Nothing Special   »   [go: up one dir, main page]

Skip to main content
Log in

Normalized filter pool for prior modeling of nature images

  • Original Paper
  • Published:
Machine Vision and Applications Aims and scope Submit manuscript

Abstract

Markov random field (MRF), as one of special undirected graphs, is widely used in modeling priors of natural images. Targeting to learn better prior models from a given database, we explore the natural image statistics at different scales and build normalized filter pool, a kind of high-order MRF, for prior learning of nature images. The main contribution of the proposed model is that we construct a multi-scale MRF model through constraining the norms of filters in kernel space and integrate all the filtering responses in a unified framework. We formulate both learning and inference as constrained optimization problems and solve them using augmented Lagrange method. The experiment results demonstrate that the normalization of filters at different scales helps to achieve fast convergence in learning stage and obtain superior performance in image restoration, e.g., image denoising and image inpainting.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Baker, S., Scharstein, D., Lewis, J.P., Roth, S., Black, M.J., Szeliski, R.: A database and evaluation methodology for optical flow. Int. J. Comput. Vis. 92(1), 1–31 (2011)

    Article  Google Scholar 

  2. Black, M.J., Rangarajan, A.: On the unification of line processes, outlier rejection, and robust statistics with applications in early vision. Int. J. Comput. Vis. 19(1), 57–92 (1996)

    Article  Google Scholar 

  3. Blunsden, S., Atallah, L.: Investigating the effects of scale in MRF texture classification. In: VIE (2005)

  4. Boykov, Y., Veksler, O., Zabih, R.: Fast approximate energy minimization via graph cuts. IEEE Trans. Pattern Anal. Mach. Intell. 23(11), 1222–1239 (2001)

    Article  Google Scholar 

  5. Buades, A., Coll, B., Morel, J.M.: A non-local algorithm for image denoising. In: IEEE Conference on Computer Vision and Pattern Recognition (2005)

  6. Chen, J., Nunez-Yanez, J., Achim, A.: Video super-resolution using generalized gaussian Markov random fields. IEEE Signal Process. Lett. 19(2), 63–66 (2012)

    Article  Google Scholar 

  7. Cho, T.S., Zitnick, C.L., Joshi, N., Kang, S.B., Szeliski, R., Freeman, W.T.: Image restoration by matching gradient distributions. IEEE Trans. Pattern Anal. Mach. Intell. 34(4), 683–694 (2012)

    Article  Google Scholar 

  8. Freeman, W.T., Pasztor, E.C., Carmichael, O.T.: Learning low-level vision. Int. J. Comput. Vis. 40(1), 25–47 (2000)

    Article  MATH  Google Scholar 

  9. Geman, S., Geman, D.: Stochastic relaxation, Gibbs distribution and Bayesian restoration of images. IEEE Trans Pattern Anal. Mach. Intell. 9(9), 721–741 (1984)

    Article  MATH  Google Scholar 

  10. Hinton, G.: Product of experts. In: ICANN (1999)

  11. Huang, J.: Statistics of Nature Images and Models. PhD thesis, Brown University (2000)

  12. Ishikawa, H.: Higher-order clique reduction in binary graph cut. In: IEEE Conference on Computer Vision and Pattern Recognition (2009)

  13. Kohli, P., Kumar, M.P.: Energy minimization for linear envelope MRFs. In: IEEE Conference on Computer Vision and Pattern Recognition (2010)

  14. Komodakis, N., Paragios, N.: (2009) Beyond pairwise energies: efficient optimization for higher-order MRFs. In: IEEE Conference on Computer Vision and Pattern Recognition

  15. Köster, U., Lindgren, J., Hyvärinen, A.: Estimating Markov random field potentials for natural images. In: ICA (2009)

  16. Li, S.Z.: Markov Random Field Modeling in Image Analysis, 3rd edn. Springer, New York (2009)

  17. Liu, C., Pizer, S.M., Joshi, S.: A Markov random field approach to multi-scale shape analysis. In: SSVM (2003)

  18. Lyu, S., Simoncelli, E.P., Hughes, H.: Statistical modeling of images with fields of Gaussian scale mixtures. In: NIPS (2006)

