Image inpainting using a modified Cahn-Hilliard equation

Image inpainting is the process of filling in missing parts of damaged images based on information gleaned from surrounding areas. We propose a model for inpainting binary images using a modified Cahn-Hilliard equation, and develop very efficient numerical techniques for its solution. The Cahn-Hilliard equation is fourth order, and nicely allows for isophote directions to be matched at the boundary of inpainting regions. Our model has two scales, the diffuse interface scale, &egr;, on which it can accomplish topological transitions, and the feature scale of the image.;We show via simulations that a dynamic two step method involving the diffuse interface scale allows us to connect regions across large inpainting domains. For the model problem of stripe inpainting, we show that this issue is related to a bifurcation structure with respect to the diffuse interface scale &egr;. Future directions for this model will account for grayscale inpainting, and may incorporate wavelet methods.