A related inpainting model was proposed by Esedoglu and Shen [16] and is based on the very successfully Mumford-Shah image segmentation model. This model is also good for local inpainting but shares the same problem as the TV model in that it cannot reconnect separated parts of broken objects far apart. To fix this problem, the same authors of [16] proposed the Mumford-Shah-Euler inpainting model which in the same fashion of the Euler’s elastica model uses the information encoded in the curvature to reconnect smoothly the level lines. More recently, in separate works, Bertozzi, Esedoglu and Gillete [3] proposed a model to inpaint binary images based on the Cahn-Hilliard equation and Grossauer and Scherzer [17] proposed a model based on the complex Ginzburg-Landau equation. It remains to develop fast multigrid methods for these models.