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Zhou, Bin; Mu, Chun-Lai; Feng, Jun; Wei, Wei

Continuous level anisotropic diffusion for noise removal. (English) Zbl 1252.94029

Appl. Math. Modelling 36, No. 8, 3779-3786 (2012).
Summary: We present a new approach to anisotropic diffusion and noise removal. Several functionals are introduced to a variational model. The diffusion behavior is governed by a nonlinear partial differential equation. A dynamic threshold function plays an important role in the continuous level anisotropic diffusion and a related optimization problem is presented. The noise can be removed while the edge well preserved. Multi-level noise or multi-level edge can be handled automatically. Finally, the accuracy and efficiency of the proposed method are verified by several numerical experiments.

MSC:

94A08 Image processing (compression, reconstruction, etc.) in information and communication theory

Keywords:

noise removal; anisotropic diffusion; variational model; threshold function; continuous level
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References:

[1] El-Fallah, A. I.; Ford, G. E., Mean curvature evolution and surface area scaling in image filtering, IEEE Trans. Image Process., 6, 5, 750-753 (2002)
[2] Perona, P.; Malik, J., Scale-space and edge detection using anisotropic diffusion, IEEE Trans. Pattern Anal. Machine Intelligence, 12, 7, 629-639 (1990)
[3] Yezzi, A., Modified curvature motion for image smoothing and enhancement, IEEE Transactions on Image Processing, 7, 3, 345-352 (2002)
[4] L.I. Rudin, S. Osher. Total variation based image restoration with free local constraints. in: IEEE Int. Conf. Image Process., 1994. Proceedings. ICIP-94., pp. 31-35, 1994.; L.I. Rudin, S. Osher. Total variation based image restoration with free local constraints. in: IEEE Int. Conf. Image Process., 1994. Proceedings. ICIP-94., pp. 31-35, 1994.
[5] Rudin, L. I.; Osher, S.; Fatemi, E., Nonlinear total variation based noise removal algorithms, Physica D: Nonlinear Phenomena, 60, 1-4, 259-268 (1992) · Zbl 0780.49028
[6] Moroney, T. J.; Turner, I. W., A finite volume method based on radial basis functions for two-dimensional nonlinear diffusion equations, Appl. Math. Model., 30, 10, 1118-1133 (2006) · Zbl 1099.65114
[7] A. Kuijper, p-Laplacian driven image processing. in: IEEE Int. Conf. Image Process., 2007. ICIP 2007., vol. 5, pp. 257-260, 2007.; A. Kuijper, p-Laplacian driven image processing. in: IEEE Int. Conf. Image Process., 2007. ICIP 2007., vol. 5, pp. 257-260, 2007.
[8] Catté, F.; Lions, P. L.; Morel, J. M.; Coll, T., Image selective smoothing and edge detection by nonlinear diffusion, SIAM J. Numer. Anal., 29, 1, 182-193 (1992) · Zbl 0746.65091
[9] Lysaker, M.; Lundervold, A.; Tai, X. C., Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time, IEEE Trans. Image Process., 12, 12, 1579-1590 (2004) · Zbl 1286.94020
[10] You, Y. L.; Kaveh, M., Fourth-order partial differential equations for noise removal, IEEE Trans. Image Process., 9, 10, 1723-1730 (2002) · Zbl 0962.94011
[11] Malladi, R.; Sethian, J. A., A unified approach to noise removal, image enhancement, and shape recovery, IEEE Trans. Image Process., 5, 11, 1554-1568 (2002)
[12] Lee, S. H.; Seo, J. K., Noise removal with Gauss curvature-driven diffusion, IEEE Trans. Image Process., 14, 7, 904-909 (2005)
[13] Whitaker, R. T.; Pizer, S. M., A multi-scale approach to nonuniform diffusion, CVGIP Image Understand., 57 (1993), 99-99
[14] Koenderink, J. J., The structure of images, Biol. Cybernetics, 50, 5, 363-370 (1984) · Zbl 0537.92011
[15] A.P. Witkin. Scale-space filtering. in: Proc. 8th Int. Joint Conference Artificial Intelligence, vol. 2, pages 1019-1022. Morgan Kaufmann Publishers Inc., 1983.; A.P. Witkin. Scale-space filtering. in: Proc. 8th Int. Joint Conference Artificial Intelligence, vol. 2, pages 1019-1022. Morgan Kaufmann Publishers Inc., 1983.
[16] Aubert, G.; Kornprobst, P., Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (2006), Springer-Verlag: Springer-Verlag New York Inc · Zbl 1110.35001
[17] Chambolle, A.; Lions, P. L., Image recovery via Total Variation minimization and related problems, Numerische Mathematik, 76, 2, 167-188 (1997) · Zbl 0874.68299
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