F-transform-Based Optimization for Image Restoration (Inpainting)
Irina Perfilieva · 2018
In image processing, the inpainting (image restoration) problem is often considered with respect to the interpolation. We involve into the solution of this problem the F-transform-based nonlocal operators that define a new type of functionals, extending the ability of classical PDE-based algorithms in handling textures and repetitive structures. We showed that in the particular space with a fuzzy partition, the nonlocal Laplacian and partial derivatives can be represented by the F0- and F1-transforms. For the inpainting problem specified by relatively large damaged areas, we propose a new total variation model with the F-transform-based nonlocal operators. We show that the proposed model together with the corresponding algorithm increase the quality of a (usually considered) patch-based searching algorithm.