Inpainting in discrete Sobolev spaces: structural information for uncertainty reduction
This work addresses uncertainty reduction in image inpainting, presenting an incremental improvement for computer vision applications.
The authors tackled the inpainting problem by developing a new mathematical functional incorporating finite differences and a priority index for scanning order, which improved reconstruction quality by reducing uncertainty in patch-based methods.
In this article, using an exemplar-based approach, we investigate the inpainting problem, introducing a new mathematical functional, whose minimization determines the quality of the reconstructions. The new functional expression takes into account of fnite differences terms, in a similar fashion to what happens in the theoretical Sobolev spaces. Moreover, we introduce a new priority index to determine the scanning order of the points to inpaint, prioritizing the uncertainty reduction in the choice. The achieved results highlight important theoretical-connected aspects of the inpainting by patch procedure.