Application of iterative Jacobi method for an anisotropic di usion in image processing

Document Type : Research Articles


1 Department of Mathematics, Khorasgan (Isfahan) Branch, Islamic Azad University, Isfahan, Iran.

2 Department of Mathematics, Faculty of sciences, University of Isfahan, Isfahan, Iran.


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.

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