Khanian, M., Davari, A. (2012). Application of iterative Jacobi method for an anisotropic di usion in image processing. Theory of Approximation and Applications, 8(2), 41-48.
M Khanian; A. Davari. "Application of iterative Jacobi method for an anisotropic di usion in image processing". Theory of Approximation and Applications, 8, 2, 2012, 41-48.
Khanian, M., Davari, A. (2012). 'Application of iterative Jacobi method for an anisotropic di usion in image processing', Theory of Approximation and Applications, 8(2), pp. 41-48.
Khanian, M., Davari, A. Application of iterative Jacobi method for an anisotropic di usion in image processing. Theory of Approximation and Applications, 2012; 8(2): 41-48.
Application of iterative Jacobi method for an anisotropic di usion in image processing
1Department of Mathematics, Khorasgan (Isfahan) Branch, Islamic Azad University, Isfahan, Iran.
2Department of Mathematics, Faculty of sciences, University of Isfahan, Isfahan, Iran.
Abstract
Image restoration has been an active research area. Di erent formulations are e ective in high quality recovery. Partial Di erential Equations (PDEs) have become an important tool in image processing and analysis. One of the earliest models based on PDEs is Perona-Malik model that is a kind of anisotropic di usion (ANDI) lter. Anisotropic di usion lter has become a valuable tool in di erent elds of image processing specially denoising. This lter can remove noises without degrading sharp details such as lines and edges. It is running by an iterative numerical method. Therefore, a fundamental feature of anisotropic di usion procedure is the necessity to decide when to stop the iterations. This paper proposes the modi ed stopping criterion that from the viewpoints of complexity and speed is examined. Experiments show that it has acceptable speed without su ering from the problem of computational complexity.
Article Title [Persian]
Application of iterative Jacobi method for
an anisotropic di usion in image
processing
Authors [Persian]
M. Knanian1; A. Davari2
1Department of Mathematics, Khorasgan (Isfahan) Branch, Islamic Azad
University, Isfahan, Iran.
2Department of Mathematics, Faculty of sciences, University of Isfahan,
Isfahan, Iran.
Abstract [Persian]
Image restoration has been an active research area. Di erent formulations are e ective in high quality recovery. Partial Di erential Equations (PDEs) have become an important tool in image processing and analysis. One of the earliest models based on PDEs is Perona-Malik model that is a kind of anisotropic di usion (ANDI) lter. Anisotropic di usion lter has become a valuable tool in di erent elds of image processing specially denoising. This lter can remove noises without degrading sharp details such as lines and edges. It is running by an iterative numerical method. Therefore, a fundamental feature of anisotropic di usion procedure is the necessity to decide when to stop the iterations. This paper proposes the modi ed stopping criterion that from the viewpoints of complexity and speed is examined. Experiments show that it has acceptable speed without su ering from the problem of computational complexity.
Keywords [Persian]
Image restorationŲ Anisotropic di usionŲ iterative numerical
method
References
[1] P. Perona, J. Malik, Scale space and edge detection using anisotropic di usion, IEEE Trans. Pattern Anal. Mach. Intell.,12,629-639 (1990). [2] I. Capuzzo Dolcetta, R. Ferretti, Optimal stopping time formulation of adaptive image ltering, Appl.Math. Optim. 43, 245-258 (2001). [3] G. Gilboa, N. Sochen, Y.Y. Zeevi, Estimation of optimal PDE-based denoising in the SNR sense, IEEE Trans. Image Proc. 15, 2269-2280 (2006). [4] H. Molhem, R. Pourgholi, M. Borghei, A numerical approach for solving a nonlinear inverse di usion problem by Tikhonov regularization, Mathematics Scienti c Journal, Vol. 7, No. 2, 39-54(2012). [5] P. Mrazek, M. Navara, Selection of optimal stopping time for nonlinear di usion ltering, Int. J. Comput. Vision. 52, 189-203 (2003).
[6] A. Ilyevsky, E. Turkel, Stopping criteria for anisotropic PDEs in image processing, J. Sci. Compute. 45, 337-347, (2010). [7] Z. Wang, A.C. Bovick, H.R. Sheikh , E.P. Simoncelli, A novel kernel- based framework for facial-image hallucination Structural Similarity, IEEE Transactions on Image Processing. 13, No. 4, pp. 600-612 (2004).
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