Skip to main content

From Ordinal to Euclidean Reconstruction with Partial Scene Calibration

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1506))

Abstract

Since uncalibrated images permit only projective reconstruction, metric information requires either camera or scene calibration. We propose a stratified approach to projective reconstruction, in which gradual increase in domain information for scene calibration leads to gradual increase in 3D information. Our scheme includes the following steps: (1) Register the images with respect to a reference plane; this can be done using limited scene information, e.g., the knowledge that two pairs of lines on the plane are parallel. We show that this calibration is sufficient for ordinal reconstruction - sorting the points by their height over the reference plane. (2) If available, use the relative height of two additional out-of-plane points to compute the height of the remaining points up to constant scaling. Our scheme is based on the dual epipolar geometry in the reference frame, which we develop below. We show good results with five sequences of real images, using mostly scene calibration that can be inferred directly from the images themselves.

MI and DW are supported in part by DARPA through ARL Contract DAAL01-97-K-0101. This research was done while DW was on sabbatical at NECI Princeton.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Irani, P. Anandan, and D. Weinshall. From Reference Frames to Reference Planes: Multi-view Parallax Geometry and Applications In Proc. 5th ECCV, Freiburg, Germany, June 1998.

    Google Scholar 

  2. B. Boufama, D. Weinshall, and M. Werman. Shape from motion algorithms: a comparative analysis of scaled orthography and perspective. In Proc. 3rd ECCV, pages 199–204, Stockholm, Sweden, 1994.

    Google Scholar 

  3. S. Carlsson. Duality of reconstruction and positioning from projective views. In Workshop on Representations of Visual Scenes, 1995.

    Google Scholar 

  4. S. Carlsson and D. Weinshall. Dual Computation of Projective Shape and Camera Positions from Multiple Images. IJCV, 27(3), 1998.

    Google Scholar 

  5. A. Criminisi, I. Reid, and A. Zisserman. Duality, rigidity, and planar parallax. In Proc. 5th ECCV, Freiburg, Germany, June 1998.

    Google Scholar 

  6. O.D. Faugeras. What can be seen in three dimensions with an uncalibrated stereo rig? In Proc. 1st ECCV, pages 563–578, Santa Margarita Ligure, May 1992.

    Google Scholar 

  7. O.D. Faugeras. Stratification of three-dimensional vision:projective, affine and metric representations. JOSA, 12(3):465–484, March 1995.

    Google Scholar 

  8. O. Faugeras and B. Mourrain. On the geometry and algebra of the point and line correspondences between N images. In Proc. ECW. Xidian University Press, 1995.

    Google Scholar 

  9. Richard Hartley. Euclidean Reconstruction from Uncalibrated Views. In Applications of Invariance in Computer Vision, J.L. Mundy, D. Forsyth, and A. Zisserman (Eds.), Springer-Verlag, 1993.

    Google Scholar 

  10. M. Irani and P. Anandan. Parallax geometry of pairs of points for 3D scene analysis. In Proc. 3rd ECCV, Cambridge, UK, April 1996.

    Google Scholar 

  11. M. Irani and P. Anandan. A unified approach to moving object detection in 2D and 3D scenes. IEEE Trans. on PAMI, in press.

    Google Scholar 

  12. J. J. Koenderink and A. J. van Doorn. Affine structure from motion. JOSA, 8(2):377–385, 1991.

    Google Scholar 

  13. R. Kumar, P. Anandan, and K. Hanna. Direct recovery of shape from multiple views: a parallax based approach. In Proc 12th ICPR, 1994.

    Google Scholar 

  14. R. Mohr,, L. Quan, F. Veillon, and B. Boufama. Relative 3D reconstruction using multiple uncalibrated images. RT 84-IMAG-12 LIFIA, Uni. of Grenoble, 1992.

    Google Scholar 

  15. H. S. Sawhney, J. Oliensis, and A. R. Hanson. Description and reconstruction from image trajectories of rotational motion. In Proc. 3rd ICCV, Osaka, Japan, 1990.

    Google Scholar 

  16. L. Robert and O.D. Faugeras. Relative 3D Positioning and 3D Convex Hull Computation from a Weakly Calibrated Stereo Pair. J. Imaging and Vision Compting, 13(3), 1995.

    Google Scholar 

  17. M. Pollyfeys, R. Koch, and L. van Gool. Self-calibration and Metric Reconstruction in Spite of Varying and Unknown Internal Camera Parameters. In Proc. 6th ICCV, Mumbai, India, January 1998.

    Google Scholar 

  18. A. Shashua and N. Navab. Relative affine structure: Theory and application to 3D reconstruction from perspective views. In Proc. CVPR:483–489, Seattle, 1994.

    Google Scholar 

  19. R. Szeliski and H. Shum. Creating full view panoramic mosaics and texture-mapped models. In Proc. SIGGRAPH 97, pp. 251–258, Los Angels, 1997.

    Google Scholar 

  20. D. Weinshall, M. Werman, and A. Shashua. Shape Tensors for Efficient and Learnable Indexing. In Workshop on Representations of Visual Scenes, 1995.

    Google Scholar 

  21. A. Zisserman. Active Visual Navigation using Non-Metric Structure. In Proc. 5th ICCV, Boston, USA, 1995.

    Google Scholar 

  22. Z. Zhang, R. Weiss and A. Hanson. Obstacle Detection Using Qualitative and Quantitative 3D Reconstruction. In IEEE PAMI, 19(2):15–26, January 1997.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Weinshall, D., Anandan, P., Irani, M. (1998). From Ordinal to Euclidean Reconstruction with Partial Scene Calibration. In: Koch, R., Van Gool, L. (eds) 3D Structure from Multiple Images of Large-Scale Environments. SMILE 1998. Lecture Notes in Computer Science, vol 1506. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49437-5_14

Download citation

  • DOI: https://doi.org/10.1007/3-540-49437-5_14

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65310-3

  • Online ISBN: 978-3-540-49437-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics