Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
SpringerLink
Log in

A Parallel Proximal Splitting Method for Disparity Estimation from Multicomponent Images Under Illumination Variation

  • Published:
Journal of Mathematical Imaging and Vision Aims and scope Submit manuscript

Abstract

Proximal splitting algorithms play a central role in finding the numerical solution of convex optimization problems. This paper addresses the problem of stereo matching of multi-component images by jointly estimating the disparity and the illumination variation. The global formulation being non-convex, the problem is addressed by solving a sequence of convex relaxations. Each convex relaxation is non trivial and involves many constraints aiming at imposing some regularity on the solution. Experiments demonstrate that the method is efficient and provides better results compared with other approaches.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Algorithm 1
Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Notes

  1. Constraint \(S_{2}'\) will be substituted for S 2 in some of our experiments.

  2. http://vision.middlebury.edu/stereo/.

  3. http://vasc.ri.cmu.edu/idb/html/jisct/.

References

  1. Kolmogorov, V., Zabih, R.: Computing visual correspondence with occlusions using graph cuts. In: Proc. IEEE Int. Conf. Comput. Vis, Vancouver, BC, Canada, Jul. 9–12, vol. 2, pp. 508–515 (2001)

    Google Scholar 

  2. Boykov, Y., Veksler, O., Zabih, R.: Fast approximate energy minimization via graph cuts. IEEE Trans. Pattern Anal. Mach. Intell. 23(11), 1222–1239 (2011)

    Article  Google Scholar 

  3. Klaus, A., Sormann, M., Karner, K.: Segment-based stereo matching using belief propagation and a self-adapting dissimilarity measure. In: Proc. Int. Conf. Pattern Recognition, Hong Kong, Aug. 20–24, vol. 3, pp. 15–18 (2006)

    Google Scholar 

  4. Yang, Q., Wang, L., Yang, R., Wang, S., Liao, M., Nistér, D.: Realtime global stereo matching using hierarchical belief propagation. In: Proc. British Machine Vision Conference, Edinburgh, UK, Sept. 4–7, pp. 989–998 (2006).

    Google Scholar 

  5. Deriche, R., Kornprobst, P., Aubert, G.: Optical-flow estimation while preserving its discontinuities: A variational approach. In: Li, S., Mital, D., Teoh, E., Wang, H. (eds.) Recent Developments in Computer Vision. Lecture Notes in Computer Science, vol. 1035, pp. 69–80. Springer, Berlin (1996)

    Chapter  Google Scholar 

  6. Miled, W., Pesquet, J.-C., Parent, M.: Disparity map estimation using a total variation bound. In: The 3rd Canadian Conf. on Computer and Robot Vision, Quebec, Canada, June, pp. 48–55 (2006)

    Google Scholar 

  7. Miled, W., Pesquet, J.-C., Parent, M.: A convex optimisation approach for depth estimation under illumination variation. IEEE Trans. Image Process. 18(4), 813–830 (2009)

    Article  MathSciNet  Google Scholar 

  8. Cox, I.J., Roy, S., Hingorani, S.L.: Dynamic histogram warping of image pairs for constant image brightness. In: Proc. Int. Conf. Image Process, Washington, DC, Oct. 23–26, vol. 2, pp. 366–369 (1995)

    Chapter  Google Scholar 

  9. Zabih, R., Woodfill, J.: Non-parametric local transforms for computing visual correspondence. In: Proc. Eur. Conf. Comput. Vis, Stockholm, Sweden, May 2–6, pp. 15–158 (1994)

    Google Scholar 

  10. Davis, J.E., Yang, R., Wang, L.: BRDF invariant stereo using light transport constancy. In: Proc. IEEE Int. Conf. Comput. Vis, Beijing, China, Oct. 15–21, vol. 1, pp. 436–443 (2005)

    Google Scholar 

  11. Gennert, M.A.: Brightness-based stereo matching. In: Proc. IEEE Int. Conf. Comput. Vis, Tampa, FL, Dec. 5–8, pp. 139–143 (1988)

    Google Scholar 

  12. Pesquet, J.-C., Pustelnik, N.: A parallel inertial proximal optimization method. Pac. J. Optim. 8(2), 273–305 (2012)

    MathSciNet  MATH  Google Scholar 

  13. Fusiello, A., Trucco, E., Verri, A.: A compact algorithm for rectification of stereo pairs. Mach. Vis. Appl. 12(1), 16–22 (2000)

