Inpainting in discrete Sobolev spaces: structural information for uncertainty reduction

TL;DR

This paper introduces a novel exemplar-based inpainting method utilizing a new functional inspired by Sobolev spaces and a priority index to reduce uncertainty, enhancing reconstruction quality.

Contribution

It proposes a new mathematical functional and priority index for inpainting, integrating Sobolev space concepts to improve structural information preservation and uncertainty reduction.

Findings

Functional based on finite differences improves inpainting quality.

Priority index effectively reduces uncertainty during inpainting.

Theoretical insights connect patch-based inpainting with Sobolev space properties.

Abstract

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.