Berlin, pp. 14–31.

    Google Scholar 

  • Hartley, R. and Zisserman, A. 2000. Multiple View Geometry in Computer Vision. Cambridge University Press: Cambridge.

    Google Scholar 

  • Hartley, R., Dano, N., and Kaucic, R. 2001. Plane-based projective reconstruction. In Int. Conf. Computer Vision, Vancouver, Canada, pp. 420–427.

  • Heyden, A. 1998. Reduced multilinear constraints-theory and experiments. Int. J. Computer Vision, 30(1):5–26.

    Google Scholar 

  • Heyden, A. and Åström, K. 1995. A canonical framework for sequences of images. In IEEE Workshop on Representation of Visual Scenes, P. Anandan (Ed.), Boston, USA.

  • Heyden, A. and Åström, K. 1997. Simplifications of multilinear forms for sequences of images. Image and Vision Computing, 15(10):749–757.

    Google Scholar 

  • Heyden, A., Berthilsson, R., and Sparr, G. 1999. An iterative factorization method for projective structure and motion from image sequences. Image and Vision Computing, 17(13):981–991.

    Google Scholar 

  • Irani, M. and Anandan, P. 1996. Parallax geometry of pairs of points for 3d scene analysis. In European Conf. Computer Vision, Cambridge, UK, Springer-Verlag, pp. 17–30.

    Google Scholar 

  • Irani, M., Anandan, P., and Weinshall, D. 1998. From reference frames to reference planes: Multi-view parallax geometry and applications. In European Conf. Computer Vision, Freiburg, Germany, Springer-Verlag, pp. 829–845.

    Google Scholar 

  • Jacobs, D. 1997. Linear fitting with missing data for structure-from-motion. In IEEE Conf. Computer Vision and Pattern Recognition, San Juan, Puerto Rico, pp. 206–212.

  • Koch, R., Pollefeys, M., and VanGool, L. 1998. Multi viewpoint stereo from uncalibrated video sequences. In European Conf. Computer Vision, Freiburg, Germany, Springer-Verlag, pp. 55–65.

    Google Scholar 

  • Krames, J. 1942. Über die bei der Hauptaufgabe der Luftphotogram-metrie auftretenden “gefährlichen” Flächen. Bildmessung und Luftbildwesen, 17, Heft 1/2:1–18.

    Google Scholar 

  • Kumar, R., Anandan, P., and Hanna, K. 1994. Direct recovery of shape from multiple views: A parallax based approach. In Int. Conf. Pattern Recognition, Jerusalem, Israel, pp. 685–688.

  • Liebowitz, D. and Zisserman, A. 1999. Combining scene and auto-calibration constraints. In Int. Conf. Computer Vision, Kerkyra, Greece, pp. 293–300.

  • Maybank, S.J. 1992. Theory of Reconstruction from Image Motion. Springer-Verlag: Berlin.

    Google Scholar 

  • Oliensis, J. 1995. Multiframe structure from motion in perspective. In Workshop on Representations of Visual Scenes, Boston, USA, pp. 77–84.

  • Oliensis, J. 1999. A multi-frame structure-from-motion algorithm under perspective projection. Int. J. Computer Vision, 34(2/3):163–192.

    Google Scholar 

  • Oliensis J. and Genc, Y. 1999. Fast algorithms for projective multi-frame structure from motion. In Int. Conf. Comp. Vision, Kerkyra, Greece, pp. 536–542.

  • Qian, C. and Medioni, G. 1999. Efficient iterative solution to M-view projective reconstruction problem. In IEEE Conf. Computer Vision and Pattern Recognition, Fort Collins, Colorado, pp. 55–61.

  • Quan, L. 1994. Invariants of 6 points from 3 uncalibrated images. In European Conf. Computer Vision, Stockholm, Sweden, Springer-Verlag, pp. 459–470.

    Google Scholar 

  • Quan, L., Heyden A., and Kahl, F. 1999. Minimal projective reconstruction with missing data. In IEEE Conf. Computer Vision and Pattern Recognition, Fort Collins, Colorado, pp. 210–216.

  • Rother, C. 2000. A new approach for vanishing point detection in architectural environments. In 11th British Machine Vision Conference, Bristol, UK, pp. 382–391.

  • Rother, C. and Carlsson, S. 2001. Linear multi view reconstruction and camera recovery. In Int. Conf. Computer Vision, Vancouver, Canada, pp. 42–51.

  • Schaffalitzky, F., Zisserman, A., Hartley, R.I., and Torr, P.H.S. 2000. A six point solution for structure and motion. In European Conf. Computer Vision, Dublin, Ireland, Springer-Verlag, pp. 632–648.

    Google Scholar 

  • Sparr, G. 1996. Simultaneous reconstruction of scene structure and camera locations from uncalibrated image sequences. In IEEE Conf. Computer Vision and Pattern Recognition, Vienna, Austria, pp. 328–333.

  • Sturm, P. and Triggs, B. 1996. A factorization based algorithm for multi-image projective structure and motion. In European Conf. Computer Vision, Cambridge, UK, Springer-Verlag, pp. 709–719.

    Google Scholar 

  • Svedberg, D. and Carlsson, S. 1999. Calibration, pose and novel views from single images of constrained scenes. In Scandanavian Conf. Image Analysis, Kangerlussuaq, Greenland, pp. 111–118.

  • Tomasi, C. and Kanade, T. 1992. Shape and motion from image streams under orthography: A factorization method. Int. J. Computer Vision, 9(2):137–154.

    Google Scholar 

  • Triggs, B. 2000. Plane + parallax, tensors and factorization. In European Conf. Computer Vision, Dublin, Ireland, Springer-Verlag, pp. 522–538.

    Google Scholar 

  • Triggs, B., McLauchlan, P., Hartley, R., and Fitzgibbon, A. 1999. Bundle adjustment-A modern synthesis. In IEEE Workshop on Vision Algorithms, Kerkyra, Greece, pp. 298–376.

  • Weinshall, D., Anandan, P., and Irani, M. 1998. From ordinal to euclidean reconstruction with partial scene calibration. In Workshop on 3D Structure from Multiple Images of Large-scale Environments (SMILE-98), R. Koch and L. Van Gool (Eds.), LNCS, vol. 1506, Springer-Verlag: Berlin, pp. 208–223.

    Google Scholar 

  • Weinshall, D., Werman, M., and Shashua, A. 1995. Shape tensors for efficient and learnable indexing. In IEEE Workshop on Representation of Visual Scenes, pp. 58–65.

Download references

Author information

Authors and Affiliations

  1. Department of Numerical Analysis and Computer Science, KTH, Computational Vision and Active Perception Laboratory (CVAP), SE-100 44, Stockholm, Sweden

    Carsten Rother & Stefan Carlsson

Authors
  1. Carsten Rother
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stefan Carlsson
    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

Rother, C., Carlsson, S. Linear Multi View Reconstruction and Camera Recovery Using a Reference Plane. International Journal of Computer Vision 49, 117–141 (2002). https://doi.org/10.1023/A:1020189404787

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1020189404787

Search

Navigation