Abstract
The Perona-Malik (PM) model is used successfully in image processing to eliminate noise while preserving edges; however, this model has a major drawback: it tends to make the image look blocky. This work proposes to modify the PM model by introducing the Caputo-Fabrizio fractional gradient inside the diffusivity function. Experiments with natural images show that our model can suppress efficiently the blocky effect. Also, our model has good performance in visual quality, high peak signal-to-noise ratio (PSNR), and lower value of mean absolute error (MAE) and mean square error (MSE).
Highlights
Introduction and Some Basic DefinitionsImage processing based on partial differential equations (PDEs) is mainly used for smoothing and restoration purposes
To solve numerically the new fractional Perona-Malik model, we propose to discretize the Caputo-Fabrizio derivative based on the forward finite difference scheme in the interval 1⁄20, x
Our model is compared with the classical Perona-Malik (PM) anisotropic diffusion model
Summary
Image processing based on partial differential equations (PDEs) is mainly used for smoothing and restoration purposes. Typical PDE techniques for image smoothing regard the original image as initial states of a parabolic process and extract filtered versions from its temporal evolution. Uðx, y, tÞ represents the image intensity values in the position ðx, yÞ ∈ Ω ⊂ R2 for a time t, ∂Ω is the smooth boundary, and u0ðx, yÞ is the original image. It is a classical result that for any bounded u ∈ CðR2Þ, the linear diffusion process ∂uðx, y, ∂t tÞ = Δuðx, y, tÞ, Ω ×. Ð0, T, ð1Þ uðx, y, 0Þ = u0ðx, yÞ, ∂Ω, ð2Þ possesses the solution uðx, y, tÞ =.
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