Image Inpainting Models Using Fractional Order Anisotropic Diffusion

In this paper, two non-linear anisotropic diffusion models based on fractional calculus for removing of superimposed text and scratches are presented. The first model is based on fractional order anisotropic diffusion. It utilizes the image characteristics based on the norm of the gradient flow with fractional order. The performance of the gradient flow with fractional order is better to hold and complete the texture elements of an image. The Euler -Lagrange equation of this model can be viewed as the generalization of anisotropic diffusion equations with second and fourth order. The second model is based on fractional order anisotropic diffusion with adaptive p-Laplacian variation model. It utilizes the image characteristics based on the p-Laplace norm of gradient with fractional order. The adaptive parameter p is used to propagate the pixel information flexibly according to local geometrical characteristics. These models can enhance and fill the texture elements of images and enormously discard speckle and staircase effects. In this work, Discrete Fourier Transform (DFT) is used to calculate the fractional order derivative. Simulation results emphasize that the proposed models yield good visual effects and better peak signal to noise ratio, structural similarity, and mutual information.