Minimal Surfaces for Stereo

  • Chris Buehler
  • Steven J. Gortler
  • Michael F. Cohen
  • Leonard McMillan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2352)


Determining shape from stereo has often been posed as a global minimization problem. Once formulated, the minimization problems are then solved with a variety of algorithmic approaches. These approaches include techniques such as dynamic programming min-cut and alpha-expansion. In this paper we show how an algorithmic technique that constructs a discrete spatial minimal cost surface can be brought to bear on stereo global minimization problems. This problem can then be reduced to a single min-cut problem. We use this approach to solve a new global minimization problem that naturally arises when solving for three-camera (trinocular) stereo. Our formulation treats the three cameras symmetrically, while imposing a natural occlusion cost and uniqueness constraint.


Minimal Surface Uniqueness Constraint Dual Graph Primal Graph Spatial Complex 
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.


  1. 1.
    N. Ayache and C. Hansen. Rectification of images for binocular and trinocular stereovision. Proc. International Conference on Pattern Recognition 1998, pages 11–16.Google Scholar
  2. 2.
    H. Baker. Depth from edge and intensity based stereo. PhD thesis, University of Illinois at Urbina Chanmpaign, 1981.Google Scholar
  3. 3.
    P. Belumeur and D. Mumford. A bayesian treatment of the stereo correspondance problem using half-occluded regions. IEEE CVPR’ 92.Google Scholar
  4. 4.
    S. Birchfield and C. Tomasi. A pixel dissimilarity measure that is insensitive to image sampling. IEEE PAMI, 20(4):401–406, 1998.Google Scholar
  5. 5.
    C. Chekuri, A. Goldberg, D. Karger, M. Levine, and C. Stein. Experimental study of minimum cut algorithms. Proc ACM SODA, 1997.Google Scholar
  6. 6.
    B. Cherkassky and A. Goldberg. Prf library from
  7. 7.
    T. Cormen, C. Leiserson, and R. Rivest. Introduction to Algorithms. MIT Press, 2001.Google Scholar
  8. 8.
    I. Cox, S. Hingorani, B. Maggas, and S. Rao. A maximum likelihood stereo algorithm. Computer vision and image understanding, 63(3), 1996.Google Scholar
  9. 9.
    D. Geiger, B. Landendorf, and A. Yuille. Occlusion and binocular stereo. IJCV, 14:211–226, 1995.CrossRefGoogle Scholar
  10. 10.
    Aaron Isaksen. toys dataset by request.Google Scholar
  11. 11.
    H. Ishikawa and D. Geiger. Occlusions, discontinuities, and epipolar lines in stereo. Proc. ECCV98.Google Scholar
  12. 12.
    V. Kolmogorov and R. Zabih. Computing visual correspondence with occlusions using graph cuts. Proc. ICCV 2001.Google Scholar
  13. 13.
    Y. Ohta and T. Kanade. Stereo by intra and inter scanline search using dynamic programming. IEEEPAMI, 7(2):139–154, 1985.Google Scholar
  14. 14.
    J. O’Rourke. Computational Geometry in C. Cambridge University Press, 1994.Google Scholar
  15. 15.
    S. Roy and I. Cox. A maximum-flow formulation of the n-camera stereo correspondence problem. Proc. ICCV 1998.Google Scholar
  16. 16.
    S. Seitz and C. Dyer. Photorealistic scene reconstruction by voxel coloring. IJCV, 35(2):151–173, 1999.CrossRefGoogle Scholar
  17. 17.
    D. Snow, P. Viola, and R. Zabih. Exact voxel occupancy with graph cuts. Proc. IEEE CVPR 2000.Google Scholar
  18. 18.
    J. Sullivan. A Crystalline Approximation Theorem for Hypersurfaces. PhD thesis, Dept. of Mathematics, Princeton University, 1990.Google Scholar
  19. 19.
    Y. Boykov, O. Veksler, and R. Zabih. Fast approximate energy minimization via graph cuts. Proc. ICCV 1999.Google Scholar
  20. 20.
    Y. Boykov, O. Veksler, and R. Zabih. Markov random fields with efficient approximations. Proc. IEEE CVPR 1998.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Chris Buehler
    • 1
  • Steven J. Gortler
    • 2
  • Michael F. Cohen
    • 3
  • Leonard McMillan
    • 4
  2. 2.Harvard UniversityUSA
  3. 3.Microsoft ResearchUSA

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