    Article  Google Scholar 

  14. Tsai, D., Lin, C., Chen, J.: The evaluation of normalized cross correlations for defect detection. Pattern Recognit. Lett. 24(15), 2525–2535 (2003)

    Article  MATH  Google Scholar 

  15. Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259–268 (1992)

    Article  MATH  Google Scholar 

  16. Combettes, P.L., Pesquet, J.-C.: Image restoration subject to a total variation constraint. IEEE Trans. Image Process. 13(9), 1213–1222 (2004)

    Article  Google Scholar 

  17. Combettes, P.L., Pesquet, J.-C.: A proximal decomposition method for solving convex variational inverse problems. Inverse Probl. 24(6), 27 (2008)

    Article  MathSciNet  Google Scholar 

  18. Pustelnik, N., Chaux, C., Pesquet, J.-C.: Parallel ProXimal algorithm for image restoration using hybrid regularization. IEEE Trans. Image Process. 20(9), 2450–2462 (2011)

    Article  MathSciNet  Google Scholar 

  19. Aujol, J.F., Aubert, G., Blanc-Féraud, L., Chambolle, A.: Image decomposition into a bounded variation component and an oscillating component. J. Math. Imaging Vis. 22(1), 71–88 (2005)

    Article  Google Scholar 

  20. Chambolle, A., DeVore, R.A., Lee, N.-Y., Lucier, B.J.: Nonlinear wavelet image processing: variational problems, compression and noise removal through wavelet shrinkage. IEEE Trans. Image Process. 7, 319–335 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  21. Han, D., Larson, D.R.: Frames, Bases, and Group Representations. Mem. Amer. Math. Soc., vol. 147, p. 94. AMS, Providence (2000)

    Google Scholar 

  22. Mallat, S.: A Wavelet Tour of Signal Processing. Academic Press, San Diego (1997)

    Google Scholar 

  23. Lefkimmiatis, S., Bourquard, A., Unser, M.: Hessian-based norm regularization for image restoration with biomedical applications. IEEE Trans. Image Process. 21(3), 983–995 (2012)

    Article  MathSciNet  Google Scholar 

  24. Moreau, J.J.: Fonctions convexes duales et points proximaux dans un espace hilbertien. C. R. Acad. Sci. 255, 2897–2899 (1962)

    MathSciNet  MATH  Google Scholar 

  25. Combettes, P.L.: The foundations of set theoretic estimation. Proc. IEEE 81(2), 182–208 (1993)

    Article  Google Scholar 

  26. Combettes, P.L., Pesquet, J.-C.: Proximal splitting methods in signal processing. In: Bauschke, H.H., Burachik, R., Combettes, P.L., Elser, V., Luke, D.R., Wolkowicz, H. (eds.) Fixed-Point Algorithms for Inverse Problems in Science and Engineering, pp. 185–212. Springer, New York (2011)

    Chapter  Google Scholar 

  27. Youla, D.C., Webb, H.: Image restoration by the method of convex projections: Part I - theory. IEEE Trans. Med. Imaging 1(2), 81–94 (1982)

    Article  Google Scholar 

  28. van den Berg, E., Friedlander, M.P.: Probing the Pareto frontier for basis pursuit solutions. SIAM J. Sci. Comput. 31(2), 890–912 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  29. Eldar, Y.C., Mishali, M.: Robust recovery of signals from a structured union of subspaces. IEEE Trans. Inf. Theory 55(11), 5302–5316 (2009)

    Article  MathSciNet  Google Scholar 

  30. Afonso, M., Bioucas-Dias, J., Figueiredo, M.A.T.: An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems. IEEE Trans. Image Process. 20(3), 681–695 (2011)

    Article  MathSciNet  Google Scholar 

  31. Setzer, S., Steidl, G., Teuber, T.: Deblurring Poissonian images by split Bregman techniques. J. Vis. Commun. Image Represent. 21, 193–199 (2010)

