A variational model for filling-in gray level and color images

A variational approach for filling-in regions of missing data in gray-level and color images is introduced in this paper. The approach is based on joint interpolation of the image gray-levels and gradient/isophores directions, smoothly extending in an automatic fashion the isophote lines into the holes of missing data. This interpolation is computed solving the variational problem via its gradient descent flow, which lends to a set of coupled second order partial differential equations, one for the gray-levels and one for the gradient orientations. The process underlying this approach can be considered as an interpretation of the Gestaltist's principle of good continuation. No limitations are imposed on the topology of the holes, and all regions of missing data can be simultaneously processed, even if they are surrounded by completely different structures. Applications of this technique include the restoration of old photographs and removal of superimposed text like dates, subtitles, or publicity. Examples of these applications are given.