Nowadays, most of the methods used to restore the images are extensively using the partial differential equations (PDE's). The use of the PDE's can model the image in the continuous spatial domain as well as the transform domains (Fourier, Wavelet) for the higher efficiency. This paper proposes the fractional order non-linear anisotropic diffusion based on the PDE's for the restoration of the multispectral foggy images. It has application in the fields like image denoising, image inpainting and image defogging etc. The main concept is to express the anisotropic diffusion in the form of an optimization problem so that its behavior can be analyzed. Thus, gradient descent method is used for the energy functional minimization. To restore the images, we have used the anisotropic diffusion with p-Laplace norm for adaptive diffusion which enhances diffusion in order to preserve edges and high frequency components for the better restoration. A regularization term is also used to balance the diffusion. Anisotropic diffusion allows the modeling of the numerical schemes for the implementation of the method which can be done by using the finite difference schemes, finite element/volume schemes, using the radial basis functions and the wavelets.

This is poster number 3 in Poster Session

Authors:

Savita Nandal (Department of Mathematics Indian Institute of Technology Roorkee, )

Kumar Sanjeev (Department of Mathematics, Indian institute of Technology Roorkee, )

Keywords:

airlight map, contrast gain, fractional order, image defogging, image enhancement, nonlinear anisotropic diffusion, nonlinear optimization, p-laplace, partial differential equation models