Abstract
This paper proposes a difference scheme based on nonlinear diffusion Perona-Malik model for numerical calculation in image restoration. Our scheme can adapt to determine the tangent directions to the isophote lines based on two mutually orthogonal directional derivatives, which results that diffusion is along the edges as much as possible. One of typical edge stopping functions for Perona-Malik model is modified in order to improve robust calculation and satisfy the compatibility, stability and convergence for our numerical scheme. Computer experimental results indicate that the algorithm corresponding to our numerical scheme is very efficient for noise removal in regardless whether the noise is serious or not.
Chapter PDF
Similar content being viewed by others
Keywords
References
Aubert, G., Kornprobst, P.: Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations. Applied Mathematical Sciences. Springer, New York (2002)
Chan, T.F., Shen, J.: Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods. SIAM, Philadelphia (2005)
Aubert, G., Kornprobst, P.: Mathematics of Image Processing. Encyclopedia of Mathematical Physics 3, 1–9 (2006)
Perona, P., Malik, J.: Scale-space and Edge Detection using Anisotropic Diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence 12(7), 629–639 (1990)
Catté, F., Lions, P.L., Morel, J.M., et al.: Image Selective Smoothing and Edge Detection by Nonlinear Diffusion. SIAM Journal of Numerical Analysis 29, 182–193 (1992)
Colombo, M., Gobbino, M.: Slow Time Behavior of the Semidiscrete Perona-Malik Scheme in One Dimension. SIAM Journal of Mathematical Analysis 43(6), 2564–2600 (2011)
Guo, Z., Sun, J., Zhang, D., et al.: Adaptive Perona-Malik Model Based on the Variable Exponent for Image Denoising. IEEE Transactions on Image Processing 21(3), 958–967 (2012)
Kichenassamy, S.: The Perona-Malik paradox. SIAM Journal of Applied Mathematics 57(5), 1328–1342 (1997)
Maiseli, B., Elisha, O., Mei, J., et al.: Edge Preservation Image Enlargement and Enhancement Method Based on the Adaptive Perona-Malik Non-linear Diffusion Model. IET Image Processing 8(12), 753–760 (2014)
Koenderink, J.J.: The Structure of Images. Biological Cybernetics 50, 363–370 (1984)
ter Bart, M.: Haar Romeny: Geometry-driven Diffusion in Computer Vision. Computational Imaging and Vision. Kluwer Academic Publishers, Dordrecht (1994)
Xiao, Z., Xu, Z., Zhang, F., et al.: ESPI Filtering Method Based on Anisotropic coherence Diffusion and Perona-Malik Diffusion. Chinese Optics Letters 11, 101101-1–101101-4 (2013)
Lax, P.D., Richtmyer, R.D.: Survey of the Stability of Linear Finite Difference Equations. Connumcarrons on Pure and Applied Mathematics ix, 267–293 (1956)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ruan, Z., Shen, Y., Liu, F. (2015). Modified Numerical Scheme for Perona-Malik Model in Image Restoration. In: Zha, H., Chen, X., Wang, L., Miao, Q. (eds) Computer Vision. CCCV 2015. Communications in Computer and Information Science, vol 546. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48558-3_37
Download citation
DOI: https://doi.org/10.1007/978-3-662-48558-3_37
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-48557-6
Online ISBN: 978-3-662-48558-3
eBook Packages: Computer ScienceComputer Science (R0)