Advertisement

Revisiting Loss-Specific Training of Filter-Based MRFs for Image Restoration

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8142)

Abstract

It is now well known that Markov random fields (MRFs) are particularly effective for modeling image priors in low-level vision. Recent years have seen the emergence of two main approaches for learning the parameters in MRFs: (1) probabilistic learning using sampling-based algorithms and (2) loss-specific training based on MAP estimate. After investigating existing training approaches, it turns out that the performance of the loss-specific training has been significantly underestimated in existing work. In this paper, we revisit this approach and use techniques from bi-level optimization to solve it. We show that we can get a substantial gain in the final performance by solving the lower-level problem in the bi-level framework with high accuracy using our newly proposed algorithm. As a result, our trained model is on par with highly specialized image denoising algorithms and clearly outperforms probabilistically trained MRF models. Our findings suggest that for the loss-specific training scheme, solving the lower-level problem with higher accuracy is beneficial. Our trained model comes along with the additional advantage, that inference is extremely efficient. Our GPU-based implementation takes less than 1s to produce state-of-the-art performance.

Keywords

Training Dataset Training Scheme Image Denoising Level Problem Denoising 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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
  2. 2.
    Barbu, A.: Training an active random field for real-time image denoising. IEEE Trans. on Image Proc. 18(11), 2451–2462 (2009)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Colson, B., Marcotte, P., Savard, G.: An overview of bilevel optimization. Annals OR 153(1), 235–256 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.O.: Image denoising by sparse 3-d transform-domain collaborative filtering. IEEE Trans. on Image Proc. 16(8), 2080–2095 (2007)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Domke, J.: Generic methods for optimization-based modeling. Journal of Machine Learning Research - Proceedings Track 22, 318–326 (2012)Google Scholar
  6. 6.
    Elad, M., Aharon, M.: Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans. on Image Proc. 15(12), 3736–3745 (2006)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Gao, Q., Roth, S.: How well do filter-based MRFs model natural images? In: Pinz, A., Pock, T., Bischof, H., Leberl, F. (eds.) DAGM and OAGM 2012. LNCS, vol. 7476, pp. 62–72. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  8. 8.
    Hinton, G.E.: Training products of experts by minimizing contrastive divergence. Neural Computation 14(8), 1771–1800 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Huang, J., Mumford, D.: Statistics of natural images and models. In: CVPR, Fort Collins, CO, USA, pp. 541–547 (1999)Google Scholar
  10. 10.
    Jancsary, J., Nowozin, S., Rother, C.: Loss-specific training of non-parametric image restoration models: A new state of the art. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part VII. LNCS, vol. 7578, pp. 112–125. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  11. 11.
    Liu, D.C., Nocedal, J.: On the limited memory BFGS method for large scale optimization. Mathematical Programming 45(1), 503–528 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Mairal, J., Bach, F., Ponce, J., Sapiro, G., Zisserman, A.: Non-local sparse models for image restoration. In: ICCV, pp. 2272–2279 (2009)Google Scholar
  13. 13.
    Peyré, G., Fadili, J.: Learning analysis sparsity priors. In: Proc. of Sampta 2011 (2011), http://hal.archives-ouvertes.fr/hal-00542016/
  14. 14.
    Roth, S., Black, M.J.: Fields of experts. International Journal of Computer Vision 82(2), 205–229 (2009)CrossRefGoogle Scholar
  15. 15.
    Samuel, K.G.G., Tappen, M.: Learning optimized MAP estimates in continuously-valued MRF models. In: CVPR (2009)Google Scholar
  16. 16.
    Schmidt, U., Gao, Q., Roth, S.: A generative perspective on MRFs in low-level vision. In: CVPR, pp. 1751–1758 (2010)Google Scholar
  17. 17.
    Schmidt, U., Schelten, K., Roth, S.: Bayesian deblurring with integrated noise estimation. In: CVPR, pp. 2625–2632 (2011)Google Scholar
  18. 18.
    Tappen, M.F., Liu, C., Adelson, E.H., Freeman, W.T.: Learning gaussian conditional random fields for low-level vision. In: CVPR, pp. 1–8 (2007)Google Scholar
  19. 19.
    Tappen, M.F.: Utilizing variational optimization to learn markov random fields. In: CVPR, pp. 1–8 (2007)Google Scholar
  20. 20.
    Weiss, Y., Freeman, W.T.: What makes a good model of natural images? In: CVPR (2007)Google Scholar
  21. 21.
    Zhang, H., Zhang, Y., Li, H., Huang, T.S.: Generative bayesian image super resolution with natural image prior. IEEE Trans. on Image Proc. 21(9), 4054–4067 (2012)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Zoran, D., Weiss, Y.: From learning models of natural image patches to whole image restoration. In: ICCV, pp. 479–486 (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Institute for Computer Graphics and VisionTU GrazAustria

Personalised recommendations