Application of iterative Jacobi method for an anisotropic diusion in image processing
Subject Areas : Applied Mathematics
1 - Department of Mathematics, Khorasgan (Isfahan) Branch, Islamic Azad
University, Isfahan, Iran.
2 - Department of Mathematics, Faculty of sciences, University of Isfahan,
Isfahan, Iran.
Keywords: Image restoration, Anisotropic diusion, iterative numerical method,
Abstract :
Image restoration has been an active research area. Dierent formulations are eective in high qualityrecovery. Partial Dierential Equations (PDEs) have become an important tool in image processingand analysis. One of the earliest models based on PDEs is Perona-Malik model that is a kindof anisotropic diusion (ANDI) lter. Anisotropic diusion lter has become a valuable tool indierent elds of image processing specially denoising. This lter can remove noises without degradingsharp details such as lines and edges. It is running by an iterative numerical method. Therefore, afundamental feature of anisotropic diusion procedure is the necessity to decide when to stop theiterations. This paper proposes the modied stopping criterion that from the viewpoints of complexityand speed is examined. Experiments show that it has acceptable speed without suering from theproblem of computational complexity.
[1] P. Perona, J. Malik, Scale space and edge detection using anisotropic
diusion, 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 diusion problem by Tikhonov regularization,
Mathematics Scientic Journal, Vol. 7, No. 2, 39-54(2012).
[5] P. Mrazek, M. Navara, Selection of optimal stopping time for nonlinear
diusion 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).