Abstract
This paper is about extending the classical Non-Local Means (NLM) denoising algorithm using general shapes instead of square patches. The use of various shapes enables to adapt to the local geometry of the image while looking for pattern redundancies. A fast FFT-based algorithm is proposed to compute the NLM with arbitrary shapes. The local combination of the different shapes relies on Stein’s Unbiased Risk Estimate (SURE). To improve the robustness of this local aggregation, we perform an anistropic diffusion of the risk estimate using a properly modified Perona-Malik equation. Experimental results show that this algorithm improves the NLM performance and it removes some visual artifacts usually observed with the NLM.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Perona, P., Malik, J.: Scale space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12, 629–639 (1990)
Alvarez, L., Guichard, F., Lions, P.L., Morel, J.M.: Axioms and fundamental equations of image processing. Arch. Rational Mech. Anal. 123(3), 199–257 (1993)
Weickert, J.: Anisotropic diffusion in image processing. European Consortium for Mathematics in Industry. B. G. Teubner, Stuttgart (1998)
Yaroslavsky, L.P.: Digital picture processing. Springer Series in Information Sciences, vol. 9. Springer, Berlin (1985)
Tomasi, C., Manduchi, R.: Bilateral filtering for gray and color images. In: ICCV, pp. 839–846 (1998)
Lepski, O.V., Mammen, E., Spokoiny, V.G.: Optimal spatial adaptation to inhomogeneous smoothness: an approach based on kernel estimates with variable bandwidth selectors. Ann. Statist. 25(3), 929–947 (1997)
Polzehl, J., Spokoiny, V.G.: Adaptive weights smoothing with applications to image restoration. J. R. Stat. Soc. Ser. B Stat. Methodol. 62(2), 335–354 (2000)
Katkovnik, V., Foi, A., Egiazarian, K.O., Astola, J.T.: Directional varying scale approximations for anisotropic signal processing. In: EUSIPCO, pp. 101–104 (2004)
Buades, A., Coll, B., Morel, J.M.: A review of image denoising algorithms, with a new one. Multiscale Model. Simul. 4(2), 490–530 (2005)
Awate, S.P., Whitaker, R.T.: Unsupervised, information-theoretic, adaptive image filtering for image restoration. IEEE Trans. Pattern Anal. Mach. Intell. 28(3), 364–376 (2006)
Kervrann, C., Boulanger, J.: Optimal spatial adaptation for patch-based image denoising. IEEE Trans. Image Process. 15(10), 2866–2878 (2006)
Aharon, M., Elad, M., Bruckstein, A.: K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans. Signal Process. 54(11), 4311–4322 (2006)
Mairal, J., Sapiro, G., Elad, M.: Learning multiscale sparse representations for image and video restoration. Multiscale Model. Simul. 7(1), 214–241 (2008)
Mairal, J., Bach, F., Ponce, J., Sapiro, G., Zisserman, A.: Non-local sparse models for image restoration. In: ICCV (2009)
Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.O.: Image denoising by sparse 3-D transform-domain collaborative filtering. IEEE Trans. Image Process. 16(8), 2080–2095 (2007)
Salmon, J., Strozecki, Y.: From patches to pixels in non-local methods: Weighted-Average reprojection. In: ICIP (2010)
Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.O.: BM3D image denoising with shape-adaptive principal component analysis. In: Proc. Workshop on Signal Processing with Adaptive Sparse Structured Representations, SPARS 2009 (2009)
Duval, V., Aujol, J.F., Gousseau, Y.: On the parameter choice for the non-local means. Technical Report hal-00468856, HAL (2010)
Stein, C.M.: Estimation of the mean of a multivariate normal distribution. Ann. Statist. 9(6), 1135–1151 (1981)
Van De Ville, D., Kocher, M.: SURE-based Non-Local Means. IEEE Signal Process. Lett. 16, 973–976 (2009)
Blu, T., Luisier, F.: The SURE-LET approach to image denoising. IEEE_J_IP 16(11), 2778–2786 (2007)
Ramani, S., Blu, T., Unser, M.: Monte-Carlo SURE: a black-box optimization of regularization parameters for general denoising algorithms. IEEE Trans. Image Process. 17(9), 1540–1554 (2008)
Donoho, D.L., Johnstone, I.M.: Adapting to unknown smoothness via wavelet shrinkage. J. Amer. Statist. Assoc. 90(432), 1200–1224 (1995)
Salmon, J.: On two parameters for denoising with Non-Local Means. IEEE Signal Process. Lett. 17, 269–272 (2010)
Zimmer, S., Didas, S., Weickert, J.: A rotationally invariant block matching strategy improving image denoising with non-local means. In: LNLA (2008)
Wang, J., Guo, Y.W., Ying, Y., Liu, Y.L., Peng, Q.S.: Fast non-local algorithm for image denoising. In: ICIP, pp. 1429–1432 (2006)
Darbon, J., Cunha, A., Chan, T.F., Osher, S., Jensen, G.J.: Fast nonlocal filtering applied to electron cryomicroscopy. In: ISBI, pp. 1331–1334 (2008)
Dalalyan, A.S., Tsybakov, A.B.: Aggregation by exponential weighting, sharp pac-bayesian bounds and sparsity. Mach. Learn. 72(1-2), 39–61 (2008)
Salmon, J., Le Pennec, E.: NL-Means and aggregation procedures. In: ICIP, pp. 2977–2980 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Deledalle, CA., Duval, V., Salmon, J. (2012). Anisotropic Non-Local Means with Spatially Adaptive Patch Shapes. In: Bruckstein, A.M., ter Haar Romeny, B.M., Bronstein, A.M., Bronstein, M.M. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2011. Lecture Notes in Computer Science, vol 6667. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24785-9_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-24785-9_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24784-2
Online ISBN: 978-3-642-24785-9
eBook Packages: Computer ScienceComputer Science (R0)