Skip to main content
SpringerLink
Log in

Contextual Inference in Contour-Based Stereo Correspondence

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

Abstract

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.

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

  • Alibhai, S. and Zucker, S.W. 2000. Contour-based Correspondence for Stereo. In ECCV.

  • Barnard, S.T. and Fischler, M.A. 1982. Computational Stereo. ACM Computing Surveys, 14(4):553–572.

    Article  Google Scholar 

  • 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 

  • Brown, M.Z., Bruschka, D., and Hager, G.D. 2003. Advances in Computational Stereo. IEEE Trans. on PAMI, 25(8):993–1008.

    Google Scholar 

  • Canny, J. 1986. A Computational Approach to Edge Detection. IEEE Trans. on PAMI, 8(6):679–698.

    Google Scholar 

  • 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 

  • Cipolla, R. and Giblin, P. 2000. Visual Motion of Curves and Surfaces. Cambridge Univ. Press.

  • Cipolla, R. and Zisserman, A. 1992. Qualitative Surface Shape from Deformation of Image Curves. International Journal of Computer Vision, 8:53–69.

    Article  Google Scholar 

  • David, C. and Zucker, S.W. 1990. Potentials, Valleys, and Dynamic Global Coverings. International Journal of Computer Vision, 5:219–238.

    Article  Google Scholar 

  • Dhond, U.R. and Aggarwal, J.K. 1989. Structure from stereo—A review. IEEE Trans. on Systems, Man, and Cybernetics, 19(6):1489–1510.

    Article  MathSciNet  Google Scholar 

  • do Carmo, M.P. 1976. Differential Geometry of Curves and Surfaces. Prentice-Hall, Inc.

  • Faugeras, O. 1993. Three-Dimensional Computer Vision. The MIT Press.

  • Faugeras, O. and Robert, L. 1996. What Can Two Images Tell Us About a Third One?. International Journal of Computer Vision, 18:5–19.

    Article  Google Scholar 

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

  • Howard, I.P. and Rogers, B.J. 1995. Binocular Vision and Stereopsis. Oxford Univ. Press.

  • Hubel, D.H. and Wiesel, T.N. 1977. Functional Architecture of Macaque Monkey Visual Cortex. Proc. R. Soc. Lond. B., 198:1–59.

    Article  Google Scholar 

  • Hummel, R.A. and Zucker, S.W. 1983. On the Foundations of Relaxation Labeling Processes. IEEE Trans. on PAMI, 5(3):267–287.

    MATH  Google Scholar 

  • Iverson, L.A. and Zucker, S.W. 1995. Logical/Linear Operators for Image Curves. IEEE Trans. on PAMI, 17(10):982–996.

    Google Scholar 

  • Jones, D.G. and Malik, J. 1992. Determining Three-Dimensional Shape from Orientation and Spatial Frequency Disparities. In ECCV.

  • 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 

  • 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 

  • Maciel, J. and Costeira, J.P. 2003. A Global Solution to Sparse Correspondence Problems. IEEE Trans. on PAMI, 25(2):187–199.

    Google Scholar 

  • Marr, D. 1982. Vision. W.H. Freeman and Company.

  • Marr, D. and Poggio, T. 1976. Cooperative Computation of Stereo Disparity. Science, 194:283–287.

    Google Scholar 

  • Marr, D. and Poggio, T. 1979. A Computational Theory of Human Stereo Vision. Proc. Royal Soc. London B, 204:301–328.

    Article  Google Scholar 

  • Medioni, G. and Nevatia, R. 1985. Segment-Based Stereo Matching. CVGIP, 31(1):2–18.

    Google Scholar 

  • Nasrabadi, N.M. 1992. A Stereo Vision Technique Using Curve-Segments and Relaxation Matching. IEEE Trans. on PAMI, 14(5):566–572.

    Google Scholar 

  • Nemhauser, G.L. and Wolsey, L.A. 1988. Integer and Combinatorial Optimization. John Wiley & Sons Inc.

  • Parent, P. and Zucker, S.W. 1989. Trace Inference, Curvature Consistency, and Curve Detection. IEEE Trans. on PAMI, 11(8):823–839.

    Google Scholar 

  • 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 

  • Poggio, G.F. and Poggio T. 1984. The analysis of stereopsis. Annual Review of Neuroscience, 7: 379–412.

    Article  Google Scholar 

  • 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 

  • Richard, A.F. 1985. Primates in Nature. W.H. Freeman and Company.

  • Robert, L. and Faugeras, O. 1991. Curve-Based Stereo: Figural Continuity And Curvature. In Proc. IEEE Conf. on Computer Vision and Pattern Recognition.

  • 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.

    Article  MATH  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • 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 

  • Zhang, Z. 2000. A Flexible New Technique for Camera Calibration. IEEE Trans. on PAMI, 22(11):1330–1334.

    Google Scholar 

  • 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 

  • 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.

  • 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 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Yale University, New Haven, CT, 06520, U.S.A.

    Gang Li & Steven W. Zucker

Authors
  1. Gang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Steven W. Zucker
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gang Li.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, G., Zucker, S.W. Contextual Inference in Contour-Based Stereo Correspondence. Int J Comput Vision 69, 59–75 (2006). https://doi.org/10.1007/s11263-006-6853-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11263-006-6853-9

Keywords

Search

Navigation