Advertisement

Stable Bounded Canonical Sets and Image Matching

  • John Novatnack
  • Trip Denton
  • Ali Shokoufandeh
  • Lars Bretzner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3757)

Abstract

A common approach to the image matching problem is representing images as sets of features in some feature space followed by establishing correspondences among the features. Previous work by Huttenlocher and Ullman [1] shows how a similarity transformation – rotation, translation, and scaling – between two images may be determined assuming that three corresponding image points are known. While robust, such methods suffer from computational inefficiencies for general feature sets. We describe a method whereby the feature sets may be summarized using the stable bounded canonical set (SBCS), thus allowing the efficient computation of point correspondences between large feature sets. We use a notion of stability to influence the set summarization such that stable image features are preferred.

Keywords

Reference Image Scale Invariant Feature Transform Image Match Integer Programming Problem Improve Approximation Algorithm 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Huttenlocher, D.P., Ullman, S.: Recognizing solid objects by alignment with an image. International Journal of Computer Vision 5(2), 195–212 (1990)CrossRefGoogle Scholar
  2. 2.
    Lindeberg, T.: Detecting Salient Blob–Like Image Structures and Their Scales With a Scale–Space Primal Sketch—A Method for Focus–of–Attention. IJCV 11, 283–318 (1993)CrossRefGoogle Scholar
  3. 3.
    Bretzner, L., Lindeberg, T.: Qualitative multi-scale feature hierarchies for object tracking. Journal of Visual Communication and Image Representation 11, 115–129 (2000)CrossRefGoogle Scholar
  4. 4.
    Goemans, M.X., Williamson, D.P.: Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming. J. Assoc. Comput. Mach. 42, 1115–1145 (1995)zbMATHMathSciNetGoogle Scholar
  5. 5.
    Denton, T., Abrahamson, J., Shokoufandeh, A.: Approximation of canonical sets and their application to 2d view simplification. In: CVPR, vol. 2, pp. 550–557 (2004)Google Scholar
  6. 6.
    Denton, T., Demirci, M.F., Abrahamson, J., Shokoufandeh, A.: Selecting canonical views for view-based 3-d object recognition. In: ICPR, pp. 273–276 (2004)Google Scholar
  7. 7.
    Cover, T., Thomas, J.: Elements of Information Theory: Rate Distortion Theory. John Wiley & Sons, Chichester (1991)zbMATHCrossRefGoogle Scholar
  8. 8.
    Tishby, N., Pereira, F., Bialek, W.: The information bottleneck method. In: Proceedings of the 37-th Annual Allerton Conference on Communication, Control and Computing, pp. 368–377 (1999)Google Scholar
  9. 9.
    Hermes, L., Zoller, T., Buhmann, J.M.: Parametric distributional clustering for image segmentation. In: Proceedings, European Conference on Computer Vision, pp. 577–591 (2002)Google Scholar
  10. 10.
    Gordon, S., Greenspan, H., Goldberger, J.: Applying the information bottleneck principle to unsupervised clustering of discrete and continuous image representations. In: Proceedings, International Conference on Computer Vision, Nice, France (2003)Google Scholar
  11. 11.
    Liu, H., Motoda, H.: Feature transformation and subset selection. IEEE Intelligent Systems 13, 26–28 (1998)Google Scholar
  12. 12.
    Cyr, C.M., Kimia, B.: 3d object recognition using shape similarity-based aspect graph. In: 8th Inter. Conf. Comp. Vision, pp. 254–261 (2001)Google Scholar
  13. 13.
    Goemans, M.X., Williamson, D.P.: 878-approximation algorithms for max cut and max 2sat. In: Twenty-sixth Annual ACM Symposium on Theory of Computing, New York, pp. 422–431 (1994)Google Scholar
  14. 14.
    Goemans, M.X.: Semidefinite programming in combinatorial optimization. Mathematical Programming 79, 143–161 (1997)MathSciNetzbMATHGoogle Scholar
  15. 15.
