Abstract
The knowledge of the noise level within an image is a valuable information for many image processing applications. Estimating the noise level function (NLF) requires the identification of homogeneous regions, upon which the noise parameters are computed. Sutour et al. have proposed a method to estimate this NLF based on the search for homogeneous regions of square shape. We generalize this method to the search for homogeneous regions with arbitrary shape thanks to the tree of shapes representation of the image under study, thus allowing a more robust and precise estimation of the noise level function.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ballester, C., Caselles, V., Monasse, P.: The tree of shapes of an image. ESAIM Control. Optim. Calc. Var. 9, 1–18 (2003)
Beaurepaire, L., Chehdi, K., Vozel, B.: Identification of the nature of noise and estimation of its statistical parameters by analysis of local histograms. In: 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 4, pp. 2805–2808. IEEE (1997)
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)
Carlinet, E., Géraud, T.: MToS: a tree of shapes for multivariate images. IEEE Trans. Image Process. 24(12), 5330–5342 (2015)
Carlinet, E., Géraud, T., Crozet, S.: The tree of shapes turned into a max-tree: a simple and efficient linear algorithm. In: Proceedings of the 24th IEEE International Conference on Image Processing (ICIP), Athens, Greece, pp. 1488–1492 (2018)
Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40(1), 120–145 (2011)
Crozet, S., Géraud, T.: A first parallel algorithm to compute the morphological tree of shapes of \(n\)D images. In: Proceedings of the 21st IEEE International Conference on Image Processing (ICIP), Paris, France, pp. 2933–2937 (2014)
Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.: BM3D image denoising with shape-adaptive principal component analysis. In: SPARS 2009-Signal Processing with Adaptive Sparse Structured Representations (2009)
Deledalle, C.A., Duval, V., Salmon, J.: Non-local methods with shape-adaptive patches (NLM-SAP). J. Math. Imaging Vis. 43(2), 103–120 (2012)
Donoho, D.L.: De-noising by soft-thresholding. IEEE Trans. Inf. Theory 41(3), 613–627 (1995)
Droske, M., Rumpf, M.: Multiscale joint segmentation and registration of image morphology. IEEE Trans. Pattern Anal. Mach. Intell. 29(12), 2181–2194 (2007)
Freeman, W.T., Jones, T.R., Pasztor, E.C.: Example-based super-resolution. IEEE Comput. Graph. Appl. 2, 56–65 (2002)
Géraud, T., Carlinet, E., Crozet, S., Najman, L.: A quasi-linear algorithm to compute the tree of shapes of nD images. In: Hendriks, C.L.L., Borgefors, G., Strand, R. (eds.) ISMM 2013. LNCS, vol. 7883, pp. 98–110. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38294-9_9
Kendall, M.G.: The treatment of ties in ranking problems. Biometrika 33(3), 239–251 (1945). http://www.jstor.org/stable/2332303
Kendall, M.G.: A new measure of rank correlation. Biometrika 30(1/2), 81–93 (1938)
Liu, C., Freeman, W.T., Szeliski, R., Kang, S.B.: Noise estimation from a single image. In: 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 1, pp. 901–908. IEEE (2006)
Liu, X., Tanaka, M., Okutomi, M.: Single-image noise level estimation for blind denoising. IEEE Trans. Image Process. 22(12), 5226–5237 (2013)
Mäkitalo, M., Foi, A.: Noise parameter mismatch in variance stabilization, with an application to poisson-Gaussian noise estimation. IEEE Trans. Image Process. 23(12), 5348–5359 (2014)
Monasse, P., Guichard, F.: Fast computation of a contrast-invariant image representation. IEEE Trans. Image Process. 9(5), 860–872 (2000)
Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Commun. Pure Appl. Math. 42(5), 577–685 (1989)
Pyatykh, S., Hesser, J.: Image sensor noise parameter estimation by variance stabilization and normality assessment. IEEE Trans. Image Process. 23(9), 3990–3998 (2014)
Sutour, C., Deledalle, C.A., Aujol, J.F.: Estimation of the noise level function based on a nonparametric detection of homogeneous image regions. SIAM J. Imaging Sci. 8(4), 2622–2661 (2015)
Walker, J.S.: Combined image compressor and denoiser based on tree-adapted wavelet shrinkage. Opt. Eng. 41(7), 1520–1528 (2002)
Xu, Y., Géraud, T., Najman, L.: Hierarchical image simplification and segmentation based on Mumford-Shah-salient level line selection. Pattern Recognit. Lett. 83, 278–286 (2016)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Esteban, B., Tochon, G., Géraud, T. (2019). Estimating the Noise Level Function with the Tree of Shapes and Non-parametric Statistics. In: Vento, M., Percannella, G. (eds) Computer Analysis of Images and Patterns. CAIP 2019. Lecture Notes in Computer Science(), vol 11679. Springer, Cham. https://doi.org/10.1007/978-3-030-29891-3_33
Download citation
DOI: https://doi.org/10.1007/978-3-030-29891-3_33
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-29890-6
Online ISBN: 978-3-030-29891-3
eBook Packages: Computer ScienceComputer Science (R0)