    Article  Google Scholar 

  32. Attouch, H., Soueycatt, M.: Augmented Lagrangian and proximal alternating direction methods of multipliers in Hilbert spaces—applications to games, PDE’s and control. Pac. J. Optim. 5(1), 17–37 (2009)

    MathSciNet  MATH  Google Scholar 

  33. Chen, G., Teboulle, M.: A proximal-based decomposition method for convex minimization problems. Math. Program., Ser. A 64(1), 81–101 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  34. Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40(1), 120–145 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  35. Esser, E., Zhang, X., Chan, T.: A general framework for a class of first order primal-dual algorithms for convex optimization in imaging science. SIAM J. Imaging Sci. 3(4), 1015–1046 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  36. Combettes, P.L., Dũng, Ð., Vũ, B.C.: Proximity for sums of composite functions. J. Math. Anal. Appl. 320(2), 680–688 (2011)

    Article  Google Scholar 

  37. Briceño-Arias, L.M., Combettes, P.L.: A monotone + skew splitting model for composite monotone inclusions in duality. SIAM J. Optim. 21(4), 1230–1250 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  38. Combettes, P.L., Pesquet, J.-C.: Primal-dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum type monotone operators. Set-Valued Var. Anal. 20(2), 307–330 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  39. Pustelnik, N., Pesquet, J.-C., Chaux, C.: Relaxing tight frame condition in parallel proximal methods for signal restoration. IEEE Trans. Signal Process. 60(2), 968–973 (2012)

    Article  MathSciNet  Google Scholar 

  40. Yoon, K.-J., Kweon, I.-S.: Adaptive support-weight approach for correspondence search. IEEE Trans. Pattern Anal. Mach. Intell. 28(4), 650–656 (2006)

    Article  Google Scholar 

  41. Yuille, A.L., Poggio, T.: A generalized ordering constraint for stereo correspondence. Technical report aim-777 (1984)

  42. Pock, T., Schoenemann, T., Graber, G., Bischof, H., Cremers, D.: A convex formulation of continuous multilabel problems. In: Proc. Eur. Conf. Comput. Vis, Marseille, France, Oct., pp. 792–805 (2008)

    Google Scholar 

  43. Wang, L., Yang, R.: Global stereo matching leveraged by sparse ground control points. In: Proc. IEEE Conf. Comput. Vis. and Patt. Rec, Colorado Springs, USA, Jun. 20–25, pp. 3033–3040 (2011)

    Google Scholar 

  44. Min, D., Lu, J., Do, M.: A revisit to cost aggregation in stereo matching: how far can we reduce its computational redundancy? In: Proc. IEEE Int. Conf. Comput. Vis, Barcelona, Spain, Nov., pp. 1567–1574 (2011)

    Google Scholar 

  45. Mukherjee, D., Wang, G., Wu, J.: Stereo matching algorithm based on curvelet decomposition and modified support weights. In: Proc. Int. Conf. Acoust., Speech Signal Process, Dallas, Texas, USA, Mar. 14–19, pp. 758–761 (2010)

    Google Scholar 

Download references

Acknowledgements

We would like to thank Prof. Wided Miled for providing us with her codes. We would also like to thank Dr. Raffaele Gaetano and Giovanni Chierchia for their implementation of our approach on GPU architectures.

Author information

Authors and Affiliations

  1. Laboratoire d’Informatique Gaspard Monge—CNRS UMR 8049, Université Paris-Est, 77454, Marne la Vallée Cedex 2, France

    C. Chaux, M. El-Gheche & J.-C. Pesquet

  2. Department of Telecommunications, Faculty of Engineering, Holy-Spirit University of Kaslik, P.O. Box 446, Jounieh, Lebanon

    J. Farah

  3. Signal and Image Proc. Dept., Telecom ParisTech, 75014, Paris, France

    B. Pesquet-Popescu

Authors
  1. C. Chaux
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. El-Gheche
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. Farah
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J.-C. Pesquet
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. B. Pesquet-Popescu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. Chaux.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chaux, C., El-Gheche, M., Farah, J. et al. A Parallel Proximal Splitting Method for Disparity Estimation from Multicomponent Images Under Illumination Variation. J Math Imaging Vis 47, 167–178 (2013). https://doi.org/10.1007/s10851-012-0361-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10851-012-0361-z

Keywords

Search

Navigation