Variational Non-Local Image Inpainting
Non-local methods for image denoising and inpainting have gained considerable
attention in recent years. This is in part due to their superior performance in
textured images, a known weakness of purely local methods. Local methods on the
other hand have demonstrated to be very appropriate for the recovering of
geometric structures such as image edges. The synthesis of both types of
methods is a trend in current research. Variational analysis in particular is
an appropriate tool for a unified treatment of local and non-local methods.
We propose a general variational framework for non-local image
inpainting, from which important and representative previous inpainting
schemes can be derived, in addition to leading to novel ones.
The model can also be adapted to the related problem of interpolating a
sparsely sampled image. The resulting variational formulation encourages
the transfer of information between similar image patches. Contrary to the
classical inpainting problem, no complete patches are available from the
sparse image samples, and the patch similarity criterion has to be redefined
as here proposed. Initial experimental results with the proposed framework, at
very low sampling densities, are very encouraging.