  19. Martin, D., Fowlkes, C., Tal, D., Malik, J.: A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In: International Conference on Computer Vision (2001)

  20. Murphy, K.: https://github.com/bayesnet/bnt (2014). Accessed 17 Apr 2014

  21. Nocedal, J., Wright, S.J.: Numerical Optimization, 2nd edn. Springer, New York (2006)

  22. Paget, R., Longstaff, I.D.: Texture synthesis via a noncausal nonparametric multiscale Markov random field. IEEE Trans. Image Process. 7(6), 925–931 (1998)

    Article  Google Scholar 

  23. Paulsen, R.R., Brentzen, J.A., Larsen, R.: Markov random field surface reconstruction. IEEE Trans. Vis. Comput. Graph. 16, 636–646 (2010). doi:10.1109/TVCG.2009.208

    Article  Google Scholar 

  24. Portilla, J., Strela, V., Wainwright, M.J., Simoncelli, E.P.: Image denoising using scale mixtures of Gaussians in the wavelet domain. IEEE Trans. Image Process. 12(11), 1338–1351 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  25. Roth, S., Black, M.J.: On the spatial statistics of optical flow. In: International Conference on Computer Vision (2005)

  26. Roth, S., Black, M.J.: Steerable random fields. In: International Conference on Computer Vision (2007)

  27. Roth, S., Black, M.J.: Fields of experts. Int. J. Comput. Vis. 82(2), 205–229 (2009)

    Article  Google Scholar 

  28. Rother, C., Kohli, P., Feng, W., Jia, J.: (2009) Minimizing sparse higher order energy functions of discrete variables. In: IEEE Conference on Computer Vision and Pattern Recognition

  29. Ruderman, D.L.: The statistics of natural images. Netw. Comput. Neural Syst. 5, 517–548 (1994)

    Article  MATH  Google Scholar 

  30. Ruderman, D.L.: Origins of scaling in natural images. Vis. Res. 37(23), 3385–3398 (1997)

    Article  Google Scholar 

  31. Schmidt, U., Gao, Q., Roth, S.: A generative perspective on MRFs in low-level vision. In: IEEE Conference on Computer Vision and Pattern Recognition (2010)

  32. Tappen, M.F., Russell, B.C., Freeman, W.T.: Exploiting the sparse derivative prior for super-resolution and image demosaicing. In: International Workshop on Statistical and Computational Theories of Vision at ICCV (2003)

  33. Teh, Y.W., Welling, M., Osindero, S., Hinton, G.E.: Energy-based models for sparse overcomplete representations. J. Mach. Learn. Res. 4, 1235–1260 (2003)

    MathSciNet  MATH  Google Scholar 

  34. Wang, Y., Zhu, S.: Perceptual scale-space and its applications. Int. J. Comput. Vis. 80(1), 143–165 (2008)

    Article  Google Scholar 

  35. Weiss, Y., Freeman, W.T.: What makes a good model of natural images? In: IEEE Conference on Computer Vision and Pattern Recognition (2007)

  36. Woodford, O.J., Reid, I.D., Torr, P.H.S., Fitzgibbon, A.W.: Fields of experts for image-based rendering. In: British Conference on Machine and Computer Vision (2006)

  37. Zhu, S.C., Mumford, D.: Prior learning and Gibbs reaction–diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 19(11), 1236–1250 (1997)

    Article  Google Scholar 

Download references

Acknowledgments

We would like thank all the reviewers. This work was supported in part by NSFC (No. 61305026).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yangang Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Y., Suo, J. & Dai, Q. Normalized filter pool for prior modeling of nature images. Machine Vision and Applications 27, 437–446 (2016). https://doi.org/10.1007/s00138-016-0753-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00138-016-0753-y

Keywords

Navigation