ECCV 2004: Computer Vision - ECCV 2004 pp 509-520 | Cite as

Iso-disparity Surfaces for General Stereo Configurations

  • Marc Pollefeys
  • Sudipta Sinha
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3023)

Abstract

This paper discusses the iso-disparity surfaces for general stereo configurations. These are the surfaces that are observed at the same resolution along the epipolar lines in both images of a stereo pair. For stereo algorithms that include smoothness terms either implicitly through area-based correlation or explicitly by using penalty terms for neighboring pixels with dissimilar disparities these surfaces also represent the implicit hypothesis made during stereo matching. Although the shape of these surfaces is well known for the standard stereo case (i.e. fronto-parallel planes), surprisingly enough for two cameras in a general configuration to our knowledge their shape has not been studied. This is, however, very important since it represents the discretisation of stereo sampling in 3D space and represents absolute bounds on performance independent of later resampling. We prove that the intersections of these surfaces with an epipolar plane consists of a family of conics with three fixed points. There is an interesting relation to the human horopter and we show that for stereo the retinas act as if they were flat. Further we discuss the relevance of iso-disparity surfaces to image-pair rectification and active vision. In experiments we show how one can configure an active stereo head to align iso-disparity surfaces to scene structures of interest such as a vertical wall, allowing better and faster stereo results.

Keywords

Stereo Vision Active Vision Stereo Match Stereo Pair Warping Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aguilonius, F.: Opticorum Libri Sex, Ex off. Plantiniana apud viduam et filios Jo. Moreti, Antwerpen 1613Google Scholar
  2. 2.
    Aloimonos, Y., Weiss, I., Bandyopadhyay, A.: Active vision. In: Proc. ICCV, pp. 35-54 (1987)Google Scholar
  3. 3.
    Alvarez, L., Deriche, R., Sánchez, J., Weickert, J.: Dense Disparity Map Estimation Respecting Image Discontinuities: A PDE and Scale-Space Based Approach. Journal of Visual Communication and Image Representation 13(1/2), 3–21 (2002)CrossRefGoogle Scholar
  4. 4.
    Ayache, N., Hansen, C.: Rectification of images for binocular and trinocular stereovision. In: Proc. International Conference on Pattern Recognition, pp. 11–16 (1988)Google Scholar
  5. 5.
    Bajcsy, R.: Active Perception. Proc. of the IEEE 76, 996–1005 (1988)CrossRefGoogle Scholar
  6. 6.
    Burt, P., Wixson, L., Salgian, G.: Electronically Directed ’Focal’ Stereo. In: Proc. ICCV, pp. 97–101 (1995)Google Scholar
  7. 7.
    Chasles, M.: Traité des Sections Coniques. Gauthier-Villars, Paris (1865)Google Scholar
  8. 8.
    Fransisco, A., Bergholm, F.: On the Importance of Being Asymmetric in Stereopsis–Or Why We Should Use Skewed Parallel Cameras. IJCV 29(3), 181–202 (1998)CrossRefGoogle Scholar
  9. 9.
    Gluckman, J., Nayar, S.: Rectifying Transformations That Minimize Resampling Effects. In: Proc. CVPR, vol. 1, pp. 111–117 (2001)Google Scholar
  10. 10.
    Hartley, R.: Theory and practice of projective rectification. IJCV 35(2), 115–127 (1999)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Howard, I., Rogers, B.: Depth perception. In: Seeing in Depth, Porteous, vol. 2 (2002)Google Scholar
  12. 12.
    Jenkin, M., Tsotsos, J.: Active stereo vision and cyclotorsion. In: Proc. CVPR, pp. 806—811 (1994)Google Scholar
  13. 13.
    Laveau, S., Faugeras, O.: Oriented projective geometry for computer vision. In: Buxton, B.F., Cipolla, R. (eds.) ECCV 1996. LNCS, vol. 1064, pp. 147–156. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  14. 14.
    Levin, J.: Mathematical models for determining the intersections of quadric surfaces. Computer Graphics and Image Processing 11(1), 73–87 (1979)CrossRefGoogle Scholar
  15. 15.
    Loop, C., Zhang, Z.: Computing Rectifying Homographies for Stereo Vision. In: Proc. CVPR, vol. I, pp. 125–131 (1999)Google Scholar
  16. 16.
    Ogle, K.: An analytic treatment of the longitudinal horopter; its mesaurements and the application to related phenomena especially to the relative size and shape of the ocular images. Journal of Optical Society of America 22, 665–728 (1932)CrossRefGoogle Scholar
  17. 17.
    Ogle, K.: Researches in Binocular Vision. W.B. Saunders company, Philadelphia & London (1950)Google Scholar
  18. 18.
    Olson, T.: Stereopsis of Verging Systems. In: Proc. CVPR, pp. 55-60 (1993)Google Scholar
  19. 19.
    Papadimitriou, D., Dennis, T.: Epipolar line estimation and rectification for stereo images pairs. IEEE Transactions on Image Processing 3(4), 672–676 (1996)CrossRefGoogle Scholar
  20. 20.
    Pollefeys, M., Koch, R., Van Gool, L.: A simple and efficient rectification method for general motion. In: Proc. ICCV, pp. 496–501 (1999)Google Scholar
  21. 21.
    Roy, S., Meunier, J., Cox, I.: Cylindrical rectification to minimize epipolar distortion. In: Proc. CVPR, pp. 393–399 (1997)Google Scholar
  22. 22.
    Scharstein, D., Szeliski, R.: A Taxonomy and Evaluation of Dense Two-Frame Stereo Correspondence Algorithms. IJCV 47(1-3), 7–42 (2002)MATHCrossRefGoogle Scholar
  23. 23.
    Völpel, B., Theimer, W.M.: Localization Uncertainty In Area-Based Stereo Algorithms. TSMC (25), 1628–1634 (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Marc Pollefeys
    • 1
  • Sudipta Sinha
    • 1
  1. 1.Department of Computer ScienceUniversity of North CarolinaChapel Hill

Personalised recommendations