A variational model for disocclusion

In this paper we study a variational approach for filling-in regions of missing data in 2D and 3D digital images. Applications of this technique include the restoration of old photographs and removal of superimposed text like dates, subtitles, or publicity, or the zooming of images. The approach presented here, initially introduced in [C. Ballester et al., 2001], is based on a joint interpolation of the image gray-levels and gradient/isophotes directions, smoothly extending the isophote lines into the holes of missing data. The process underlying this approach can be considered as an interpretation of the Gestaltist's principle of good continuation. After discussing the model, we present the numerical algorithm used to minimize it and display some numerical experiments.