International Journal of Computer Vision

, Volume 69, Issue 1, pp 59–75 | Cite as

Contextual Inference in Contour-Based Stereo Correspondence

  • Gang Li
  • Steven W. Zucker


Standard approaches to stereo correspondence have difficulty when scene structure does not lie in or near the frontal parallel plane, in part because an orientation disparity as well as a positional disparity is introduced. We propose a correspondence algorithm based on differential geometry, that takes explicit advantage of both disparities. The algorithm relates the 2D differential structure (position, tangent, and curvature) of curves in the left and right images to the Frenet approximation of the (3D) space curve. A compatibility function is defined via transport of the Frenet frames, and they are matched by relaxing this compatibility function on overlapping neighborhoods along the curve. The remaining false matches are concurrently eliminated by a model of “near” and “far” neurons derived from neurobiology. Examples on scenes with complex 3D structures are provided.


stereo correspondence curve matching position disparity orientation disparity relaxation labeling 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Alibhai, S. and Zucker, S.W. 2000. Contour-based Correspondence for Stereo. In ECCV.Google Scholar
  2. Barnard, S.T. and Fischler, M.A. 1982. Computational Stereo. ACM Computing Surveys, 14(4):553–572.CrossRefGoogle Scholar
  3. Ben-Shahar, O. and Zucker, S.W. 2003. The Perceptual Organization of Texture Flow: A Contextual Inference Approach. IEEE Trans. on PAMI, 25(4):401–417.Google Scholar
  4. Brown, M.Z., Bruschka, D., and Hager, G.D. 2003. Advances in Computational Stereo. IEEE Trans. on PAMI, 25(8):993–1008.Google Scholar
  5. Canny, J. 1986. A Computational Approach to Edge Detection. IEEE Trans. on PAMI, 8(6):679–698.Google Scholar
  6. Christmas, W.J., Kittler, J., and Petrou, M. 1995. Structural Matching in Computer Vision Using Probabilistic Relaxation. IEEE Trans. on PAMI, 17(8):749–764.Google Scholar
  7. Cipolla, R. and Giblin, P. 2000. Visual Motion of Curves and Surfaces. Cambridge Univ. Press.Google Scholar
  8. Cipolla, R. and Zisserman, A. 1992. Qualitative Surface Shape from Deformation of Image Curves. International Journal of Computer Vision, 8:53–69.CrossRefGoogle Scholar
  9. David, C. and Zucker, S.W. 1990. Potentials, Valleys, and Dynamic Global Coverings. International Journal of Computer Vision, 5:219–238.CrossRefGoogle Scholar
  10. Dhond, U.R. and Aggarwal, J.K. 1989. Structure from stereo—A review. IEEE Trans. on Systems, Man, and Cybernetics, 19(6):1489–1510.MathSciNetCrossRefGoogle Scholar
  11. do Carmo, M.P. 1976. Differential Geometry of Curves and Surfaces. Prentice-Hall, Inc.Google Scholar
  12. Faugeras, O. 1993. Three-Dimensional Computer Vision. The MIT Press.Google Scholar
  13. Faugeras, O. and Robert, L. 1996. What Can Two Images Tell Us About a Third One?. International Journal of Computer Vision, 18:5–19.CrossRefGoogle Scholar
  14. Hartley, R. and Zisserman, A. 2000. Multiple View Geometry in Computer Vision. Cambridge Univ. Press.Google Scholar
  15. Howard, I.P. and Rogers, B.J. 1995. Binocular Vision and Stereopsis. Oxford Univ. Press.Google Scholar
  16. Hubel, D.H. and Wiesel, T.N. 1977. Functional Architecture of Macaque Monkey Visual Cortex. Proc. R. Soc. Lond. B., 198:1–59.CrossRefGoogle Scholar
  17. Hummel, R.A. and Zucker, S.W. 1983. On the Foundations of Relaxation Labeling Processes. IEEE Trans. on PAMI, 5(3):267–287.zbMATHGoogle Scholar
  18. Iverson, L.A. and Zucker, S.W. 1995. Logical/Linear Operators for Image Curves. IEEE Trans. on PAMI, 17(10):982–996.Google Scholar
