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.
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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)
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)
Blunsden, S., Atallah, L.: Investigating the effects of scale in MRF texture classification. In: VIE (2005)
Boykov, Y., Veksler, O., Zabih, R.: Fast approximate energy minimization via graph cuts. IEEE Trans. Pattern Anal. Mach. Intell. 23(11), 1222–1239 (2001)
Buades, A., Coll, B., Morel, J.M.: A non-local algorithm for image denoising. In: IEEE Conference on Computer Vision and Pattern Recognition (2005)
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)
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)
Freeman, W.T., Pasztor, E.C., Carmichael, O.T.: Learning low-level vision. Int. J. Comput. Vis. 40(1), 25–47 (2000)
Geman, S., Geman, D.: Stochastic relaxation, Gibbs distribution and Bayesian restoration of images. IEEE Trans Pattern Anal. Mach. Intell. 9(9), 721–741 (1984)
Hinton, G.: Product of experts. In: ICANN (1999)
Huang, J.: Statistics of Nature Images and Models. PhD thesis, Brown University (2000)
Ishikawa, H.: Higher-order clique reduction in binary graph cut. In: IEEE Conference on Computer Vision and Pattern Recognition (2009)
Kohli, P., Kumar, M.P.: Energy minimization for linear envelope MRFs. In: IEEE Conference on Computer Vision and Pattern Recognition (2010)
Komodakis, N., Paragios, N.: (2009) Beyond pairwise energies: efficient optimization for higher-order MRFs. In: IEEE Conference on Computer Vision and Pattern Recognition
Köster, U., Lindgren, J., Hyvärinen, A.: Estimating Markov random field potentials for natural images. In: ICA (2009)
Li, S.Z.: Markov Random Field Modeling in Image Analysis, 3rd edn. Springer, New York (2009)
Liu, C., Pizer, S.M., Joshi, S.: A Markov random field approach to multi-scale shape analysis. In: SSVM (2003)
Lyu, S., Simoncelli, E.P., Hughes, H.: Statistical modeling of images with fields of Gaussian scale mixtures. In: NIPS (2006)
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)
Murphy, K.: https://github.com/bayesnet/bnt (2014). Accessed 17 Apr 2014
Nocedal, J., Wright, S.J.: Numerical Optimization, 2nd edn. Springer, New York (2006)
Paget, R., Longstaff, I.D.: Texture synthesis via a noncausal nonparametric multiscale Markov random field. IEEE Trans. Image Process. 7(6), 925–931 (1998)
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
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)
Roth, S., Black, M.J.: On the spatial statistics of optical flow. In: International Conference on Computer Vision (2005)
Roth, S., Black, M.J.: Steerable random fields. In: International Conference on Computer Vision (2007)
Roth, S., Black, M.J.: Fields of experts. Int. J. Comput. Vis. 82(2), 205–229 (2009)
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
Ruderman, D.L.: The statistics of natural images. Netw. Comput. Neural Syst. 5, 517–548 (1994)
Ruderman, D.L.: Origins of scaling in natural images. Vis. Res. 37(23), 3385–3398 (1997)
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)
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)
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)
Wang, Y., Zhu, S.: Perceptual scale-space and its applications. Int. J. Comput. Vis. 80(1), 143–165 (2008)
Weiss, Y., Freeman, W.T.: What makes a good model of natural images? In: IEEE Conference on Computer Vision and Pattern Recognition (2007)
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)
Zhu, S.C., Mumford, D.: Prior learning and Gibbs reaction–diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 19(11), 1236–1250 (1997)
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We would like thank all the reviewers. This work was supported in part by NSFC (No. 61305026).
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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
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DOI: https://doi.org/10.1007/s00138-016-0753-y