Morphologically invariant PDE inpaintings

Abstract

This paper studies the PDE method for image inpaintings. Image inpainting is essentially an image interpolation problem, with wide applications in film and photo restoration, text removal, special effects in movies, disocclusion, digital zoom-in, and edge-based image compression and coding. Bertalmio, Sapiro, Caselles, and Ballester (2000) [3] first innovatively introduced the PDE method for the inpainting problem. Ever since, the authors of the present paper have worked along this line and developed the PDE method, mostly inspired by the Bayesian and variational method (especially by good image {\rm prior} models). The current paper has two major goals. First, by surveying all the recent PDE inpainting techniques, we intend to develop a unified viewpoint based on two infinitesimal mechanisms: transportation and curvature driven diffusions (CDD). Furthermore, based this knowledge, we construct a new class of third order inpainting PDEs, which is derived from the set of axioms (or principles) refined from the existing works: morphological invariance, rotational invariance, stability principle, and linearity principle.