  19. Jones, D.G. and Malik, J. 1992. Determining Three-Dimensional Shape from Orientation and Spatial Frequency Disparities. In ECCV.Google Scholar
  20. Krol, J.D. and van de Grind, W.A. 1980. The Double-nail Illusion: Experiments on Binocular Vision with Nails, Needles, and Pins. Perception, 9:651–669.Google Scholar
  21. Lehky, S. and Sejnowski, T. 1990. Neural model of stereoacuity and depth interpolation based on a distributed representation of stereo disparity. J. Neurosci, 10:2281–2299.Google Scholar
  22. Maciel, J. and Costeira, J.P. 2003. A Global Solution to Sparse Correspondence Problems. IEEE Trans. on PAMI, 25(2):187–199.Google Scholar
  23. Marr, D. 1982. Vision. W.H. Freeman and Company.Google Scholar
  24. Marr, D. and Poggio, T. 1976. Cooperative Computation of Stereo Disparity. Science, 194:283–287.Google Scholar
  25. Marr, D. and Poggio, T. 1979. A Computational Theory of Human Stereo Vision. Proc. Royal Soc. London B, 204:301–328.CrossRefGoogle Scholar
  26. Medioni, G. and Nevatia, R. 1985. Segment-Based Stereo Matching. CVGIP, 31(1):2–18.Google Scholar
  27. Nasrabadi, N.M. 1992. A Stereo Vision Technique Using Curve-Segments and Relaxation Matching. IEEE Trans. on PAMI, 14(5):566–572.Google Scholar
  28. Nemhauser, G.L. and Wolsey, L.A. 1988. Integer and Combinatorial Optimization. John Wiley & Sons Inc.Google Scholar
  29. Parent, P. and Zucker, S.W. 1989. Trace Inference, Curvature Consistency, and Curve Detection. IEEE Trans. on PAMI, 11(8):823–839.Google Scholar
  30. Poggio, G.F. and Fischer, B. 1977. Binocular interaction and depth sensitivity in striate and prestriate cortex of behaving rhesus monkey. J. Neurophys. 40: 1392–1405.Google Scholar
  31. Poggio, G.F. and Poggio T. 1984. The analysis of stereopsis. Annual Review of Neuroscience, 7: 379–412.CrossRefGoogle Scholar
  32. Pollard, S.B., Mayhew, J.E.W., and Frisby, J.P. 1985. PMF: A Stereo Correspondence Algorithm Using A Disparity Gradient Limit. Perception, 14:449–470.Google Scholar
  33. Richard, A.F. 1985. Primates in Nature. W.H. Freeman and Company.Google Scholar
  34. Robert, L. and Faugeras, O. 1991. Curve-Based Stereo: Figural Continuity And Curvature. In Proc. IEEE Conf. on Computer Vision and Pattern Recognition.Google Scholar
  35. Scharstein, D. and Szeliski, R. 2002. A Taxonomy and Evaluation of Dense Two-Frame Stereo Correspondence Algorithms. International Journal of Computer Vision, 47(1/2/3):7–42.CrossRefzbMATHGoogle Scholar
  36. Schmid, C. and Zisserman, A. 2000. The Geometry and Matching of Lines and Curves Over Multiple Views. International Journal of Computer Vision, 40(3):199–233.CrossRefzbMATHGoogle Scholar
  37. Shan, Y. and Zhang, Z. 2002. New Measurements and Corner-Guidance for Curve Matching with Probabilistic Relaxation. International Journal of Computer Vision, 46(2):157–171.CrossRefzbMATHGoogle Scholar
  38. Wildes, R.P. 1991. Direct Recovery of Three-Diemensional Scene Geometry from Binocular Stereo Disparity. IEEE Trans. on PAMI, 13(8):761–774.Google Scholar
  39. Zhang, Z. 2000. A Flexible New Technique for Camera Calibration. IEEE Trans. on PAMI, 22(11):1330–1334.Google Scholar
  40. Zitnick, C. and Kanade, T. 2000. A Cooperative Algorithm for Stereo Mathching and Occlusion Detection. IEEE Trans. on PAMI, 22(7):675–684.Google Scholar
  41. Zucker, S.W. 2004. Which Computation Runs in Visual Cortical Columns?. In J.L. van Hemmen and T. Sejnowski (Eds.), Problems in Systems Neuroscience, Oxford University Press, InPress.Google Scholar
  42. Zucker, S.W., Dobbins, A., and Iverson, L. 1989. Two Stages of Curve Detection Suggest Two Styles of Visual Computation. Neural Computation, 1:68–81.Google Scholar

Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.Department of Computer ScienceYale UniversityNew HavenU.S.A.

Personalised recommendations