Linear Programming Matching and Appearance-Adaptive Object Tracking

  • Hao Jiang
  • Mark S. Drew
  • Ze-Nian Li
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3757)

Abstract

In this paper, we present a novel successive relaxation linear programming scheme for solving the important class of consistent labeling problems for which an L1 metric is involved. The unique feature of the proposed scheme is that we use a much smaller set of basis labels to represent the label space. In a coarse to fine manner, the approximation improves during iteration. The proposed scheme behaves very differently from other methods in which the label space is kept constant in the solution process, and is well suited for very large label set matching problems. Based on the proposed matching scheme, we develop a robust multi-template tracking method. We also increase the efficiency of the template searching by a Markov model. The proposed tracking method uses a small number of graph templates and is able to deal with cases in which objects change appearance drastically due to change of aspect or object deformation.

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References

  1. 1.
    Ishikawa, H.: Global Optimization using Embedded Graphs, Ph.D. Dissertation, NYU (May 2000)Google Scholar
  2. 2.
    Breuel, T.M.: A comparison of search strategies for geometric branch and bound algorithms. In: ECCV, vol. III, pp. 837–850 (2002)Google Scholar
  3. 3.
    Rosenfeld, A., Hummel, R.A., Zucker, S.W.: Scene labeling by relaxation operations. IEEE Trans. Systems, Man, and Cybernetics 6(6), 420–433 (1976)MATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Besag, J.: On the statistical analysis of dirty pictures. J. R. Statis. Soc. Lond. B 48, 259–302 (1986)MATHMathSciNetGoogle Scholar
  5. 5.
    Boykov, Y., Veksler, O., Zabih, R.: Fast approximate energy minimization via graph cuts. PAMI 23, 1222–1239 (2001)Google Scholar
  6. 6.
    Pearl, J.: Probabilistic reasoning in intelligent systems – Networks of plausible inference. Morgan-Kaufmann, San Francisco (1988)Google Scholar
  7. 7.
    Weiss, Y., Freeman, W.T.: On the optimality of solutions of the max-product belief propagation algorithm in arbitrary graphs. IEEE Trans. on Information Theory 47(2), 736–744 (2001)MATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Felzenszwalb, P.F., Huttenlocher, D.P.: Efficient belief propagation for early vision. In: CVPR, vol. I, pp. 261–268 (2004)Google Scholar
  9. 9.
    Kolmogorov, V., Zabih, R.: Multi-camera scene reconstruction via graph cuts. In: ECCV, vol. III, pp. 82–96 (2002)Google Scholar
  10. 10.
    Kolmogorov, V., Zabih, R.: Computing visual correspondence with occlusions using graph cuts. In: ICCV, vol. II, pp. 508–515 (2001)Google Scholar
  11. 11.
    Sun, J., Shum, H.Y., Zheng, N.N.: Stereo matching using belief propagation. PAMI 25(7), 787–800 (2003)Google Scholar
  12. 12.
    Coughlan, J.M., Ferreira, S.J.: Finding deformable shapes using loopy belief propagation. In: ECCV, vol. III, pp. 453–468 (2002)Google Scholar
  13. 13.
    Luo, B., Hancock, E.R.: Structural matching using the EM algorithm and singular value decomposition. PAMI 23, 1120–1136 (2001)Google Scholar
  14. 14.
    Chui, H., Rangarajan, A.: A new algorithm for non-rigid point matching. In: CVPR, vol. II, pp. 44–51 (2000)Google Scholar
  15. 15.
    Rangarajan, A., Chui, H.L., Bookstein, F.L.: The softassign procrustes matching algorithm. In: Information Processing in Medical Imaging, pp. 29–42. Springer, Heidelberg (1997)Google Scholar
  16. 16.
    Tao, P.D., Phong, T.Q., Horaud, R., Quan, L.: Stability of Lagrangian duality for nonconvex quadratic programming solution methods and applications to computer vision. Mathematical Modelling and Numerical Analysis 31(1), 57–90 (1997)MATHGoogle Scholar
  17. 17.
    Bai, X., Yu, H., Hancock, E.: Graph matching using embedding and semidefinite programming. In: BMVC (2004)Google Scholar
  18. 18.
    Ben-Ezra, M., Peleg, S., Werman, M.: Real-time motion analysis with linear programming. In: ICCV, pp. 703–709 (1999)Google Scholar
  19. 19.
    Kleinberg, J., Tardos, E.: Approximation algorithms for classification problems with pairwise relationships: metric labeling and Markov random fields. In: IEEE Symposium on Foundations of Computer Science, pp. 14–23 (1999)Google Scholar
  20. 20.
    Chekuri, C., Khanna, S., Naor, J., Zosin, L.: Approximation algorithms for the metric labeling problem via a new linear programming formulation. In: Symp. on Discrete Algs, pp. 109–118 (2001)Google Scholar
  21. 21.
    Comaniciu, D., Ramesh, V., Meer, P.: Real-time tracking of non-rigid objects using mean shift. In: CVPR, vol. II, pp. 142–149 (2000)Google Scholar
  22. 22.
    Black, M.J., Jepson, A.D.: Eigentracking: robust matching and tracking of articulated objects using a view-based representation. In: ECCV, pp. 329–342 (1996)Google Scholar
  23. 23.
    Morency, L.P., Rahimi, A., Darrell, T.: Adaptive view-based appearance models. In: CVPR, vol. I, pp. 803–810 (2003)Google Scholar
  24. 24.
    Jiang, H., Li, Z.N., Drew, M.S.: Optimizing motion estimation with linear programming and detail-preserving variational method. In: CVPR, vol. I, pp. 738–745 (2004)Google Scholar
  25. 25.
    Jiang, H., Li, Z.N., Drew, M.S.: Posture recognition with convex programming. In: ICME (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Hao Jiang
    • 1
  • Mark S. Drew
    • 1
  • Ze-Nian Li
    • 1
  1. 1.School of Computing ScienceSimon Fraser UniversityBurnabyCanada

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