    Mahajan, S., Ramesh, H.: Derandomizing approximation algorithms based on semidefinite programming. SIAM Journal on Computing 28, 1641–1663 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Huttenlocher, D., Ullman, S.: Object recognition using alignment. In: Proceedings, First International Conference on Computer Vision, London, UK, pp. 102–111 (1987)Google Scholar
  17. 17.
    Huttenlocher, D., Ullman, S.: Recognizing solid objects by alignment with an image. International Journal of Computer Vision 5, 195–212 (1990)CrossRefGoogle Scholar
  18. 18.
    Irani, S., Raghavan, P.: Combinatorial and experimental results for randomized point matching algorithms. In: SCG 1996: Proceedings of the twelfth annual symposium on Computational geometry, pp. 68–77. ACM Press, New York (1996)CrossRefGoogle Scholar
  19. 19.
    Ratan, A.L., Grimson, W.E.L., Wells, W.M.I.: Object detection and localization by dynamic template warping. International Journal on Computer Vision 36, 131–147 (2000)CrossRefGoogle Scholar
  20. 20.
    Meer, P., Lenz, R., Ramakrishna, S.: Efficient invariant representations. Int. J. Comput. Vision 26, 137–152 (1998)CrossRefGoogle Scholar
  21. 21.
    Harris, C., Stephens, M.: A combined corner and edge detector. In: 4th ALVEY vision conference, pp. 147–151 (1988)Google Scholar
  22. 22.
    Lowe, D.G.: Object recognition from local scale-invariant features. In: Proc. of the International Conference on Computer Vision ICCV, Corfu., pp. 1150–1157 (1999)Google Scholar
  23. 23.
    Blum, A.L., Langley, P.: Selection of relevant features and examples in machine learning. Artificial Intelligence 97, 245–271 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Berchtold, S., Böhm, C., Kriegel, H.P.: The pyramid-tree: Breaking the curse of dimensionality. In: Haas, L.M., Tiwary, A. (eds.) SIGMOD 1998, Proceedings ACM SIGMOD International Conference on Management of Data, Seattle, Washington, USA, June 2-4, pp. 142–153. ACM Press, New York (1998)CrossRefGoogle Scholar
  25. 25.
    Pagel, B.U., Korn, F., Faloutsos, C.: Deflating the dimensionality curse using multiple fractal dimensions. In: ICDE 2000: Proceedings of the 16th International Conference on Data Engineering, p. 589. IEEE Computer Society, Washington (2000)Google Scholar
  26. 26.
    Gary, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-completeness. Freeman, San Francisco (ND2,SR1) (1979)Google Scholar
  27. 27.
    Garey, M.R., Johnson, D.S.: Computers and intractability: A guide to the theory of NP-completeness. W.H. Freeman and Co., Baltimore (1979)zbMATHGoogle Scholar
  28. 28.
    Ehrgott, M.: Multicriteria Optimization. Lecture Notes in Economics and Mathematical Systems, vol. 491. Springer, New York (2000)zbMATHGoogle Scholar
  29. 29.
    Miettinen, K.M.: Nonlinear Multiobjective Optimization. Kluwer Academic Publishers, Dordrecht (1999)zbMATHGoogle Scholar
  30. 30.
    Alizadeh, F.: Interior point methods in semidefinite programming with applications to combinatorial optimization. SIAM J. Optim. 5, 13–51 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  31. 31.
    Toh, K.C., Todd, M.J., Tutuncu, R.: SDPT3 — a Matlab software package for semidefinite programming. Optimization Methods and Software 11, 545–581 (1999)CrossRefMathSciNetGoogle Scholar
  32. 32.
    Golub, G., Loan, C.: Matrix Computations. The Johns Hopkins University Press, Baltimore (1996)zbMATHGoogle Scholar
  33. 33.
    Nene, S.A., Nayar, S.K., Murase, H.: Columbia object image library, Coil (1996)Google Scholar
  34. 34.
    Demirci, M.F., Shokoufandeh, A., Dickinson, S., Keselman, Y., Bretzner, L.: Many-to-many graph feature matching using spherical coding of directed graphs. In: ECCV (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • John Novatnack
    • 1
  • Trip Denton
    • 1
  • Ali Shokoufandeh
    • 1
  • Lars Bretzner
    • 2
  1. 1.Department of Computer ScienceDrexel University 
  2. 2.Computational Vision and Active Perception Laboratory, Department Of Numerical Analysis and Computer ScienceKTH, StockholmSweden

Personalised recommendations