Two anisotropic fourth‐order partial differential equations for image inpainting

Abstract

In this study, the authors propose two fourth‐order partial differential equations (PDEs) to inpaint the image. By analysing those anisotropic fourth‐order PDEs and comparing their diffusion images, the authors confirm they are forward diffusion or backward diffusion. A numerical algorithm is presented using a finite‐difference method and analyse the stability of discretisation. Finally, they show various experimental results and conclude that the proposed new models are better than the second‐order and third‐order PDEs, especially for weakening the blocky effects.