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.
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References
Barbu, A.: Training an active random field for real-time image denoising. IEEE Trans. on Image Proc. 18(11), 2451–2462 (2009)
Colson, B., Marcotte, P., Savard, G.: An overview of bilevel optimization. Annals OR 153(1), 235–256 (2007)
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)
Domke, J.: Generic methods for optimization-based modeling. Journal of Machine Learning Research - Proceedings Track 22, 318–326 (2012)
Elad, M., Aharon, M.: Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans. on Image Proc. 15(12), 3736–3745 (2006)
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)
Hinton, G.E.: Training products of experts by minimizing contrastive divergence. Neural Computation 14(8), 1771–1800 (2002)
Huang, J., Mumford, D.: Statistics of natural images and models. In: CVPR, Fort Collins, CO, USA, pp. 541–547 (1999)
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)
Liu, D.C., Nocedal, J.: On the limited memory BFGS method for large scale optimization. Mathematical Programming 45(1), 503–528 (1989)
Mairal, J., Bach, F., Ponce, J., Sapiro, G., Zisserman, A.: Non-local sparse models for image restoration. In: ICCV, pp. 2272–2279 (2009)
Peyré, G., Fadili, J.: Learning analysis sparsity priors. In: Proc. of Sampta 2011 (2011), http://hal.archives-ouvertes.fr/hal-00542016/
Roth, S., Black, M.J.: Fields of experts. International Journal of Computer Vision 82(2), 205–229 (2009)
Samuel, K.G.G., Tappen, M.: Learning optimized MAP estimates in continuously-valued MRF models. In: CVPR (2009)
Schmidt, U., Gao, Q., Roth, S.: A generative perspective on MRFs in low-level vision. In: CVPR, pp. 1751–1758 (2010)
Schmidt, U., Schelten, K., Roth, S.: Bayesian deblurring with integrated noise estimation. In: CVPR, pp. 2625–2632 (2011)
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)
Tappen, M.F.: Utilizing variational optimization to learn markov random fields. In: CVPR, pp. 1–8 (2007)
Weiss, Y., Freeman, W.T.: What makes a good model of natural images? In: CVPR (2007)
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)
Zoran, D., Weiss, Y.: From learning models of natural image patches to whole image restoration. In: ICCV, pp. 479–486 (2011)
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Chen, Y., Pock, T., Ranftl, R., Bischof, H. (2013). Revisiting Loss-Specific Training of Filter-Based MRFs for Image Restoration. In: Weickert, J., Hein, M., Schiele, B. (eds) Pattern Recognition. GCPR 2013. Lecture Notes in Computer Science, vol 8142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40602-7_30
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DOI: https://doi.org/10.1007/978-3-642-40602-7_30
Publisher Name: Springer, Berlin, Heidelberg
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