Two anisotropic fourth‐order partial differential equations for image inpainting. Issue 3 (1st April 2013)

• Record Type: Journal Article
• Authors: Li, Peng; Li, Shuai‐Jie; Yao, Zheng‐An; Zhang, Zu‐Jin
• Is Part Of: IET image processing. Volume 7:Issue 3(2013)
• Page Start: 260
• Page End: 269
• Publication Date: 2013-04-01
• Subjects: finite difference methods -- image texture -- numerical stability -- partial differential equations; anisotropic fourth‐order partial differential equations -- image inpainting -- anisotropic fourth‐order PDE -- diffusion images -- forward diffusion -- backward diffusion -- numerical algorithm -- finite‐difference method -- stability -- discretisation -- second‐order PDE -- third‐order PDE -- blocky effects; finite difference methods -- image texture -- numerical stability -- partial differential equations; anisotropic fourth‐order partial differential equations -- image inpainting -- anisotropic fourth‐order PDE -- diffusion images -- forward diffusion -- backward diffusion -- numerical algorithm -- finite‐difference method -- stability -- discretisation -- second‐order PDE -- third‐order PDE -- blocky effects; Image processing -- Periodicals; 621.36705
• DOI: 10.1049/iet-ipr.2012.0592
• Languages: English
• ISSNs: 1751-9659

Abstract

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.