Application of iterative Jacobi method for an anisotropic diusion in image processing

Subject Areas : Applied Mathematics

M. Knanian ¹ , A. Davari ²

1 - Department of Mathematics, Khorasgan (Isfahan) Branch, Islamic Azad University, Isfahan, Iran.
2 - Department of Mathematics, Faculty of sciences, University of Isfahan, Isfahan, Iran.

Received: 2015-09-21 Accepted : 2015-09-21 Published : 2014-12-01

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 modied 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.

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