On the image inpainting problem from the viewpoint of a nonlocal Cahn-Hilliard type equation
Antun Lovro Brkić, Darko Mitrović, Andrej Novák
Abstract
Motivated by the fact that the fractional Laplacean generates a wider choice of the interpolation curves than the Laplacean or bi-Laplacean, we propose a new non-local partial differential equation inspired by the Cahn-Hilliard model for recovering damaged parts of an image. We also note that our model is linear and that the computational costs are lower than those for the standard Cahn-Hilliard equation, while the inpainting results remain of high quality. We develop a numerical scheme for solving the resulting equations and provide an example of inpainting showing the potential of our method.
Topics & Concepts
InpaintingCahn–Hilliard equationInterpolation (computer graphics)Partial differential equationImage (mathematics)Applied mathematicsMathematicsType (biology)Computer scienceMathematical optimizationAlgorithmMathematical analysisArtificial intelligenceBiologyEcologyAdvanced Numerical Analysis TechniquesGenerative Adversarial Networks and Image SynthesisAdvanced Numerical Methods in Computational Mathematics