Variational image inpainting technique based on nonlinear second-order diffusions. (August 2016)

• Record Type: Journal Article
• Authors: Barbu, Tudor
• Is Part Of: Computers & electrical engineering. Volume 54(2016)
• Page Start: 345
• Page End: 353
• Publication Date: 2016-08
• Subjects: Partial differential equation-based image inpainting -- Variational model -- Euler–Lagrange equation -- Nonlinear diffusion-based model -- Well-posedness -- Numerical approximation scheme; Computer engineering -- Periodicals; Electrical engineering -- Periodicals; Electrical engineering -- Data processing -- Periodicals; Ordinateurs -- Conception et construction -- Périodiques; Électrotechnique -- Périodiques; Électrotechnique -- Informatique -- Périodiques; Computer engineering; Electrical engineering; Electrical engineering -- Data processing; Periodicals; Electronic journals; 621.302854
• DOI: 10.1016/j.compeleceng.2016.04.012
• Languages: English
• ISSNs: 0045-7906

Abstract

Highlights: A novel variational scheme for image inpainting is proposed in this paper, first. A nonlinear anisotropic diffusion model is obtained from this PDE variational scheme. A mathematical treatment of the obtained second-order PDE-based model is provided. An explicit finite-difference based numerical approximation scheme is constructed for it. Successful image reconstruction experiments and method comparison are also described. Abstract: We consider a novel variational model for image reconstruction, based on second-order partial differential equations, in this paper. This inpainting approach is inspired by the anisotropic diffusion-based denoising solutions. A stable variational scheme is proposed first. Then, a nonlinear differential model is derived from it, by determining the corresponding Euler–Lagrange equation and applying the steepest descent method. A rigorous mathematical treatment of this anisotropic diffusion scheme is provided next. This nonlinear second order diffusion model is then numerically approximated, a consistent and explicit finite-difference based discretization scheme being developed. Some successful image inpainting experiments and method comparison are also provided in this article. Graphical abstract: