Edge-preserving smoothing of Perona-Malik nonlinear diffusion in two-dimensions

Document Type : Research Paper


TIAD Laboratory, Department of Mathematics, Faculty of Sciences and Technics, Sultan Moulay Slimane University, Beni Mellal 23000, Morocco



It has been thirty years since Perona and Malik (PM) introduced the nonlinear diffusion equation in image processing and analysis. The problem's complexity was to find a suitable and adaptive diffusion function that smooths away noise or textures while preserving sharp edges of a sufficiently smooth intensity. This paper provides a new two-dimensional analysis of the PM diffusion equation to examine its behavior during scales and an explicit formula to select the right diffusion function adequately. In this context, we study the PM equation at the zero crossings of the first and second directional derivatives of a sufficiently smooth function in the gradient direction.


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Articles in Press, Corrected Proof
Available Online from 01 February 2024
  • Receive Date: 29 September 2020
  • Accept Date: 23 December 2023