Image Segmentation with Context

  • Anders P. Eriksson
  • Carl Olsson
  • Fredrik Kahl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4522)


We present a technique for simultaneous segmentation and classification of image partitions using combinatorial optimization techniques. By combining existing image segmentation approaches with simple learning techniques we show how prior knowledge can be incorporated into the visual grouping process through the formulation of a quadratic binary optimization problem. We further show how such to efficiently solve such problems through relaxation techniques and trust region methods. This has resulted in an method that partitions images into a number of disjoint regions based on previously learned example segmentations. Preliminary experimental results are also presented in support of our suggested approach.


Image Segmentation Gaussian Mixture Model Trust Region Relaxation Technique Trust Region Method 
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.
    Wolkowicz, H., Saigal, R., Vandenberghe, L. (eds.): Handbook of Semidefinite Programming. Kluwer Academic Publishers, Dordrecht (2000)Google Scholar
  2. 2.
    Kolmogorov, V., Zabih, R.: What energy functions can be minimized via graph cuts? IEEE Trans. Pattern Analysis and Machine Intelligence 26(2), 147–159 (2004)CrossRefGoogle Scholar
  3. 3.
    Boykov, Y., Veksler, O., Zabih, R.: Fast approximate energy minimization via graph cuts. IEEE Trans. Pattern Analysis and Machine Intelligence 23(11), 1222–1239 (2001)CrossRefGoogle Scholar
  4. 4.
    Olsson, C., Eriksson, A.P., Kahl, F.: Solving large scale binary quadratic problems: Spectral methods vs semidefinite programming. In: CVPR (2007)Google Scholar
  5. 5.
    Kolmogorov, V., Zabih, R.: Multi-camera Scene Reconstruction via Graph Cuts. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2352, pp. 82–96. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  6. 6.
    Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Trans. Pattern Analysis and Machine Intelligence 22(8), 888–905 (2000)CrossRefGoogle Scholar
  7. 7.
    Rother, C., Kolmogorov, V., Blake, A.: ”grabcut”: interactive foreground extraction using iterated graph cuts. ACM Transactions on Graphics, 309–314 (2004)Google Scholar
  8. 8.
    Rojas, M., Santos, S., Sorensen, D.: A new matrix-free algorithm for the large-scale trust-region subproblem. SIAM Journal on optimization 11(3), 611–646 (2000)CrossRefMathSciNetzbMATHGoogle Scholar
  9. 9.
    Rojas, M., Santos, S., Sorensen, D.: Lstrs: Matlab software for large-scale trust-region subproblems and regularization. Technical Report 2003-4, Department of Mathematics, Wake Forest University (2003)Google Scholar
  10. 10.
    Fletcher, R.: Practical Methods of Optimization. John WIley & Sons, Chichester (1987)zbMATHGoogle Scholar
  11. 11.
    Sorensen, D.: Minimization of a large-scale quadratic fuction subject to a spherical constraint. SIAM J. Optim. 7(1), 141–161 (1997)CrossRefMathSciNetzbMATHGoogle Scholar
  12. 12.
    Sorensen, D.: Newton’s method with a model trust region modification. SIAM Journal on Nomerical Analysis 19(2), 409–426 (1982)CrossRefMathSciNetzbMATHGoogle Scholar
  13. 13.
    Rendl, F., Wolkowicz, H.: A semidefinite framework for trust region subproblems with applications to large scale minimization. Math. Prog. Ser. B 77(2), 273–299 (1997)MathSciNetGoogle Scholar
  14. 14.
    Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)zbMATHGoogle Scholar
  15. 15.
    Moré, J., Sorensen, D.: Computing a trust region step. SIAM J. Sci. Stat. Comput. 4(3), 553–572 (1983)CrossRefzbMATHGoogle Scholar
  16. 16.
    Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the em algorithm. J. R. Stat. Soc. (1977)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Anders P. Eriksson
    • 1
  • Carl Olsson
    • 1
  • Fredrik Kahl
    • 1
  1. 1.Centre for Mathematical Sciences, Lund University, LundSweden

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