title: Strong-continuation, contrast-invariant inpainting with a third-order optimal PDE.
abstract: PDE-based image inpainting has become a very active area of research after the pioneering works of Masnou and Morel, Bertalmío et al., and Ballester et al. In this paper, we take a different approach, inspired by the excellent work of Caselles et al. We view the inpainting problem as a particular case of image interpolation in which we intend to propagate level lines. Expressing this in terms of local neighborhoods and using a Taylor expansion we derive a third-order PDE that performs inpainting. This PDE is optimal in the sense that it is the most accurate third-order PDE which can ensure continuation of level lines. The continuation is strong, allowing the restoration of thin structures occluded by a wide gap. The result is also contrast invariant. This is a novel PDE, which, in both its accuracy and contrast invariance, outperforms the approaches cited above.
authors.affiliation: Departament de Tecnologia, Universitat Pompeu Fabra, Barcelona, Spain. marcelo.bertalmio@upf.edu
authors.forename: Marcelo
authors.initials: M
authors.lastname: Bertalmío
mesh_terms: D000465:Algorithms; D016477:Artifacts; D003196:Computer Graphics; D003198:Computer Simulation; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods*; D015233:Models, Statistical; D009716:Numerical Analysis, Computer-Assisted; D010151:Paintings; D012815:Signal Processing, Computer-Assisted; D013269:Stochastic Processes